PSI - Issue 77

C.F.F. Gomes et al. / Procedia Structural Integrity 77 (2026) 95–102 Gomes et al. / Structural Integrity Procedia 00 (2026) 000–000

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Three adhesives with different mechanical behaviors (brittle to ductile) were selected: Araldite ® AV138 (brittle epoxy), Araldite ® 2015 (moderate ductility epoxy), and Sikaforce ® 7752 (ductile polyurethane). The mechanical and fracture properties of the adhesives were obtained through experimental tests. Bulk specimens with the dimensions mentioned in ISO 527-2 were produced by compression molding and tested in a universal testing machine to obtain the tensile properties. Thick Adherend Shear Test (TAST) followed the ISO 11003-2 standard to estimate the shear properties. Double-Cantilever Beam (DCB) and End-Notched Failure (ENF) tests were performed to obtain the G IC (critical energy release rate in mode I) and G IIC (critical energy release rate at mode II), respectively. 2.3. Numerical modelling conditions The 6.21 version of the Abaqus ® software was used in a static/implicit analysis with consideration of geometrical non linearities. A triangular mixed mode cohesive law was chosen to describe the adhesive layer. The parameters are the tensile and shear stiffness ( K n and K s ), cohesive tractions in tension and shear ( t n 0 and t s 0 ), and G IC and G IIC . More details of this model are given in reference (Rocha and Campilho 2018). Axisymmetric 2D elements were chosen for the model construction. Deformable four-node axisymmetric elements (CAX4) were selected for the adherends, and axisymmetric cohesive elements (COHAX4) were used for the adhesive layer. The metallic adherends were considered isotropic materials. The CFRP adherends were modelled as elastic orthotropic. The adhesive was modelled by CZM, with a single line of cohesive elements. A mesh size of 0.2×0.2 mm² was applied at the overlap edges, while a size grading functionality was used in the rest of the part to optimize simulation time (Fig. 2 shows the mesh details for L O =10 mm). The joints were totally longitudinally at one edge, while at the opposite edge, a tensile displacement were applied.

Fig. 2. Mesh and boundary conditions for a numerical model with L O =10 mm.

3. Results 3.1. CZM validation

The validity of the CZM approach was assessed by comparing numerical predictions with experimental data. The adhesives used for validation correspond to those detailed in Section 2.2. The selected tubular joint configuration featured L O between 20 and 40 mm, d SI =20 mm, and t A =0.2 mm. The adherends were manufactured through turning with a carbide insert end mill, followed by drilling end holes using a carbide drill. Surface preparation included grit blasting with corundum sand to enhance adhesion, followed by degreasing. The adhesive was applied to both bonding surfaces. After curing, excess adhesive was removed by milling. Mechanical testing was conducted using a Shimadzu Autograph AG-X universal testing machine with a 100 kN load cell, under ambient conditions and a loading rate of 1 mm/min. Five specimens were tested for each joint configuration. The CZM numerical simulations adhered to the methodology outlined in Section 2.3. The maximum load ( P m ), including average values and deviations, was plotted against L O in Fig.3, and compared to the numerical predictions. Both experimental and numerical analyses revealed cohesive failure within the adhesive layer. The numerical approach yielded highly accurate predictions for joints with the AV138 and 2015. Deviations between experimental and numerical P m values for the AV138 were 2.4% for L O =20 mm and 4.7% for L O =40 mm. For the 2015, discrepancies were 6.1% and 2.9% for L O =20 mm and L O =40 mm, respectively. However, the tubular joints bonded with the 7752 exhibited larger deviations, with numerical predictions