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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without embe dded XFEM, to aid in the later comparison between joint configurations. Following, the joints’ strength was predicted by XFEM modelling. Independently of the analysis type, the models were constructed with continuum solid elements, although including plasticity. Thus, hexahedral solid elements (C3D8 from Abaqus ® ) were selected for both the adherends and adhesive. The weld-nugget was placed collinear with the adhesive in the hybrid joints, thus with a similar thickness to t A , to simplify the analysis and promote smooth crack growth. The main purpose of the stress analysis is the extraction of stress distributions along the adhesive layer’s length in the elastic domain. Thus, in this case continuum elements with elastic properties were employed to model the adhesive. Moreover, the mesh was highly refined, considering ten finite elements through-thickness, which was necessary to accurately capture the large stress gradients (Weiland et al. 2020). In the strength analysis (including XFEM), the adhesive layer was modelled by solid elements including crack propagation possibility by XFEM. A less refined mesh was used, with one solid element in the adhesive to model the thickness.

Fig. 3. Mesh refinement and boundary conditions (hybrid joint example): (a) partitioned model, (b) meshed model and (c) detail at the weld nugget.

Fig. 3 shows an example of the mesh for a hybrid joint (strength analysis), thus with a coarse mesh. The figure includes the two symmetry planes, considered to reduce the computational effort and model only ¼ of the model. The models built for the stress analysis are similar, although with a higher elements’ density. The figure also shows the models’ division into separate partitions, to help in the mesh creation process (creation of a structured mesh without distortion), in all the model except the vicinity of the weld-nugget, due to the semi-circular boundary. In this case, a free mesh was applied. The meshed models have varying mesh densities along the model boundaries, including bias effects. The weld-nugget detail is also included in Fig. 3, highlighted in different color: half the weld nugget portion in the adherends in darker grey, and the XFEM-enriched elements to promote the weld- nugget’s crack growth in black. The boundary conditions were set to replicate the proposed loading and simplify the model: the models were fixed in two orthogonal symmetry planes and a tensile displacement was applied, together with transverse restraining at the adherend’s end (shown as face A - Fig. 3). Before choosing the mesh for the P m analysis, it was necessary to perform a mesh convergence analysis. With this purpose, different meshes were produced, with one, four and ten solid elements in the adhesive thickness direction. The results showed that one element can assure smooth crack growth and precise P m predictions. This effect is easy to understand in light of the employed energy approach for crack growth in XFEM modelling. Actually, debonding depends on a damage over an area instead of discrete peak stresses, like in continuum mechanics models. As a result, if the minimum mesh refinement is guaranteed, load transfer through the damaged elements is accurately captured and the results are precise. These findings were also confirmed in previous works (Curiel Sosa and Karapurath 2012, Moreira and Campilho 2019). After reaching damage initiation, damage laws are needed. In this work, linear and exponential softening laws were tested to simulate elements’ separation. Therefore, after damage initiation, the stress-displacement relations can be linear or exponential until detachment. The parameters required for the XFEM analysis (adherends and adhesive) are given in Table 2. Table 1 data was on the basis of the adhesive’s properties, while the steel properties to simulate weld-nugget failure were obtained from material characterization performed in a former work (Marques et al. 2016).