PSI - Issue 72

C.F.F. Gomes et al. / Procedia Structural Integrity 72 (2025) 34–42

37

Table 3. Properties of DIN 55Si7 steel adherend (Valente et al. 2019).

E [GPa]

σ y [MPa]

σ f [MPa]

ε f [%]

ρ [g/cm

3 ]



210

1078

1600

6

0.3

7.8

Three different adhesives were selected, including both ductile and brittle types, enabling a broader exploration of joint behavior. The chosen adhesives were Araldite ® AV138 (epoxy-based and brittle), Araldite ® 2015 (epoxy based with moderate ductility), and Sikaforce ® 7752 (polyurethane-based, ductile but less strong). These adhesives underwent various experimental tests, resulting in the data presented in Table 4. Table 4. Mechanical and fracture properties of the selected adhesives (Neto et al. 2012, Campilho et al. 2013, Faneco et al. 2017). Property Araldite ® AV138 Araldite ® 2015 Sikaforce ® 7752 Young’s modulus, E [GPa] 4.89 ± 0.81 1.85 ± 0.21 493.81 ± 89.6 Poisson’s ratio, ν b 0.35 a 0.33 a 0.33 a Tensile yield stress, σ y [MPa] 36.49 ± 2.47 12.63 ± 0.61 3.24 ± 0.5 Tensile strength, σ f [MPa] 39.45 ± 3.18 21.63 ± 1.61 11.49 ± 0.3 Tensile failure strain, ε f [%] 1.21 ± 0.10 4.77 ± 0.15 19.18 ± 1.4 Shear modulus, G [GPa] 1.56 ± 0.01 0.56 ± 0.21 187.75 ± 16.4 Shear yield stress, τ y [MPa] 25.1 ± 0.33 14.60 ± 1.30 5.16 ± 1.1 Shear strength, τ f [MPa] 30.2 ± 0.40 17.90 ± 1.80 10.17 ± 0.6 Shear failure strain, γ f [%] 7.8 ± 0.7 43.90 ± 3.40 54.82 ± 6.4 Toughness in tension, G IC [N/mm] 0.20 b 0.43 ± 0.02 2.36 ± 0.2 Toughness in shear, G IIC [N/mm] 0.38 b 4.70 ± 0.34 5.41 ± 0.5 a Manufacturer’s data. b Estimated in reference (Neto et al. 2012). The chosen software for the static numerical simulations was Abaqus ® 6.21 (Dassault Systèmes) considering a quadratic stress criterion for damage initiation and a linear energetic criterion to assess crack growth in CZM modeling. The triangular cohesive law is widely used due to its simplicity and accuracy, involving parameters such as the tensile and shear stiffness ( K n and K s ), cohesive tractions in tension and shear ( t n 0 and t s 0 ), and fracture toughness in tension and shear ( G n c and G s c ) (Rocha and Campilho 2018). The numerical analysis uses deformable four-node axisymmetric elements (CAX4 in Abaqus ® ) and axisymmetric cohesive elements (COHAX4R in Abaqus ® ) for the adhesive layer. The model geometry was discretized into finite elements, with refined meshing in high-stress areas. The CZM meshes involved a minimum element size of 0.2×0.2 mm 2 , applied at the overlap edges of the adhesive, with size grading effects applied to reduce the computational load. 2.3. Model pre-processing

Fig. 3. Mesh details for the CZM model for L O =10 mm. Figure 3 shows the mesh details for L O =10 mm and boundary conditions. The models for stress analysis were more refined, to accurately capture peak stresses, considering a ratio 0.1× ratio in the edge size of the elements. Results were visualized, with P - δ curves being created by summing fixed-end reactions and plotting against displacement values at the opposite edge of the joint, providing comprehensive data on the adhesive joint’s behavior to be collected and analyzed in the Results section.