PSI - Issue 47

J.E.S.M. Silva et al. / Procedia Structural Integrity 47 (2023) 70–79 Silva et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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damage and the damage is propagated following a linear energetic criterion (Campilho et al. 2013). Damage propagation is modelled by a linear power law depending on G IC and G IIC . 4. Results 4.1. CZM validation Previously to the numerical analysis regarding the adhesive type effect on P m , the numerical CZM approach to TSJ design should be proper validated with experimental results. To accomplish this process, TLJ were tested as previously defined in Section 2, and an identical numerical procedure was applied to the TSJ. Fig. 5 compares the experimental P m (including average and deviation) and CZM strength predictions for the three adhesives. The P m values obtained through the triangular CZM and experiments are quite close for the AV138 and 2015. The AV138 presents the smallest differences between experimental and numerical values, of 2.4% and 4.7% for L O =20 and 40 mm, respectively. The adhesive 2015 also presents acceptable differences, with 6.1% for L O =20 mm and 2.9% for L O =40 mm. For both AV138 and 2015, the numerical P m were always lower than the experimental results. A non-negligible discrepancy was found for the 7752 results, since the numerical predictions were much lower than the experimental results, with a difference of 18.4% for L O =20 mm and 14.3% for L O =40 mm. This behaviour is caused by modelling ductile adhesives with triangular CZM laws, leading to immediate stress depreciation after reaching the cohesive strength (Campilho et al. 2013). Even so, previous works demonstrate that, even with inadequate cohesive laws, it is possible to obtain a rough estimate of the strength of the joint, provided that the cohesive parameters have been correctly estimated (Yang and Cox 2005). Therefore, the numerically obtained values are accepted for design purposes.

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Fig. 5. P m vs L O result comparison (TLJ) with three adhesives.

4.2. Stress analysis  y and  xy stresses are analysed at the adhesive mid-thickness as a function of  under linear elasticity assumptions. A normalisation process was considered by considering the average  xy , defined as  avg . Due to the scarf slope, a local reference system required, as presented in Fig. 6 . Stresses were rotated using the Mohr’s theorem and the respective transformation equations (the outputs of Abaqus ® are  x’ ,  y’ and  x’y’ , defined in the global coordinate system).