PSI - Issue 81

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

225

Fig. 4. (a) Test calculation; (b) influence of normal stiffness.

First, the effect of normal stiffness was investigated. It was expected that this parameter would not have a significant impact on the results, since the model’s boundary conditions ensured pure shear loading. This parameter varied according to the values calculated depending on Poisson`s ratio. The results confirmed the absence of the influence of this parameter, which can be seen in the Fig. 4.b. Thus, for further calculations, the previously determined value of normal stiffness 58.8MPa/mm n K = was adopted. At the next stage, the influence of the maximum stress value was investigated. In addition to the previously specified shear strength value, additional calculations were performed for the minimum min 12.74MPa  = and maximum max 16.64MPa  = values obtained from experimental data. The analysis of the obtained results confirms that it is the ultimate stress that determines the moment of the initiation of the adhesive joint failure, as shown in Fig. 5.a.

Fig. 5. (a) Influence of maximum stress; (b) influence of fracture energy.

Next, the influence of fracture energy was analyzed. The base value of the fracture energy was determined as the area under the stress-displacement curve of the cohesive zone. Considering the almost linear material's behaviour and brittle fracture upon reaching the tensile strength, the calculated value of the fracture energy was 5.97 N/mm. Subsequently, calculations were performed for values equal to 20% and 50% of the base value. The analysis of the obtained results indicates that the fracture energy determines the rate of degradation of the adhesive layer after reaching the strength limit. In particular, an increase in this parameter results in a smoother descending branch of the load displacement curve, which corresponds to a gradual loss of joint strength (Fig. 5.b). Conversely, when the fracture energy decreases, a more abrupt failure of the adhesive joint is observed. At the same time, a certain critical energy value of 4.78 N/mm was identified, below which a further decrease does not lead to changes in the failure behaviour. Based on the conducted studies, a calibrated CZM of the adhesive joint was developed, as presented in Table 4.

Table 4. Calibrated CZM parameters.

MPa mm

MPa mm

MPa mm

N mm

n K (

)

s K (

)

t K (

)

C G (

)

 ( MPa )

58.8

21

21

14.04

5.97

3.3. Cohesive contact modeling and comparative analysis The main goal of this stage of the study was to develop an alternative numerical model of adhesive joint using cohesive contact, which reproduces similar fracture mechanics but is based on a different concept of surface interaction. An important feature of this approach is that cohesive contact can be correctly implemented only in a 3D formulation. After constructing the numerical model and performing calculations using the previously defined parameters of the adhesive layer material model, a load-displacement