PSI - Issue 81

Nazar Loboda et al. / Procedia Structural Integrity 81 (2026) 221–227

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Fig. 2. Tested specimen geometry.

Table 1. Test results

Specimen Maximum load P (kN)

Shear strength  (MPa)

1 2 3 4 5

3.951 4.182 4.111 4.782 5.262

13.66 12.99 12.76 14.12 16.64 14.04

Average

Based on the results of a series of tests, load diagrams in the force-displacement coordinates were obtained for each specimen. Based on the recorded maximum forces, the shear strength value was determined, which was calculated as the ratio of the maximum force to the bonding area. The results of the calculations are presented in Table 1. For the tested specimens, the average shear strength was 14.04MPa  = . 3. Numerical Simulation 3.1. Cohesive zone model description and parameter identification For numerical analysis, the cohesive zone model (CZM) was employed with a bilinear traction-separation law, which is suitable for simulating the brittle fracture behavior observed in the adhesive layer (Campilho et al. 2013). This law defines the mechanical response through linear elastic loading followed by linear softening after damage onset. Damage initiation was governed by the Maximum Nominal Stress criterion, which assumes that failure begins when the stress reaches the critical strength value. For damage evolution, an energy-based linear softening law was adopted, defined by the critical fracture energy equal to the area under the traction-separation curve. This formulation allows for accurate reproduction of the initiation and propagation of adhesive failure (Stuparu et al. 2016, Campilho et al. 2013, Fakoor et al. 2025, Morais 2025). Thus, in order to use this model, it is necessary to determine the following parameters:

• Normal stiffness • Shear stiffnesses • Fracture energy • Maximum stress

Fig. 3. Load-displacement diagrams.

After conducting experimental studies, load-displacement diagrams were obtained for five specimens. However, only three were chosen for further analysis, as they exhibited the most linear behavior (Fig. 3). Due to the viscoelastic nature of the adhesive, it