Microsoft Word - 2178 L. Marsavina et al., Frattura ed Integrità Strutturale, 47 (2019) 266-276; DOI: 10.3221/IGF-ESIS.47.20 266 Fracture and Structural Integrity: ten years of ‘Frattura ed Integrità Strutturale’ Mechanical and fracture properties of particleboard Liviu Marsavina Politehnica University of Timisoara, Department of Mechanics and Strength of Materials, 300 222 Timisoara, Romania liviu.marsavina@upt.ro Ion Octavian Pop Universite de Limoges, GC2D, EA 3178, Egletons F-19300, France PFT Bois-Construction du Limousin, Egletons F-19300, France ion-octavian.pop@unilim.fr Emanoil Linul Politehnica University of Timisoara, Department of Mechanics and Strength of Materials, 300 222 Timisoara, Romania emanoil.linul@upt.ro, https://orcid.org/0000-0001-9090-8917 ABSTRACT. Particleboard (PB) are wood-based composites with fine wood fibers bound together by a small amount of polymeric adhesive, widely used in furniture industry and civil engineering. PB plates can be painted, laminated or veneered, and have good dimensional stability and load bearing capacity when properly designed. However, the deformation and fracture of such elements create malfunctions of structures made of MDF. This paper presents experimental results obtained for three point bending (TPB) tests, mode I and mode II fracture toughness. The bending tests were carried on rectangular specimens, while the fracture toughness tests were performed on Single Edge Notched Bend (SENB) specimens for mode I, respectively on Compact Shear (CS) specimens for mode II loadings. Digital Image Correlation technique allows the determination of the Crack Relative Displacement Factor and estimation of the Energy Release Rate. KEYWORDS. Particleboard; Fracture toughness; Digital Image Correlation. Citation: Marsavina, L., Pop, O., Linul, E., Mechanical and fracture properties of particleboard, Frattura ed Integrità Strutturale, 47 (2019) 266-276. Received: 23.08.2018 Accepted: 08.10.2018 Published: 01.01.2019 Copyright: © 2018 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. INTRODUCTION articleboard (PB) represent a class of wood-based composite with fine wood fibers bound together by a small amount of polymeric adhesive. Their main applications are in furniture industry and civil engineering [1]. PB plates can be painted, laminated or veneered, and have good dimensional stability and load bearing capacity when P http://www.gruppofrattura.it/VA/47/2178.mp4 L. Marsavina et al., Frattura ed Integrità Strutturale, 47 (2019) 266-276; DOI: 10.3221/IGF-ESIS.47.20 267 properly designed [2]. However, the deformation and fracture of such elements create malfunctions of structures made of PB. Different studies on bending properties of PB were published. In [3] design requirements for PB and Medium Density Fiberboard (MDF) plates under different loading conditions are presented. The performance of PB beams under four point bending are presented in [4]. The effect of different types of coatings on the strength and stiffness of PB are investigated in [5]. Kulman et al. [6] studied the effect of density and temperature on modulus of rupture and modulus of elasticity of PB and MDF. The fracture behavior of wood and its composites is reviewed by Stanzl-Tschegg and Navi [7]. However, only a few studies investigates the fracture toughness of PB [8-10]. The same like in the case of MDF, different values of fracture toughness were obtained: Matsumoto and Nairn [11] 2.57 MPa·m1/2 for density of 609 kg/m3, respectively 3.77 MPa·m1/2 for density of 769 kg/m3 using Compact Tension (CT) specimens, while for wedge splitting specimens and a density of 710 kg/m3 Niemz et al. [12] obtained 1.81 MPa·m1/2. Fewer investigations were carried out on mixed mode fracture toughness of PB and MDF, [13]. Today, several fracture approaches such as the Stress Intensity Factor (SIF) [14-16], the Crack Relative Displacement Factor (CRDF) [17-20] or the energy release rate [21-24] allow expressing fracture criteria. It should also be noted that usually the damage level could be evaluated from a local approach based on the mechanical fields assigned by the crack tip singularity or by a global approach using the mechanical fields far to the crack tip singularity. Starting from this analysis, in the present study, a formalism based on the SIF and the CRDF was applied to evaluate the fracture process. As will be shown latter the CRDF allows definition of the kinematic state around to the crack tip. As defined by Dubois et al. [17, 18], Pop et al. [19] and Jamaaoui et al. [25], the crack opening state represents the relative displacement between two points positioned on the upper and the lower crack flanks. Its evaluation can be performed directly from the experimental measurements. Associated more often to full fields techniques, the optical methods can be easily applied to observe and to analyze the fracture process. Today, several optical techniques and methods are developed in order to measure the different fracture properties. Among these methods, we remind here: interferometry, stereo correlation, moiré, photoelasticity, Digital Image Correlation (DIC) or mark- tracking methods [24, 26-32]. Nevertheless, their application to analyze the fracture process depends on the observation scale and the environmental boundary conditions (i.e. laboratory or in-situ). Concerning the characterization of mechanical and fracture properties of PB the DIC and the mark-tracking methods seem to be the better. For this purpose, the Crack Opening Displacement was measured by means the DIC. Associated with optical full field methods the DIC allows measure of the bi-dimensional displacement and strain fields. The interest of this method lies in its possibility to perform the measurements without contact. Moreover, the studied zone, sometimes called the zone of interest, can be easily adapted to the analyze scale (i.e. local or global). Today several algorithms to perform the DIC in order to evaluate the fracture parameters are proposed [29-37]. In the present study, the analysis was performed using Correla software’s, developed by PEM team of Pprim Institut of Poitiers [38-39]. The present paper presents the original results, obtained for two different densities and thicknesses of PB, for modulus of rupture, modulus of elasticity, the fracture toughness in mode I and predominantly mode II and the crack relative intensity factors. EXPERIMENTAL DETERMINATION OF MECHANICAL AND FRACTURE PROPERTIES Materials ests were carried out on medium density PB with thicknesses of 16 and 25 mm. The density was determined on each specimen resulting a mean density of 600 (±12) kg/m3 for the PB with 16 mm thickness, respectively 587 (±15) kg/m3 for the PB with 25 mm thickness. The specimens before testing were conditioned at 22±2°C room temperature and 65±5% relative air humidity. Bending tests The tests were performed on a Zwick Roell Z005 electromechanical universal testing machine under displacement control by setting the machine to 10 mm/min. During the test, the force versus deflection was measured by means of linear variable differential transformer (LVDT) position sensor (-/+ 0.01mm) and a load cell of 5 kN (±5%). Rectangular specimens, Fig. 1, were adopted for the Three Point Bending tests, with dimensions B (height)  B (width)  L (length). For 16 mm thickness the dimensions were B=16 mm, L=250 mm, and the span (distance between supports) S=192 mm respectively for 25 mm thickness B=25 mm, L=250 mm, and S=192 mm. The test program consisted of four test series (two different thicknesses of PB plates of 16 and 25 mm, respectively two orientations 1 and 2) with five tests in each T L. Marsavina et al., Frattura ed Integrità Strutturale, 47 (2019) 266-276; DOI: 10.3221/IGF-ESIS.47.20 268 series. Orientation 1 corresponds to an out-of-plane loading, and orientation 2 corresponds to an in-plane loading direction. Typical force - displacement curves are shown in Fig. 2. It could be observed that for orientation 1, which is the one most used for PB, higher values of loads were obtained comparing with direction 2 and a quasi-brittle behavior Figure 1: Three point bending specimen Figure 2: Typical force - displacement curves Based on the EN 310 standard [40], the Modulus of Rupture (MOR) and Modulus of Elasticity (MOE) were determined. The three point bending results are shown in Fig. 3. It could be observed that the maximum values of MOR and MOE were obtained for direction 1 and 16 mm thickness PB: 11.5 MPa, respectively 1782 MPa. The obtained values are in accordance with those from literature for PB, as follow: 11 MPa for MOR and 1725 MPa for MOE. In Fig. 3 boxes marked with 1 and 2 are related to sample orientation according to loading direction. a. Modulus of rupture b. Modulus of elasticity Figure 3: Mechanical properties of particleboard Mode I fracture toughness tests Mode I fracture toughness tests were carried out on Single Edge Notched Bend (SENB) specimens [41], Fig. 4a loaded in three point bending using Zwick Roell Z005, at room temperature, under displacement control with a loading speed of 10 mm/min. The maximum load Fmax recorded during the tests was considered to calculate Mode I fracture toughness (KIC), given by Eq. (1): 0 2 4 6 0 100 200 300 400 500 Standard trav el in mm F o rc e i n N 11.50 10.63 9.30 9.24 0 2 4 6 8 10 12 14 16_1 25_1 16_2 25_2 M o d u lu s o f ru p tu re [ M P a ] Thickness [mm] 1 2 1782.0 1245.6 1406.7 1153.6 0 500 1000 1500 2000 2500 16_1 25_1 16_2 25_2 M o d u lu s o f e la s ti c it y [ M P a ] Thickness [mm] 1 2 25_1 25_2 16_2 16_1 L. Marsavina et al., Frattura ed Integrità Strutturale, 47 (2019) 266-276; DOI: 10.3221/IGF-ESIS.47.20 269  max1/2 /IC F K f a W B W  (1) with W specimen width, B = W/2 specimen thickness and f(a/W) is dimensionless SIF for SENB specimens, calculated with the following [42]:   2 3/2 1.99 ( / )(1 / ) 2.15 3.93( / ) 2.7( / ) / 6 / (1 2 / )(1 / ) a W a W a W a W f a W a W a W a W         . (2) Specimen Thickness B [mm] Width W [mm] Crack Length a [mm] Maximum load Fmax [N] Fracture toughness KIC [MPa·m1/2] Mean Fracture toughness KIC [MPa·m1/2] I.1 23.8 50.1 24.6 466 0.868 0.841 I.2 23.6 50.1 24.5 465 0.868 I.3 23.6 50.1 24.5 454 0.847 I.4 23.6 50.1 24.5 417 0.778 I.5 23.6 50.1 24.5 452 0.843 I.6 16.3 32 17.8 178 0.784 0.736 I.7 16.1 32 16.8 154 0.618 I.8 16.2 32 18.8 149 0.740 I.9 16.1 32 17.8 153 0.682 I.10 16.1 32 17.5 198 0.855 Table 1: Mode I fracture toughness results The specimen dimensions, maximum load and mode I fracture toughness are summarized in Tab. 1. It could be observed that the maximum value of KIC = 0.841 MPa·m1/2 was obtained for the 25 mm PB thickness. On contrary, the mode I fracture toughness for 16 mm thickness was 0.736 MPa·m1/2. Mode II fracture toughness tests Compact Shear (CS) specimens [43], Fig. 4b, were used for mode II fracture toughness determination. Tests were performed on a 100 kN A009 (TC100) universal testing machine, at room temperature and using 10 mm/min displacement control. Maximum load was used to estimate the mode I and mode II stress intensity factors. The SIFs solutions could be expressed on the form:  max , ,iC i F K a f a W i I II H B   (3) with B as the specimen thickness, a as crack length and H as specimen width. A numerical calibration of the specimen was performed earlier by Petrova et. al. [44] using finite element analysis in order to determine the non-dimensional SIFs fi(a/W), resulting:     4 3 2 4 3 2 / 2.472( / ) 1.784 ( / ) 1.135( / ) 0.213( / ) 0.295 / 6.416( / ) 11.154 ( / ) 8.992( / ) 3.667( / ) 1.01 I II f a W a W a W a W a W f a W a W a W a W a W           (4) It should be noted that even if the applied load produce shear in front of the crack, a small amount of mode I still exist at the crack tip [44], so the fracture thoughness could be expressed using an effective SIF value: L. Marsavina et al., Frattura ed Integrità Strutturale, 47 (2019) 266-276; DOI: 10.3221/IGF-ESIS.47.20 270 2 2 eff I IIK K K  (5) Tab. 2 presents the specimen dimensions, maximum load, the mode I, mode II and effective SIFs. A higher value of Keff = 0.785 MPa·m1/2 was obtained for the PB with 25 mm thickness comparing with the PB of 16 mm thickness, Keff = 0.631 MPa·m1/2. a. Single Edge Notch Bend b. Compact Shear Figure 4: Test specimens for mode I and mode II fracture toughness determination. Specimen B [mm] W [mm] H [mm] a [mm] Fmax [N] KI [MPa·m1/2] KII [MPa·m1/2] Keff [MPa·m1/2] Mean Keff [MPa·m1/2] II.1 16.4 50.3 76.6 25.0 3110 0.101 0.565 0.574 0.631 II.2 16.4 50.0 76.0 25.0 3470 0.113 0.630 0.640 II.3 16.4 51.1 76.0 25.0 3700 0.120 0.672 0.682 II.4 16.4 49.3 76.3 25.6 3050 0.091 0.532 0.540 II.5 16.4 50.0 76.0 25.0 3900 0.127 0.708 0.720 II.6 24 75.0 100 48.5 5911 0.198 0.826 0.850 0.785 II.7 24 76.0 100 48.5 5189 0.174 0.725 0.746 II.8 24 76.2 100 49.2 5788 0.194 0.810 0.833 II.9 24 75.0 100 48.7 5587 0.187 0.781 0.803 II.10 24 75.4 100 47.7 4814 0.162 0.674 0.693 Table 2: Mode II fracture toughness results The obtained results are represented in the fracture envelope plot KII/KIC versus KI/KIC side by side with the analytical predictions of Maximum Tensile Stress (MTS) [45, 46], Maximum Energy Release Rate (Gmax) [47, 48] and Minimum Strain Energy Density (SED) [49, 50]. From Fig. 5, it could be observed that the MTS and SED criteria fits better with the experimental results. L. Marsavina et al., Frattura ed Integrità Strutturale, 47 (2019) 266-276; DOI: 10.3221/IGF-ESIS.47.20 271 Figure 5: Comparison between fracture criteria and experimental results CRACK RELATIVE DISPLACEMENT FACTOR ESTIMATION BY DIGITAL IMAGE CORRELATION n the present paper, the fracture process was evaluated trough two parameters, the Stress Intensity Factor and the Crack Relative Displacement Factor (CRDF), respectively. As shown above, the calculation of SIF is most often based on the analytical solutions. The analysis of the analytical equations allowing calculation the SIF shows that its estimation depends on sample geometry and the loading amplitude. Based on the displacement fields amplitude the CRDF can be related with the kinematic state near the crack tip [19, 20, 25]. In this case, the CRDF can be calculated from the displacement fields measured by optical metrologies [19, 20, 25]. In the present paper, we propose to use the Digital Image Correlation (DIC) in order to measure the displacement fields and to evaluate the CRDF. It should be added that the evaluation of CRDF allows to separate the mixed mode loading configurations and to identify the part of each mode in the fracture process. Principle of Digital Image Correlation As mentioned above, in the present study, the CRDF was investigated by means DIC. Using this optical full field method the evolution of displacement fields was recorded during the fracture test. Now concerning the principle of DIC, it is important to specify that this technique is based on comparison of two images acquired before and after sample deformation [29-31, 42]. As described in Fig. 6, the displacement was calculated in the Zone Of Interest (ZOI) meshed by small groups of pixels, called subsets [19, 20, 29-31, 51]. According with the DIC hypothesis, the light intensity distribution during the test does not change. By supposing that the displacements may be approximated as homogeneous and bilinear inside the subset, the displacement fields were estimated by searching the subset distortions in terms of translations, rotations and rigid body motions. In fact, the displacement field represents the displacement vectors of the center of gravity of all subsets. Concerning the sample preparation, it should be noted that prior to testing, a very thin black and white speckle pattern was sprayed on the specimen surface. Then, as had been indicated above the displacement fields are calculated by tracking the deformation of a random grey speckle pattern applied to sample surface. In the present study, the ZOI was meshed by using the 3232 pixels² subset sizes. The optical device configuration used in the present study consist of an AVT Marlin F-201B with a Pentax 12.5-75 mm lens and a LED light source. The measurement was realized using an Aramis a non-contact and material-independent measuring system based on digital image correlation. The image analysis was performed using Correla software’s, developed by PEM team of Pprim Institut of Poitiers [38-39]. The estimating uncertainty of displacement is about 0.026 pixels. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 K II /K Ic KI/KIc MTS SED Gmax CS 16 CS 25 SENB 16 SENB 25 I L. Marsavina et al., Frattura ed Integrità Strutturale, 47 (2019) 266-276; DOI: 10.3221/IGF-ESIS.47.20 272 Figure 6: Principle of DIC Evaluation of crack relative displacement factor As detailed in works of [19, 20, 25, 52], the CRDF is calculated from the experimental displacement field via an adjustment procedure based on an iterative Newton-Raphson algorithm (see Fig. 7). Figure 7: Methodology of CRDF calculation. This consists in a fitting of analytical solutions of Kolossov–Muskhelishvili’s series [53, 54] on the displacement fields measured by DIC. Dubois et al. [16, 17], Pop et al. [19] and Meite et al. [20] show that by using this approach, an “equivalent” displacement field can be created without experiment noises, the knowledge of the material properties or the nonlinear phenomena presence [17-20]. Then, the CRDF can be expressed as a function to the weighting coefficients of the analytical solutions of Kolossov–Muskhelishvili’s series. x1 x2 ZOI x1 x2 ZOI hsubset v s u b se t Dh D v 1 m m*Undeformed image Deformed image subset x1 x2 Subset m (4x4pixels) Subset center p ixel x 2 p ix el x 2s u b se t x1 pixel x1 subset Sample with Black and white speckle pattern ZOISubsets Optimization                     N / 2 / 2 1 1 2 1 N / 2 / 2 2 1 2 1 u A r f , A r g , u A r l , A r z ,                                    By an adjustment procedureOptimization of displacement field Experimental  displacement field Equivalent  displacement field Experimental boundary conditions  experimental noises Adjustment procedure (Newton-Raphson) Identification of the weighting coefficients 1 1 N N 0 0 1 2 1 2 1 2 1 2 0A A A A T T R x x    Rigid body motions Crack geometry Optimized fields  ( ) 11 1K 2 2 A 1         ( ) 122K 2 2 A 1          Analytical solutions of Kolossov–Muskhelishvili’s series Crack Relative Displacement Factor L. Marsavina et al., Frattura ed Integrità Strutturale, 47 (2019) 266-276; DOI: 10.3221/IGF-ESIS.47.20 273 The mean value of CRDF calculated for maximum loading given in Tabs. 1 and 2, calculated from Pop et al. [19] and Meite et al. [20] developments are resumed in Tabs. 3 and 4. The values of the weighting coefficients associated with opening and shear modes are also summarized in Tabs. 3 and 4. The weighting coefficients were estimated according with the methodology illustrated in Fig. 7. Specimens A11 [m0.5] 10-3 Mean CRDF Mode I (KI) [m0.5] 10-3 A21 [m0.5] 10-3 Mean CRDF Mode I (KII) [m0.5] 10-3 (KI)/(KII) (KI)/(KII) Tab. 1 I.1-6 9.8 0.138 0.07 0.001 125 / I.7-14 7.2 0.102 0.05 0.0008 127 / Table 3: Single Edge Notch Bend Test– Crack Relative Displacement Factor Specimens A11 [m0.5] 10-3 CRDF Mode I (KI) [m0.5] 10-3 A21 [m0.5] 10-3 CRDF Mode II (KII) [m0.5] 10-3 (KI)/(KII) (KI)/(KII) Tab. 2 II.1-5 0.8 0.012 7.5 0.105 0.11 0.18 II.6-10 2.3 0.032 10 0.142 0.23 0.24 Table 4: Compact Shear Test– Crack Relative Displacement Factor The data resumed in Tabs. 3 and 4 lead us conclude that the opening and shear modes coexist during the test. The crack path observed after the tests indicated that the crack is not rectilinear. This aspect may be connected with the experimental boundary conditions and the PB fiber orientation. It is also interesting to observe that the relationship between the CRDF corresponding to mode I and II, and the relationship to the SIF show some similarities. Pop et al [19, 20] and Meite et al. [25, 52] show also that the energy may be estimated from the CRDF and SIF values, Eq. (6). ( ) ( ) 8 F K K G     (6) where:  ( ) 1 1 8K A k    (7) where 𝐾 is the Crack Relative Displacement Factor; 𝐾 is the Stress Intensity Factor and 𝛾 1 𝑜𝑟 2 corresponds to mode 1 and mode 2; 𝐴 , 𝐴 are the weighting coefficients associated with opening and shear modes. Tab. 5 resumed the values of the energy release rate calculated from the results obtained in the Tab. 1-4. Specimens Energy release rate Mode I [J/m²] Energy release rate Mode II [J/m²] I.1-6 15.3 / I.7-14 9.8 / II.1-5 0.16 8.2 II.6-10 0.73 13.5 Table 5: Energy values. L. Marsavina et al., Frattura ed Integrità Strutturale, 47 (2019) 266-276; DOI: 10.3221/IGF-ESIS.47.20 274 CONCLUSIONS he paper presents the experimental results for mechanical and fracture properties of particleboard materials. Tab. 6 summarizes the obtained results for the two PB thicknesses corresponding to direction 2 of orientation. It could be observed that the PB with thickness of 16 mm has higher mechanical properties (Modulus of Rupture-MOR and Modulus of Elasticity-MOE); while the higher fracture toughness was obtained for PB with 25 mm thickness. Thickness MOR [MPa] MOE [MPa] KIC [MPa·m1/2] Keff [MPa·m1/2] 16 9.30 1406.7 0.736 0.631 25 9.24 1153.2 0.841 0.785 Table 6: A comparison of mechanical and fracture properties for PB Using the experimental displacements measured by Digital Image Correlation (DIC) the Crack Relative Displacement Factor (CRDF) was estimated. The evaluation of CRDF allowing to evaluate the part of each mode in the fracture process. According to presented approach, all changes in material properties can be directly correlated with the displacement measurement and implicitly with the CRDF amplitude. As shown, the calculation of CRDF may be performed without knowledge of the material constitutive law. The values of CRDF show that even for an opening mode loading, the crack path and experimental boundary conditions induce a mixed mode configuration. Even if the value of CRDF corresponding to mode II is small, the results show the presence of the mode II during the crack propagation in opening mode. As shown in Tab. 4, the relationship between the CRDF corresponding to mode I and II of fracture, and the relationship between the Stress Intensity Factor (SIF) show some similarities to the shear test. This observation allows consideration of the calculated phase angle. Moreover, the fracture energy was evaluated from the CRDF and the SIF values. 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