PSI - Issue 33

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Brito et al. / Structural Integrity Procedia 00 (2019) 000–000

R.F.N. Brito et al. / Procedia Structural Integrity 33 (2021) 665–672

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Figure 1. Geometry and general dimensions of the stepped-lap joints analyzed.

2.3. Numerical models The numerical models reproduced the experimental geometry shown in Figure 1. The numerical analyses were created and solved using the ABAQUS ® software (Abaqus 2017, Dassault Systèmes. U.S.A.). For all the models, 4 node quadrilateral elements were used. The numerical work consists of two separate stages. First, the adhesive layer is discretized only with a layer of cohesive elements (Abaqus COH2D4) and 2D plane strain elements (Abaqus CPE4) for the substrates, the global mesh is relatively coarse, approximate element size of 0.2 x 0.2 mm (based on previous experience). Second, the adhesive layer was discretized with several layers of 2D solid plane strain elements, the substrates were also discretized with this element type; the meshing in this stage was fine, approximate element size 0.02 x 0.02 mm (also based on previous experience). The first stage was used to determine the numerical P m , while the second provided the stresses along the adhesive layer. All the models were considered as 2D plane strain cases because their thickness is smaller than their width (Adams and Peppiatt, 1974). Turning to the material properties, those models for determining the stress distributions were purely elastic. The CZM models considered a quadratic nominal stress criterion (QUADS) and a triangular law (Campilho, 2017; de Sousa et al., 2017), the properties used were taken from Table 2; the CZM is briefly described later in this section. Substrate properties for the composite materials are reported in Table 1. Substrate delamination was considered by adding a line of cohesive elements of 0.02 mm between the first and second layers beneath the bonding surface. Furthermore, for evaluating the influence of substrate material has in P m , aluminum substrates were also used for the CZM models; the aluminum was a AW6082-T651 with mechanical properties: E =70.07±0.83 GPa,  y =261.67±7.65 MPa,  f =324.00±0.16 MPa, and  f =21.70±4.24% (de Sousa et al., 2017). The boundary conditions aimed to reproduce the experimental setup (Figure 1); therefore, the left vertical edge was constrained in both directions ( U x = U y = U Rz =0) whilst the right vertical edge was subjected to a horizontal displacement (  ) ( U x =  , U y =0), representing the pulling done by the UTM. Furthermore, the models were displacement-driven. Regarding the CZM, considering that the material linearly reaches a maximum load prior to its properties degrade, visible as softening, until failure; this behavior is simulated by the CZM laws. The traction-separation laws relate the force and displacement separation vectors within a cohesive mean; these laws require three parameters: critical energy release rate, the cohesive tensile strength, and the law shape (Abdel Wahab, 2015). The area below the traction separation law corresponds to the material’s toughness ( G C ) in that direction. Furthermore, as the material has different properties in tensile than in shear, a traction-separation law for each loading direction is required (both with the same shape); the mixed mode is then considered (Alfano, 2006). Several shapes for the traction-separation laws exist (Abdel Wahab, 2015), in this work the triangular shape was used, which is applicable to the chosen adhesive (de Sousa et al., 2017).