PSI - Issue 47

J.E.S.M. Silva et al. / Procedia Structural Integrity 47 (2023) 70–79 Silva et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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tubes and then they were carefully assembled. The final step was to place the specimens in a jig to ensure concentricity of the tubes, and adhesive curing was carried out for one week. After the adhesive curing procedure, its excess was removed by milling. The experimental tests were performed at room temperature with a velocity of 1 mm/min in a Shimadzu-Autograph AG-X (Shimadzu, Kyoto, Japan) machine equipped with a 100 kN load cell. For each TLJ configuration ( L O =20 and 40 mm), five specimens were tested and the load-displacement ( P -  ) curves were registered. 3. FEM models 3.1. Pre-processing The geometries described in Section 2.1 were reproduced numerically in Abaqus ® (Dassault Systèmes. R.I., USA). The axisymmetric nature of the joint allows for a two-dimensional modelling approach, reducing the computational cost. For the TSJ,  was one of the analysed parameters, and one numerical model was created per  . Once the geometries were created, two modelling approaches were followed: the first, considering the adhesive layer as a cohesive material, and the second, considering the adhesive layer as a solid elastic material. The first allows estimating P m through CZM, and includes cohesive elements that were employed for the adhesive layer, as described in reference (de Sousa et al. 2017). The second allows to evaluate stresses in the bond line, so solid elements were employed in the adhesive layer. Subsequently, the corresponding mechanical properties were assigned to every section of the models. In all cases, the adherends were considered as an elastic-plastic material following a bilinear model. The adherends were meshed with a combination of three-node and four-node axisymmetric elements (CAX4R and CAX3) due to the wedge shape in the scarf region. The adhesive layer was meshed with four-node elements, which according to the approach were: the first, with cohesive axisymmetric elements (COHAX4), and the second, with solid axisymmetric elements (CAX4R). Moreover, the mesh size was biased to reduce computational costs while maintaining element concentration in highly-stressed areas. Moreover, the geometry was partitioned to aid the meshing process, ensuring four-node elements in the adhesive layer (Fig. 2). The mesh size in the adhesive layer for the first approach was 0.2 mm × 0.2 mm, while in the second was 0.02 mm × 0.02 mm. Thus, the latter approach had 10 rows of elements in the adhesive layer. The cohesive elements employed in the first approach had their sweep direction aligned with the through-thickness direction of the adhesive layer (Barbosa et al. 2018).

Fig. 2. Close-up of the mesh in the adhesive layer of the TSJ: a) CZM models, b) stress analysis models.

As the joints tested experimentally were subjected to traction, this phenomenon was represented by constraining one end of the geometry in all directions ( U R = U  = U Z =0) while imposing a displacement ( U Z =0.4 mm) to the other end, as shown in Fig. 3. The models were solved in the ABAQUS ® environment allowing geometric and material non linearities, although the former had no effect on these models.