PSI - Issue 28

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G. Clerc et al. / Procedia Structural Integrity 28 (2020) 1761–1767 Gaspard Clerc / Structural Integrity Procedia 00 (2019) 000–000

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despite the different type of plot used in Fig. 4 and 5, for the 3-CCF the crack propagation is highly unstable. Once the rupture force is reached the deformation increases very rapidly, indicating a rapid crack growth. In comparison for the 3-ENF sample the crack propagation remains stable once the critical energy released rate value is reached. 4. Discussion The results clearly show that the calculation method is not suited to describe the behavior for the 3-CCF sample. Indeed, the rupture force was not satisfyingly calculated. Also, the propagation stability was not achieved. The reasons to explain this are still not understood in detail. The following points should be investigated: - Due to the central crack and to the position of the loading head (see Fig.2), higher friction effects are present compared to the 3-ENF sample. Those are not accounted for in the Euler-Bernoulli equation and should probably be accounted for a more accurate description of the crack growth. - For the 3-ENF sample, the flexural rigidity of the cracked part of the sample is reduced by a factor of 8. This could be different for the 3-CCF sample as both ends are not free as it is the case for the 3-ENF sample. - The Euler-Bernoulli equation is a simplification of the more complex Timoshenko beam equation. For long and slender beams, the differences between both equations are small, but increase for short and high beams. The 3-CCF sample is composed of three relatively short parts, the first glued, the non-glued and the last glued part. It could be that the Euler-Bernoulli beam equation is not suited for this type of sample. This is also suggested by the increasing difference between the calculated and tested rupture force with increasing sample height. To account for these points, a finite element model of the 3-CCF sample should be compared to the test results. Using a FEM model would allow to account for the non-linear effects mentioned above. 5. Conclusion In this example, it was shown that the basic fracture mechanics principle used to characterize 3-ENF samples cannot be directly used to design any arbitrary structures. Even for a simple sample geometry as the 3-CCF sample, no satisfying equation was obtained. This illustrates the difficulty of using fracture mechanics for engineering design of more complex and realistic structures. The use of more advanced modeling methods, such as finite element method, should probably be investigated, as it allows to consider non-linear effects such as friction and shear stresses on the beam deflection. 6. References J.G. Williams, 1987, On the calculation of energy releases rates for cracked laminates, International Journal of Fracture 36: 101-119 G. Clerc, A. J. Brunner, S. Josset, P. Niemz, F. Pichelin, J-W. G. van de Kuilen, 2019, Adhesive wood joints under quasi-static and cyclic fatigue fracture Mode II loads, International Journal of Fatigue 123: 40-52 H. Yoshiara and M. Ohta (2000). Measurement of mode II fracture toughness of wood by the end-notched flexure test Journal of Wood Science 46:273-278 Griffith, A. (1921). The phenomena of rupture and flow in solids. Philosphical Transactions of the Royal Society of London, 221:163–198. Jockwer, R. and Dietsch, P. (2018). Review of design approaches and test results on brittle failure modes of connections loaded at an angle to the grain. Engineering and Structures, 171:362–372. Bengtsson, C. and Johansson, C.-J. (2002). GIROD - Glued in Rods for Timber Structures. SP Swedisch National Testing and Research Institute, Report: 2002:26. Gustafsson, P., Serrano, E., Aicher, S., and Johansson, C.-J. (2001). A strength design equation for glued-in rods. Symposium, Joints in timber Structures; 2001; Stuttgart, Germany, RILEM:323–332.