PSI - Issue 33

M.F.M.O. Rosas et al. / Procedia Structural Integrity 33 (2021) 115–125 Rosas et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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Autograph AG-X tester (Shimadzu, Kyoto, Japan) was used to perform the tests, equipped with a 100 kN load cell, at room temperature and with 1 mm/min of velocity. The specimens tested were five for each joint configuration and resulted in load-displacement ( P -  ) curves that will allow the comparison with the numerical results.

Fig. 1. Geometry and characteristic dimensions of the tubular joints.

Table 2. Designation of the dimensions of the specimens and their values (mm). Designation Values [mm] Overlap length, L O 20 40 Adherends’ free length, L S 50 60 Joint free length, L T 80 80 Outer diameter of the inner tube, d SI 20.0 20.0 Outer diameter of the outer tube, d SE 22.4 22.4 Thickness of the inner tube , t SI 2 2 Thickness of the outer tube , t SE 2 2 Adhesive thickness, t A 0.2 0.2

2.3. Numerical modelling The numerical work was performed in Abaqus ® (Dassault Systèmes, Vélizy-Villacoublay, France). A two dimensional (2D) axisymmetric FE approximation was undertaken because of the specific characteristics of the tubular joints’ geometry. Two models were constructed: for the stress analysis and for str ength prediction. The aluminium tubes were always modelled using solid elasto-plastic elements, whose stress-strain (  -  ) curves are presented in the work of Nunes et al. (2016). With this purpose, solid axisymmetric FE elements were used (CAX4 4-node axisymmetric elements; this element type was also used in the work of Kim and Lee (2001), although in the reduced integration form). In the stress distribution analysis, the adhesive was also populated with these solid elements. In contrast, for the strength prediction analysis, the adhesive layer was modelled by one row of axisymmetric CZM elements joining both tubes (COHAX4 4-node axisymmetric cohesive elements). To model the adhesive layer’s behaviour by a continuum approach, CZM elements with a triangular shape mixed -mode law (which is defined further in this work) were used, and considered only one element through-thickness between the tubes. The numerical models used to acquire the stress distribution were more refined than the models used for the strength prediction aiming to obtain a better representation of the stress fields. The size of the adhesive layer elements in the stress models (solid elements) was 0.02 mm×0.02 mm and in the strength prediction models (CZM elements) it was 0.2 mm×0.2 mm. In both analyses, size grading effects (bias effects) were employed to reduce the computational effort. Fig. 2 presents a mesh refinement example model of a tubular joint with L O =20 mm employed in the strength analysis. Regarding the boundary conditions, the tubes were clamped at one of the edges and, for the loading conditions, longitudinal displacements were applied at the opposite edge while being transversely restrained.

Fig. 2. FE mesh detail and boundary conditions of the axisymmetric model for a tubular joint with L O =20 mm.