PSI - Issue 33

R.V.F. Faria et al. / Procedia Structural Integrity 33 (2021) 673–684 Faria et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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All criteria that are based on strains rather than stresses fail to work, with higher preponderance for the welded and hybrid joints. In these cases, the P m result closest to the experiments was offset by 611.6% (hybrid joint and MAXPE criterion). Within the scope of stress criteria, smaller P m results by more than 90% were found with the MAXPS criterion for the purely welded and hybrid joints. Additionally, the different was also close to 80% for the bonded joint. Differently from this criterion, the also stress-based QUADS and MAXS criteria provided accurate P m predictions. Between these two, the QUADS criterion is the best, giving an error of 3.9% (joint bonded). For the purely welded and hybrid joints, the errors were below 3%. The MAXS criterion was almost as good as the QUADS criterion, since the maximum error was only 4.9% (purely welded joint), while the lowest was 2.8% (hybrid joint). The conducted analysis showed that the XFEM can be precise for P m assessment of peel-dominant joints, if the stress-based QUADS and MAXS initiation criteria are selected. The obtained results in this work also agree with former works in adhesive joints’ numerical modelling, namely in the use of stress criteria for damage initiation. The MAXS damage initiation criterion was almost as good as the QUADS criterion, and slightly higher offset can be related to the lack of interaction between tension and shear loads for failure assessment (section 3.1), in a typical mixed-mode loading analysis. Xará and Campilho (2018) obtained identical conclusions to this work. The MAXE and QUADE damage initiation criteria overshot the P m test data, reinforcing the idea that criteria based on strains should not be used for failure assessment in bonded joints (Campilho et al. 2013). However, these large deviations may be influenced by using failure strains instead of plasticization strains to infer damage onset in the adhesive layer, which is in the genesis of this criterion. Actually, the Araldite ® 2015 is ductile and a significant difference exists between these two quantities and, as a result, in all joint types and both in the adhesive/weld-nugget, damage initiation takes place at a more advanced applied displacement than expected, leading to higher predicted P m as well. To improve the predictions, a modification to these criteria can be proposed, by using instead the plasticization initiation strains to replace the failure strains, possibly with better results. The MAXPS initiation criterion gives P m much lower than the experiments for all joint types. The MAXPE initiation criterion, although with more accurate predictions than the remaining stress criteria, still fails to be accurate. However, the bad performance of the MAXPS and MAXPE initiation criteria is closely related to the described approach to calculate P m , which arises from the limitations of the software embedded formulation for crack propagation analysis. Furthermore, the MAXPE initiation criterion additionally suffers by considering failure strains, as previously discussed. 4.5. P m for different propagation criteria The choice of the propagation criterion also acquires high relevancy within the scope of XFEM modelling, whose options were discussed in section 3.1, including the governing criterion equation and different damage laws. The linear softening option was tested with different α in equation (4), studying 0.5, 1 and 2 values. However, for the exponential law, just  =1 was tested. In these analyses, the initiation criterion was the QUADS criterion, showing the best result in the previous study.

Fig. 8. Experimental/numerical P m comparison between all joint types - damage propagation criteria.