PSI - Issue 41

J.E.S.M. Silva et al. / Procedia Structural Integrity 41 (2022) 36–47 Silva et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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wires with Ø0.2 mm were applied along the inner perimeter of the outer tube, to assure concentricity and a t A =0.2 mm. Afterwards, the adhesive was spread on all the bonding surfaces. Then, the tubes were carefully mounted together and positioned, the correct L O was assured by measuring with a digital calliper. Finally, the specimens were left to cure at room temperature for one week in a jig that assured the concentricity of the tubes. After cur ing, the adhesive excess was removed by milling. Five specimens for each joint configuration were tested in a Shimadzu Autograph AG-X tester (Shimadzu, Kyoto, Japan) equipped with a 100 kN load cell. The tests were performed at room temperature and with a velocity of 1 mm/min. The tests resulted in individualised load-displacement ( P -  ) curves to be compared with the numerical results.

3. Numerical work 3.1. Pre-processing

The joint geometries were constructed within the ABAQUS ® environment (ABAQUS 6.17, Dassault Systèmes. RI, USA) following Fig. 2 and the described dimensions (Section 2.1). The scarf angle (  ) was varied from 45° to 3.43° in seven non-equally spaced increments (45°,30°,20°,15°,10°, and 3.43°), a model per each angle  was created. Although three-dimensional, the geometry shown in 2.1 was modelled as an axisymmetric case since this solution requires fewer computational resources. Furthermore, the geometries tested experimentally (Section 2.3) were modelled following the approach described below to validate the numerical methodology. Although all the simulation parameters are similar between both TSJ and TLJ geometries, the procedure is described mainly for the TSJ. The numerical models followed two paths. The first one employed cohesive elements in the adhesive layer and the maximum load ( P m ) was determined from these models, similar as done in reference (de Sousa et al., 2017). The second one consisted of continuum elements in the whole geometry and was used to calculate stresses in the adhesive layer. In all cases, the adherends were meshed using continuum axisymmetric elements (CAX3 and CAX4R). The combination of 3-node and 4-node elements was necessary because of the wedge shape of the adherends. The element size varied through the adherends, leaving the smaller elements in the vicinities of the adhesive layer where higher stress concentrations are expected. The adhesive layer was meshed with one layer of 4 node cohesive axisymmetric elements with a triangular law (COHAX4) on those models corresponding to the first stage (Fig. 3 a), whilst 10 layers of 4-node continuum axisymmetric elements (CAX4R) discretised the adhesive layer on the second stage. The element size of the first stage was around 0.2 mm x 0.2 mm, whilst 0.02 mm x 0.02 mm was used for the second one (Fig. 3 a). Furthermore, the sweep direction of the cohesive elements corresponds to the adhesive layer through-thickness direction, as reported by Barbosa et al. (2018b). The adherends were considered as bilinear elastic-plastic in the first stage and linear elastic in the second. On the other hand, the joint was subjected to traction, which was modelled by constraining one of the tube ’ s ends in all directions ( U R = U  = U Z =0) while applying a displacement of 0.4 mm in the axial direction ( U Z ), as shown in Fig. 4. The models were run using a large-deformation solution algorithm within ABAQUS ® .

Fig. 3 – Details of the meshes in the bond-line of the TSJs: a) CZM models, b) stress analysis models.