PSI - Issue 28

Eda Gok et al. / Procedia Structural Integrity 28 (2020) 2043–2054 Gok et al./ Structural Integrity Procedia 00 (2019) 000–000

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PD results of ENF problem using optimum horizon and mesh sizes are compared with FEA results, analytical solution with CBT and numerical results of Turon et al. (2010) in Fig. 8 c. PD results are in very good agreement with numerical results of Turon et al. (2010), FEA and analytical solutions in linear region. Although there is a small deviation with the analytical solution after the failure initiation, the results of PD and FEA are nearly identical with the numerical solution results of Turon et al., (2010) after failure initiation as seen in Fig. 8 c. 4.2. The MMB Problem In the MMB test, the same specimen with the ENF test is considered. The positions of the Mode I and Mode II partitions of the load P in Fig. 5 are adjusted according the mode ratios of 20%, 50%, 70% and 80% . Mode ratio of 20% is applied by setting the arm distance ( ) c to 149.05 mm. Mixed mode ratios of 50%, 70% and 80% results are obtained by setting the ( ) c to 63.18 mm, 46.71 mm, 41.06 mm respectively. These ( ) c values are determined using the equations given in ASTM D6671M (2006). The boundary conditions are applied as shown in Fig. 5. For PD modelling of the MMB specimen the model is created with 3.015 m  and 5 x h   . Force displacement curves obtained from PD method are compared with the results of FEA and the analytical solution. These results are depicted in Fig. 9.

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Fig. 9. Comparison of force-displacement results of MMB problem.

These results show that in the linear region PD formulation results have good agreement with analytical and FEA results although there are minor differences after the failure initiation. 5. Conclusion In this study, analytical solution, and numerical simulations of ENF and MMB test specimens were performed. For FEA of the specimen CZM is used and two-dimensional cohesive elements are created in ABAQUS. Then, bond based PD models are implemented using a new modified bilinear material law. Obtained PD results indicates that this new PD model with bilinear constitutive relation can correctly capture the numerical results of Turon et al. (2010). Note that PD results are also validated using CZM and analytical solutions.