PSI - Issue 54

D.F.T. Carvalho et al. / Procedia Structural Integrity 54 (2024) 398–405 Carvalho et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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(Fig. 1 b). The main geometries are the overlap length ( L O ) 12.5, 25, 37.5, and 50 mm, adherends’ thickness ( t P ) 3 mm, adhesive thickness ( t A ) 0.2 mm, step transitions’ adhesive thickness ( t A1 ) 0.2 mm, joint total length ( L T ) 180 mm and width ( B ) 25 mm. The experimental tests were carried out under displacement control at a speed of 1 mm/min and at room temperature on a Shimadzu AG-X 100 universal testing machine equipped with a 100 kN load cell. At least three valid results were obtained for each type of adhesive joint analysed. a) b)

Fig. 1. Geometry of the stepped-lap joint a) and considered geometry in the bonding area b).

2.3. Numerical modelling The numerical work was performed in the Finite Element Method software Abaqus ® , from Dassault Systèmes. A two-dimensional analysis with plane strain elements and a non-linear geometric formulation was implemented (Manoj et al. 2023). Four-node quadrilateral plane strain solid elements (CPE4) were used for the adherends and for the adhesive layer was used four-node CZM elements (COH2D4) that promotes the initiation and propagation of damage or crack growth for strength prediction analyses. A continuous modelling approach was undertaken to model the adhesive layer using CZM, which translates into the implementation of a single row of cohesive elements along the entire layer. material discontinuities were considered to overcome the distortion of the CZM elements caused by the inability to model the corners between the adhesive segments of the step transition from the vertical to the horizontal branch. In a previous study (Rocha and Campilho 2018), a mesh convergence analysis was performed and it was established that if the CZM element length is taken equal to t A (cohesive element size of 0.2×0.2 mm 2 ), the accuracy of the results is guaranteed. Regarding the details of the CZM, in the work of Rocha and Campilho (2018) is given more insights about this methodology. The adhesives properties that were used in the numerical simulations are listed in Table 1 and it should be mentioned that t n 0 was taken equal to  f and the t s 0 was taken equal to  f . 3. Results 3.1. Numerical model validation The numerical procedure followed in this work was initially validated, for the previously defined geometries, by comparing the numerical results with the experimental ones. In Fig. 2 is presented the comparison between the numerical and experimental P m results for DAJ bonded with the 7752-2015-7752 (a) and 7752-AV-7752 (b). In configuration 7752-2015-7752 the difference in P m for L O =12.5 mm is only 1% and for L O =25 mm it increases to 7%, while for higher L O , which presented plasticization of the adherends, the variation was about 3%. The 7752-AV-7752 DAJ configuration showed the same trend, with a P m difference of 9% for L O =12.5 mm and maintained at around 4% for the remaining L O s. In addition, it was possible to depict premature failure of the adherend for L O of 37.5 and 50 mm, a trend that was observed in the experimental tests. Taking into account the results obtained, it can be established that the FEM-CZM approach and the material models are considered valid, enabling the parametric numerical study of the DAJ solution that will be presented in the following section.