PSI - Issue 41

T.J.S. Oliveira et al. / Procedia Structural Integrity 41 (2022) 72–81 Oliveira et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 2 – Geometry of the tubular adhesive joint.

In the construction of the numerical model, incrementation is an important aspect to consider. A small value has been chosen for the minimum size of the increment to avoid the associated convergence problems during the damage propagation phase. The boundary conditions applied to the adhesive joint are intended to emulate a torsion loading at one end of joint, whilst the other end is clamped. To apply the torsion load, a reference point was created in the middle of the tube and it was connected to the cross-sectional face at one joint end (Fig. 3), which allowed to apply a torsional angle boundary condition and thus perform the tests.

Fig. 3 – Reference point and connection to the cross-sectional joint face.

The joint meshes were built after defining the mesh sizes in each edge of the model. The areas where the largest stress gradients occur should be as refined as possible. Thus, the mesh is more refined at the overlap region (where the two tubes are joined by adhesive) and at the vicinity, as observed in Fig. 4 for the strength analysis, when compared to the adhesive-free portions of the adherends. Due to the need to obtain high precision in the computed stresses and strains, bias ratio was applied to the chosen refinement, to ensure maximum refinement at the overlap edges. In the adhesive-free portions of the model (1 and 3 in Fig. 4) the element size varied from 0.2 mm (near the overlap edges) and 3 mm (at the other edge), using a single-bias effect, i.e., grading in the direction of the overlap. In the overlap portion (2 in Fig. 4), double-bias was applied, i.e., towards both overlap edges, with a minimum size of 0.2 mm and maximum size of 1 mm. Through-thickness, single-bias was applied with higher refinement near the adhesive layer, with element sizes between 0.2 and 1.5 mm.

Fig. 4 – Example of mesh refinement.