Microsoft Word - numero_37_art_16 M. Mokhtarishirazbad et alii, Frattura ed Integrità Strutturale, 37 (2016) 114-123; DOI: 10.3221/IGF-ESIS37.16 114 Focussed on Multiaxial Fatigue and Fracture Experimental and analytical study of cracks under biaxial fatigue M. Mokhtarishirazbad, P. Lopez-Crespo, B. Moreno, D. Camas Department of Civil and Materials Engineering, University of Malaga, C/Dr Ortiz Ramos s/n, 29071, Malaga, Spain plopezcrespo@uma.es A. Lopez-Moreno Department of Materials Science and Metallurgy Engineering, University of Jaen, Campus Las Lagunillas, 23071, Jaen, Spain alopez@ujaen.es M. Zanganeh ORAU, Oak Ridge, TN, USA mohammad.zanganehgheshlaghi@nasa.gov ABSTRACT. Most mechanical components experience multi-axial cyclic loading conditions during service. Experimental analysis of fatigue cracks under such conditions is not easy and most works tend to focus more on the simpler but less realistic case of uni-axial loading. Consequently, there are many uncertainties related to the load sequence effect that are now well known and are not normally incorporated into the growth models. The current work presents a new methodology for evaluating overload effect in biaxial fatigue cracks. The methodology includes evaluation of mixed-mode (KI and KII) stress intensity factor and the Crack Opening Displacement for samples with and without overload cycle under biaxial loading. The methodology is tested under a range of crack lengths. All crack-tip information is obtained with a hybrid methodology that combines experimental full-field digital image correlation data and Williams' elastic model describing the crack-tip field. KEYWORDS. Stress intensity factor; Biaxial fatigue; Mixed-mode; Crack opening displacement. INTRODUCTION eliable life-time prediction of structural materials subjected to external loadings depends strongly on the accuracy of the fracture parameters estimation. So far, a number of successful approaches have been presented for estimating the essential fracture parameters such as stress intensity factors (SIFs) experimentally [1]. Apart from the conventional standard test methods [2], it has been shown that crack-tip fields (strain, stress and displacement field) include essential information for accurate estimation of fracture parameters [3]. A number of different techniques are able to provide both surface and bulk information. Surface techniques include photo-elasticity [4], thermo-elasticity [5], Moiré interferometry [6] and digital image correlation (DIC) [7]. Bulk techniques include neutron diffraction [8] and X-ray diffraction [9]. Among all these full-field techniques, DIC has received enormous attention recently [10,11] because of its many advantages compared to other techniques [12]. Simplicity, accuracy and flexibility are the most prominent merits of R M. Mokhtarishirazbad et alii, Frattura ed Integrità Strutturale, 37 (2016) 114-123; DOI: 10.3221/IGF-ESIS37.16 115 DIC technique for calculating displacement fields [13]. While fracture problems can be simplified by considering mode I loading, cracks in structural materials are generally under mixed-mode loading condition [3]. Therefore, estimation of the fracture parameters based on mixed-mode loading condition will be more representative of the material fracture behaviour under the actual working condition. Different optical methods have been used for obtaining full-field information required for mixed-mode loading analysis previously. Sanford and Dally [14] have determined the mixed- mode SIFs by utilizing isochromatic fringes near the crack-tip . They have reported that employing an over-deterministic approach on the data points provided by the full filed fringe patterns led to a highly accurate SIF estimation. Displacement fields derived by DIC technique has been utilized by Yoneyama et al. [15] to evaluate the mixed-mode SIFs of a polymer (polymethylmethactylate). While they used a non-linear least square method for their solutions, Réthoré et al. has develop a method based on the Lagrangian conservation law for mixed-mode SIFs estimations. A good agreement between analytical displacement fields generated based on the Muskhilishvili’s complex function approach and the experimentally measured displacement fields (obtained by DIC) has been also reported by Lopez-Crespo et al [16]. By fitting nominal and experimental data, they have determined mixed-mode SIFs for a crack in a fastener hole. For estimating the crack closure level by DIC, virtual extensometers can be introduced behind the crack-tip for local measurements of crack opening displacement. Nowell et al. [6] have compared Moiré interferometry techniques with DIC method for studying closure levels of propagating fatigue cracks. The effect of overloads on the crack growth has been studied under uniaxial loads with a number of different experimental techniques. These include photo-elasticity [17], pulse reflection microscope [18], electronic speckle pattern interferometry [19] and synchrotron X-ray diffraction [20, 21]. However, the overload effect under biaxial conditions is much less studied. In the present paper, we use a hybrid method for estimating mixed-mode SIF from in-plane crack-tip displacements obtained by DIC. This is used for studying the effect of overload under biaxial loading. The methodology can be used to evaluate crack closure level before and after applying the overload cycle from local crack opening displacement. MATERIALS AND METHODS rack propagation in a low carbon steel (St-52-3N) was studied [22]. Tab. 1 shows the composition of the alloy. Microstructural examination with the optical microscope has revealed ferrite and pearlite bands as vertical black and white bands respectively [23]. A schematic of the geometry is shown in Fig. 1. C Si Mn P S Cr Ni Mo 0.17 0.22 1.23 0.01 >0.0001 0.07 0.06 0.16 Table1. Chemical composition in weight % of St-52-3N steel. The balance is Fe. Yield stress, σy 386 MPa Ultimate tensile stress, σu 639 MPa Young’s modulus, E 206 GPa Shear Modulus 78 GPa Table 2. Monotonic properties of St-52-3N steel. A MTS 809 servo-hydraulic loading rig coupled by a biaxial extensometer Epsilon 3550 was used to apply biaxial loads under stress control mode in a similar way to previous works [22,24]. Cyclic sinus signal with axial load ratio of 0.1 (Ra = 0.1) and torsional load ratio of -1 (Rt=-1) was applied while the angle between the axial and the torsional stress, φ, was set to 45°. Fig. 2 shows how φ has been defined. In order to study the effect of the overload on the crack propagation behaviour, a 40% overload was applied when the crack length for the specimen S2 was 0.669 mm. That is, the load range in the overload cycle was 1.4 times larger than load range during the rest of the test. The cyclic loading then continued until the crack length reached 1.4 mm. Tab. 3 shows the loading condition of for samples with and without overload. C M. Mokhtarishirazbad et alii, Frattura ed Integrità Strutturale, 37 (2016) 114-123; DOI: 10.3221/IGF-ESIS37.16 116 Figure 1: Geometry of the tubular dog-bone specimen with central hole. All dimensions are in mm. Figure 2: Definition of axial and shear stress amplitude. Specimen name Hole diameter (mm) Cross section area (mm2) σmax τmax σOL τOL S1 0.333 73.4 240 138.5 - - S2 0.336 74.8 240 138.5 336 194 Table 3. Axial and shear stress values for specimens with and without overload cycle. Figure 3: The position of virtual extensometers for COD examination. The white bold mark shows the crack-tip position. M. Mokhtarishirazbad et alii, Frattura ed Integrità Strutturale, 37 (2016) 114-123; DOI: 10.3221/IGF-ESIS37.16 117 In addition, to evaluate the closure level, near tip crack opening displacement were measured by DIC [25,26]. In this regard, a virtual extensometer was appointed to measure the displacement in the crack opening direction with distances in the range of 20 to 200 μm with the interval of 20 μm behind the crack-tip. Fig 3, shows an example of the positions of the virtual extensometer. FATIGUE CRACK GROWTH ig. 4 shows how applying overload can affect the crack growth behaviour. The retardation in the crack growth after applying an overload cycle can be seen in this graph. The general regimes of crack growth rate after overload are acceleration, retardation and recovery [27]. Acceleration in crack growth rate immediate after overload has been attributed to the crack tip stretching which can lead to increasing the effective stress intensity range [27]. However, 5 cycles after the overload we did not observe such acceleration in the crack growth rate (Fig. 5). One possible reason could be the fracture of the stretched crack ligament during the overload cycle [27]. There was a retardation period in the crack growth after the overload cycle of 8000 cycles, thus increasing the total life by ~14%. Crack closure is one of the mechanisms for explaining this retardation [27,28]. The crack was extended by almost 40 μm over 2300 cycles, during this period. Retardation period usually takes hundreds of cycles, while recovery step occurs over thousands of cycles Figure 4: Evolution of crack length by number of cycles for samples with and without overload cycle. Figure 5: Crack growth rate in logarithmic scale as a function of the crack length for both samples S1 and S2. The black arrow shows where the overload cycle has been applied. F M. Mokhtarishirazbad et alii, Frattura ed Integrità Strutturale, 37 (2016) 114-123; DOI: 10.3221/IGF-ESIS37.16 118 PROCESSING OF DISPLACEMENT INFORMATION isplacement data ahead of the crack was measured by using DIC. The obtained displacement data was then fitted into Williams' series [29, 30]:                                             2 1 2 1 ( 4) ( 1) cos cos 2 2 2 2 2 ( 4) ( 1) sin sin 2 2 2 2 2 n n I n n n n I n n nr n n n u a ModeI nr n n n v a (1) and,                                               1 2 1 2 2 )4( cos 22 cos)1( 22 2 )4( sin 22 sin)1( 22 n n n n II n n n n II nnnn b r v nnnn b r u ModeII     (2) where uI and vI are horizontal and vertical displacements in mode I respectively, uII and vII are horizontal and vertical displacements in mode II respectively,  is the shear modulus,     (3 )/ (1 ) for plane stress and for plane strain condition,  is the Poisson’s ratio, r and θ are polar coordinates with the crack-tip being the origin of coordinates, and a and b are constants. Eqs. 1 and 2 can be written in terms of the SIFs and T-stress as follows:                    2 2cos ( 1 2sin ) sin ( 1 2cos ) ( 1)cos 2 2 2 2 2 2 2 2 8 I IIK Kr r T u r (3)                    2 2sin ( 1 2cos ) cos ( 1 2cos ) ( 3)sin 2 2 2 2 2 2 2 2 8 I IIK Kr r T v r (4) by using  1 2IK a ,   1 2IIK b ,  24T a (5) where KI and KII are mode I and II of SIF respectively and T represents T-stress. Having employed a post processing routine, the crack opening displacement, COD, has been determined at various distances behind crack-tip. COD was determined as follows:    2 2 2 2( ) bot bot top topCOD x u v u v (6) Where u and v are the horizontal and vertical displacement respectively, and x is the distance of the extensometer behind the crack-tip. The subscripts “top” and “bot” refer to the position of the virtual extensometer points relative to the crack line. D M. Mokhtarishirazbad et alii, Frattura ed Integrità Strutturale, 37 (2016) 114-123; DOI: 10.3221/IGF-ESIS37.16 119 RESULTS AND DISCUSSION ig. 6 shows how COD value changes by increasing the distance of the virtual extensometer from the crack-tip for crack lengths of 0.682 and 0.669 mm for sample S1 and S2 respectively. A similar trend has been previously observed [31]. The evolution of COD during a complete cycle (loading and unloading) at 60 μm behind the crack- tip for different crack lengths in samples S1 and S2 are shown in Fig. 7. The effect of applying an axial-torsional overload of 40% on the evolution of COD for sample S2 is clear in Fig. 7.b. While prior to the overload, COD at the maximum load was about 2 μm, just after overload, +5 cycles, the maximum COD reduced to about 1.2 μm. A return to the baseline closure load has been observed when the crack has progressed sufficiently beyond the overload event. It can be seen from Fig. 7.b that applying the overload reduces the COD by 49% with respect the sample S1 with no overload. This difference is more significant in Fig. 8b where the post overload situation is shown. Figure 6: COD as a function of the position of the virtual extensometer with respect to the crack-tip for: a) sample S1 with a crack length of 0.682 mm after 69000 cycles and b) sample S2 with a crack length of 0.669 mm after 56190 cycles before overload. Figure 7: COD behaviour during loading and unloading cycle for different crack lengths for sample S1 and S2. The number of cycles before and after overload where overload cycle was considered as 0 cycle, are shown in the graph b. A comparison between the COD behaviour in sample S1 and S2 in similar crack lengths was done at 60 μm behind the crack-tip and the results are shown in Fig. 8. Fig. 8.a shows the COD examination for a complete cycle for samples S1 and S2 with crack lengths of 0.669 mm and 0.682 mm respectively. The overload was not yet applied on S1 for the cycle described in Fig. 8.a. The similar COD curves for both samples can be attributed to similar crack length and loading condition for both samples. Fig. 8.b shows the evolution of a cycle in both samples once the overload has been applied to S2. The differences between S1 and S2 in Fig. 8.b are remarkable. IThe overload has a double influence on the COD: it F b a b a Loading Unloading M. Mokhtarishirazbad et alii, Frattura ed Integrità Strutturale, 37 (2016) 114-123; DOI: 10.3221/IGF-ESIS37.16 120 decreases the overall COD value and also it modifies the shape of the COD curve (Fig. 8.b). This shape modification consists of the COD curve having a change in slope at a certain load (~0.2 F/Fmax). This change in slope is often referred as knee [32,33]. In Fig. 8.c-d show the loading and unloading parts of the cycle for both samples. The beginning and the end of the cycle appears magnified in Fig. 8.c-d. The influence of overload introducing this knee is particularly evident in the unloading part of the cycle (Fig. 8.d). Figure 8: COD examination for different crack lengths of samples S1 and S2. a) COD for a crack length of 0.6 mm for both S1 and S2 before applying overload, b) difference between COD of samples S1 and S2 for crack length of 1.392 mm and 1.403 mm respectively, c) COD during the loading segment of a loading cycle, d) COD during unloading segment of a loading cycle. Displacement data ahead of the crack-tip then fitted to Williams' series in order to estimate the experimental SIFs and T- Stress values. In order to improve the quality of the SIF estimations, the recommendations given in [34] were followed. Accordingly, a high order interpolation scheme of optimized 8-tap spline was used for during DIC analysis to achieve sub- pixel accuracy. Zero-normalized sum of squared differences was set as the correlation criterion in order to vanish the effect of offset and scale in lighting [35]. The subset size was adjusted to 31×31 pixels. In addition, just 25% of the crack line was considered in the area of interest (the area where the displacement data were measured by DIC). By taking to account the size of the area of interest (0.4 ×0.4 mm2), two terms in the Williams' solution were used as suggested in [34]. In fact, neglecting T-stress which appears at the second term of Williams' series can also induce a significant error in SIFs calculations in short crack length examinations [3]. Fig. 9 illustrates the vertical displacement contour for an area of interest in front of a crack with a length of 0.479 mm of sample S2. Images were rotated 37° clockwise so that the crack line was horizontal [36]. a b c d Unloading Loading M. Mokhtarishirazbad et alii, Frattura ed Integrità Strutturale, 37 (2016) 114-123; DOI: 10.3221/IGF-ESIS37.16 121 Figure 9: The position of the area of interest for deriving the displacement field ahead of a crack with the length of 0.479 mm after 53500 cycles (sample S2). Specimen Crack length (mm) CODmax (μm) ∆KI (MPa√m) ∆KII (MPa√m) T-stress (MPa√m) S1 0.682 2.06 17.51 23.81 -669.94 S1 1.053 6.33 37.82 40.14 -1079.67 S2 0.669 1.98 13.19 23.16 -251.78 S2 1.057 0.71 9.67 23.56 -231.80 Table 4. The evaluation of SIFs and T-stress for two crack lengths in samples S1 and S2. Tab. 3 shows the results of SIF for different crack lengths. It can be seen that ∆KI, ∆KII and T-stress increase as the crack grows from 0.682 mm to 1.053 mm for sample S1. Tab. 4 also shows that applying an overload cycle in sample S2 decreases the SIFs even after propagating the crack by 0.388 mm. COD values in Tab. 4 indicate that the initial condition (crack length = 0.682 mm for S1 and crack length = 0.669 mm for S2) is equivalent for both samples. It can be seen that applying the overload drastically reduced the COD value. For the second crack length shown in Tab. 4, the COD raised to 6.33 μm in S1 and due to the overload effect, COD decreased to 0.71 μm. That is, the overload inverted the trend normally followed as the crack grows; for a similar baseline load, the COD increases as the crack grows. However, if an overload is applied, COD decreases as the crack grows, as long as the crack-tip is within the zone of influence of the overload. The ∆KI follows a similar trend to the COD. ∆KI increases more than 200% for a 54% increment in the crack length in S1. However, ∆KI decreases 27% for a 58% increment in the crack length in S2. With respect to ∆KII, an increase of about 73% can be observed in sample S1 for a crack growth of 0.371 mm, while it increases by the negligible value of 1.7% for sample S2 after the crack was propagated by 0.388 mm. A similar trend is also observed in the T-stress. While the crack length for both samples are about 1.05 mm, ∆KI for the sample which had experienced an overload is almost one fourth of the sample S1. In addition, ∆KII has increased 74% for sample S1 whereas its changes was negligible for sample S2. M. Mokhtarishirazbad et alii, Frattura ed Integrità Strutturale, 37 (2016) 114-123; DOI: 10.3221/IGF-ESIS37.16 122 CONCLUSIONS n this paper, the effect of applying a 40% overload on the behaviour of a crack under cyclic biaxial loading is studied with DIC technique. COD examinations showed the classical sequences of overload including retardation and recovery. A method including fitting the experimental displacement data to analytical solutions based on Williams' series development was also used for studying the biaxial fatigued cracks. This allowed the mixed-mode SIF (KI and KII) and the T-stress to be estimated on two different samples, one subjected to an overload event and one without an overload. Results showed that applying 40% overload led to a 27% decrease in ∆KI after the crack propagated 0.388 mm. ∆KII for the sample which did not experienced overload cycle increased by 73% for a crack growth of 0.371 mm. It was also shown that DIC can effectively be used for studding the structures under biaxial loading. ACKNOWLEDGEMENTS inancial support of Junta de Andalucía through Proyectos de Excelencia grant reference TEP-3244; and University of Malaga through Campus de Excelencia Internacional del Mar (CEIMAR) through Líneas Emergentes program and for providing PhD exchange scholarship is greatly acknowledged. REFERENCES [1] Anderson, T.L., Fracture Mechanics Fundamentals and Applications. 2nd ed. CRC Press; (1995). [2] ASTM E399-90: standard test method for plane-strain fracture toughness of metallic materials, Am Soc Test Mater Annu B Stand, 3 (1991) 451–85. [3] Suresh, S., Fatigue of Materials. 2nd ed. New York: Cambridge University Press; (1998). [4] Ramesh, K., Gupta, S., Kelkar, A.A., Evaluation of stress field parameters in fracture mechanics by photoelasticity - revisited, Eng Fract Mech,56 (1997) 25–41 and 43–5. [5] Díaz, F.A., Yates, J.R., Patterson, E.A., Some improvements in the analysis of fatigue cracks using thermoelasticity, Int J Fatigue, 26 (2004) 365–76. doi:10.1016/j.ijfatigue.2003.08.018. [6] Nowell, D., Paynter, R.J.H., De Matos, P.F.P., Optical methods for measurement of fatigue crack closure: moiré interferometry and digital image correlation, Fatigue Fract Eng Mater Struct, 33 (2010) 778–90. doi:10.1111/j.1460- 2695.2010.01447.x. [7] McNeill, S.R., Peters, W.H., Sutton, M.A., Estimation of stress intensity factor by digital image correlation, Eng Fract Mech, 28 (1987) 101–12. doi:10.1016/0013-7944(87)90124-X. [8] Smith, J., Bassim, M.N., Liu, C.D., Measurement of crack tip strains using neutron diffraction. Eng Fract Mech, 52 (1995), 843–851. [9] Lopez-Crespo, P., Withers, P.J., Yusof, F., Dai, H., Steuwer, A., Kelleher, J.F., Buslaps, T., Overload effects on fatigue crack-tip fields under plane stress conditions: surface and bulk analysis. Fatigue Fract Eng Mater Struct, 36 (2013) 75- 84. [10] Sutton, M.A., McNeill, S.R., Helm, J.D., Chao, Y.J., Advances in two-dimensional and three-dimensional computer vision, in: Rastogi PK (Eds) Photomechanics, Springer Berlin Heidelberg; (2000) 323–72. doi:10.1007/3-540-48800- 6_10. [11] Pan, B., Qian, K., Xi,e H., Asundi, A., Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review, Meas Sci Technol, 20 (2009) 062001 (17pp). doi:10.1088/0957-0233/20/6/062001. [12] Patterson, E.A., Olden, E.J., Optical analysis of crack tip stress fields: a comparative study, Fatigue Fract Eng Mater Struct, 27 (2004) 623-635. [13] Sutton, M.A., Orteu, J-J., Schreier, H.W., Image Correlation for Shape, Motion and Deformation Measurements, New York: Springer; (2009). doi:10.1007/978-0-387-78747-3. [14] Sanford, R.J., Dally, J.W., A general method for determining mixed-mode stress intensity factors from isochromatic fringe patterns, Eng Fract Mech, 11 (1979) 621–33. doi:10.1016/0013-7944(79)90123-1. [15] Yoneyama, S., Ogawa, T., Kobayashi, Y., Evaluating mixed-mode stress intensity factors from full-field displacement fields obtained by optical methods, Eng Fract Mech, 74 (2007) 1399–412. doi:10.1016/j.engfracmech.2006.08.004. [16] López-Crespo, P., Burguete, R.L., Patterson, E.A., Shterenlikht, A., Withers, P.J., Yates, J.R., Study of a crack at a fastener hole by digital image correlation, Exp Mech, 49 (2009) 551–9. doi:10.1007/s11340-008-9161-1. I F M. Mokhtarishirazbad et alii, Frattura ed Integrità Strutturale, 37 (2016) 114-123; DOI: 10.3221/IGF-ESIS37.16 123 [17] Colombo, C., Vergani, L., A numerical and experimental study of crack tip shielding in presence of overloads., Eng Fract Mech, 77 (2010) 1644-1655. [18] Zybell, L., Chaves, H., Kuna, M., Mottitschka, T., Pusch, G., Biermann, H., Optical in situ investigations of overload effects during fatigue crack growth in nodular cast iron, Eng Fract Mech, 95 (2012) 45-56. [19] Vasco-Olmo, J.M., Díaz, F.A., Patterson, E.A., Experimental evaluation of shielding effect on growing fatigue cracks under overloads using ESPI., Int J Fatigue, 2 (2016) 117-126. [20] Lopez-Crespo, P., Steuwer, A., Buslaps, T., Tai, Y.H., Lopez-Moreno, A., Yates, J.R., et al, Measuring overload effects during fatigue crack growth in bainitic steel by synchrotron X-ray diffraction. Int J Fatigue, 71 (2015) 11–6. doi:10.1016/j.ijfatigue.2014.03.015. [21] Lopez-Crespo, P., Mostafavi, M., Steuwer, A., Kelleher, J.F., Buslaps, T., Withers, P.J., Characterisation of overloads in fatigue by 2D strain mapping at the surface and in the bulk, Fatigue Fract Eng Mater Struct, (2016) accepted. doi: 101111/ffe12463. [22] Lopez-Crespo, P., Moreno, B., Lopez-Moreno, A., Zapatero, J., Study of crack orientation and fatigue life prediction in biaxial fatigue with critical plane models, Eng Fract Mech, 136 (2015) 115-130. [23] Lopez-Crespo, P., Moreno, B., Lopez-Moreno, A., Zapatero, J., Characterisation of crack-tip fields in biaxial fatigue based on high-magnification image correlation and electro-spray technique, Int J Fatigue, 71 (2014) 17–25. doi:10.1016/j.ijfatigue.2014.02.016. [24] Lopez-Crespo, P., Garcia-Gonzalez, A., Moreno, B., Lopez-Moreno, A., Zapatero, J., Some observations on short fatigue cracks under biaxial fatigue. Theor Appl Fract Mech, 80 (2015) 96-103. [25] de Matos, P.F.P., Nowell, D., Experimental and numerical investigation of thickness effects in plasticity-induced fatigue crack closure, Int J Fatigue, 31 (2009) 1795–804. doi:10.1016/j.ijfatigue.2008.12.003. [26] Yusof, F., Lopez-Crespo, P., Withers, P.J., Effect of overload on crack closure in thick and thin specimens via digital image correlation, Int J Fatigue 56 (2013) 17–24. doi:10.1016/j.ijfatigue.2013.07.002. [27] Carlson, R., Kardomateas, G., Bates, P., The effects of overloads in fatigue crack growth, Int J Fatigue, 13 (1991) 453–60. doi:10.1016/0142-1123(91)90479-I. [28] Jones, R.E., Fatigue crack growth retardation after single-cycle peak overload in Ti-6Al-4V titanium alloy, Eng Frac Mech, 5 (1973) 585-604. doi:10.1016/0013-7944(73)90042-8. [29] Williams, M.L., On the stress distribution at the base of a stationary crack, J Appl Mech, 24 (1957) 109–14. doi:10.1115/1.3640470. [30] Zanganeh, M., Lopez-Crespo, P., Tai, Y.H., Yates, J.R., Locating the crack tip using displacement field data: a comparative study, Strain, 49 (2013) 102-115. [31] Beretta, S., Rabbolini, S., Bello, A.D., Multi-scale crack closure measurement with digital image correlation on Haynes 230, Frat Ed Integrità Strutt, 33 (2015) 174–82. doi:10.3221/IGF-ESIS.33.22. [32] Joyce, J.A., Sutton, G.E., An automated method of computered-controlled low-cycle fatigue crack growth testing using the eslastic-plastic parameter cyclic J, Automated test methods for fracture and fatigue crack growth, in: W.H. Cullen, R. W. Landgraf, L. R. Kaizand, and J. H. Underwood (Eds), American Society for Testing and Materials, (1985)225-247. [33] Lopez-Crespo, P., Shterenlikht, A., Yates, J.R., Patterson, E.A., Withers, P.J., Some experimental observations on crack closure and crack-tip plasticity, Fatigue Fract Eng Mater Struct, 32 (2009) 418-429. [34] Mokhtarishirazabad, M., Lopez-Crespo, P., Moreno, B., Lopez-Moreno, A., Zanganeh, M., Evaluation of crack-tip fields from DIC data: A parametric study, Int J Fatigue, (2016). doi:10.1016/j.ijfatigue.2016.03.006. [35] Sutton, M.A., Orteu, J-J., Schreier, H.W., Image correlation for shape, motion and deformation measurements, New York: Springer ( 2009). http://dx.doi.org/10.1007/978-0-387-78747-3. [36] Lopez-Crespo, P., Shterenlikht, A., Patterson, E.A., Yates, J.R., Withers, P.J., The stress intensity of mixed mode cracks determined by digital image correlation, J Strain Anal Eng Des, 43 (2008) 769–80. doi:10.1243/03093247JSA419. << /ASCII85EncodePages false /AllowTransparency false /AutoPositionEPSFiles true /AutoRotatePages /None /Binding /Left /CalGrayProfile (Dot Gain 20%) /CalRGBProfile (sRGB IEC61966-2.1) /CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2) /sRGBProfile (sRGB IEC61966-2.1) /CannotEmbedFontPolicy /Error /CompatibilityLevel 1.4 /CompressObjects /Tags /CompressPages true /ConvertImagesToIndexed true /PassThroughJPEGImages true /CreateJobTicket false /DefaultRenderingIntent /Default /DetectBlends true /DetectCurves 0.0000 /ColorConversionStrategy /CMYK /DoThumbnails false /EmbedAllFonts true /EmbedOpenType false /ParseICCProfilesInComments true /EmbedJobOptions true /DSCReportingLevel 0 /EmitDSCWarnings false /EndPage -1 /ImageMemory 1048576 /LockDistillerParams false /MaxSubsetPct 100 /Optimize true /OPM 1 /ParseDSCComments true /ParseDSCCommentsForDocInfo true /PreserveCopyPage true /PreserveDICMYKValues true /PreserveEPSInfo true /PreserveFlatness true /PreserveHalftoneInfo false /PreserveOPIComments true /PreserveOverprintSettings true /StartPage 1 /SubsetFonts true /TransferFunctionInfo /Apply /UCRandBGInfo /Preserve /UsePrologue false /ColorSettingsFile () /AlwaysEmbed [ true ] /NeverEmbed [ true ] /AntiAliasColorImages false /CropColorImages true /ColorImageMinResolution 300 /ColorImageMinResolutionPolicy /OK /DownsampleColorImages true /ColorImageDownsampleType /Bicubic /ColorImageResolution 300 /ColorImageDepth -1 /ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold 1.50000 /EncodeColorImages true /ColorImageFilter /DCTEncode /AutoFilterColorImages true /ColorImageAutoFilterStrategy /JPEG /ColorACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /ColorImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /GrayImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile () /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False /CreateJDFFile false /Description << /ARA /BGR /CHS /CHT /CZE /DAN /DEU /ESP /ETI /FRA /GRE /HEB /HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. 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