PSI - Issue 47

J.B.S. Nóbrega et al. / Procedia Structural Integrity 47 (2023) 408–416 Nóbrega et al./ Structural Integrity Procedia 00 (2023) 000–000

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The connector elements were used to connect the motion and the relative position between the rollers and the fulcrum. The interaction between the rollers and the adhesive joint was established through contact definitions. In this case, the left-side roller was able to contact the lower face of the flexible adherend. The right-side roller contacted the lower face of the rigid adherend, as shown in Figure 3. The contact definitions were hard contact in the normal direction and frictionless in the tangent direction. An explicit contact definition was employed because these models were solved using the Abaqus Explicit solver. In addition, the mass of each roller was calculated and added to their respective centres. Regarding the boundary conditions, the fulcrum of the testing jig was constrained in both horizontal and vertical directions while the out-of-plane rotation was left free (Figure 3); as a result, the testing jig pivots around the said point, as occurs in the experimental case. The model was displacement driven, so a displacement  of 110 mm in the vertical direction was imposed (Figure 3). The chosen displacement is not enough to fully separate both adherends but is enough to obtain the 25 mm + 75 mm required by the standard (ASTM, 2004). The geometry was meshed mostly with four-node elements; however, the rigid adherend had a combination of four-node (CPE4R) and three-node (CPE3) elements, allowing to have a structured mesh in the interface while a relatively free mesh was used on the opposite face, as shown in Figure 4. This allowed to reduce computational costs and speed up the solution. The bond line was meshed with 1933 four-node cohesive elements (COH2D4), between both substrates sum 38299 CPE4R and 633 CPE3 elements while the connectors sum 798 R2D2 elements. Thus, the model has a total of 43204 nodes and 41663 elements. The element size in the bond line was 0.2 mm x 0.1 mm, the former in the through-thickness direction. The element size in the flexible adherend was 0.1 mm x 0.1 mm. The rigid substrate had variable element sizes from 0.1 mm to 1 mm. The small element size was necessary for the contact definitions, otherwise, the model did not converge, as observed during several tests done by the authors.

Figure 4. Close up of the mesh in the vicinities of the left-side roller.

The models were run using the Abaqus Explicit solver and material and geometrical non-linearities were considered. 3. Results 3.1. Experimental results In agreement with ASTM D 3167 (ASTM, 2004), it is required to extract the average peel force during the test ( P avg ), the maximum peel force ( P max ), and the minimum peel force ( P min ); also, the failure modes (i.e., cohesive,