PSI - Issue 33

R.F.N. Brito et al. / Procedia Structural Integrity 33 (2021) 665–672 Brito et al. / Structural Integrity Procedia 00 (2019) 000–000

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2.4. Obtaining P m and stress distributions The reaction force at the fixed end of the joint was calculated throughout the simulations. Being the force reported per node, the total reaction force, at the given increment, was the sum of the horizontal component of the force ( R x ). Once the simulation was completed, numerical P m was considered as the maximum reaction force attained. From the models fully created with continuum elements, stresses, strains, and damage variables were obtained at the adhesive layer’s mid-thickness. Nevertheless, these variables were normalized with respect to L O to allow comparison; on the other hand, stresses are normalized against the mean shear stress (  avg ) in the joint (da Silva et al., 2009). 3. Results and Discussion 3.1. Joint strength, P m From the experimental testing, it can be observed that P m is proportional to L O with a linear relationship, which was expected because the bonded areas increased, as shown in Figure 2. The variability amongst the experimental data was low (range 3.2% to 5.2%); however, the joint configurations with the two central L O were the most scattered (4.7% and 5.2%, respectively). The joint with L O =12.5 mm attained a P m of 2406 N, being the weakest configuration. Conversely, the joint with L O =50 mm reached a P m of 11500 N, around 3.5 times the P m of the weakest joint. The numerically predicted P m is reported in Figure 2, aiming to ease comparison with the experimental data; overall, a good agreement with the experimental data was obtained. The higher deviation with respect to the experimental data (16.7 %) was observed in the joint with the smallest L O , overpredicting P m . The deviation reduced as L O increased (6.7% and 0.0%; L O =25.0 and 37.5 mm, respectively); however, for the larger L O it underpredicted P m (-0.6%). Although there is a good agreement between experimental and numerical values for these joint configurations, the differences can be attributed to the yielding of the adhesive layer, which is more present in larger L O than in smaller ones. Furthermore, the triangular CZM law used does not accurately capture this behavior, which is better captured by trapezoidal CZM laws (de Sousa et al., 2017); despite of this, research has indicated that the use of triangular CZM laws provide satisfactory results without the complexity (Campilho et al., 2013).

Figure 2. Numerical and experimental relationships between P m and L O .