PSI - Issue 81

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

224

was not possible to clearly distinguish elastic and plastic zones, therefore, since these diagrams have irregularities, it was decided to determine the characteristic points (initial linear zone and maximum load) and conduct analytical calculations for these points in order to obtain average values. The determined key points of load and displacement for each specimen are presented in Table 2. The next step was to calculate the value of the shear modulus according to Eq. (1). As a result, the average value of the adhesive shear modulus was determined. However, to define the shear stiffness of the adhesive for use in the material properties of CZM, Eq. (2) must be applied. Considering that the average thickness t of the adhesive is 0.2 mm, then 21MPa/mm s t K K = = . P t G F l   = =   (1)

G

K K

= =

(2)

s

t

t

Table 2. Shear modulus calculation. Points Load P (kN)

Displacement l  (mm)

Shear modulus G (MPa)

1 2 3 4 5

3.95

0.57 0.34 0.86 0.44 0.88

4.6 4.5 3.2 5.2 3.6 4.2

2.3

4.11

3.4

4.78

Average

In addition to the shear stiffness, it is necessary to determine the normal stiffness. For this purpose, Eq. (3) was applied. The Poisson's ratio for adhesives is generally considered to be within the range of 0.3 to 0.4. Therefore, the normal stiffness was calculated for three values of Poisson's ratio. As a result of this calculation, three values of the normal stiffness were obtained and are presented in Table 3. In subsequent calculations, the influence of this parameter was examined, and the value that provided the most representative results was selected for all further calculations. ( ) ( ) 2 1 2 1 n t G K K t   + = = + (3)

Table 3. Normal stiffness calculation.

Poisson's ratio 

Normal stiffness

n K ( MPa/mm )

0.3

54.6 56.7 58.8

0.35

0.4

Since experimental studies were conducted to determine the shear strength, and the load on the specimens corresponded to the conditions of pure shear, only the maximum shear stress was specified for the numerical model, which is 14.04MPa  = . The fracture energy used in the initial calculations was selected approximately and is equal to 5N/mm C G = . 3.2. Finite element modeling and parametric analysis After determining the initial material parameters for the adhesive layer, numerical modeling was performed using the finite element method. The geometric parameters of the computational model correspond to the overall dimensions of the specimens used in the experimental studies. Since the load on the specimen was applied under pure shear conditions, a 2D model in a plane strain state was developed to simplify calculations. At the verification stage of the calculation model, a test numerical simulation was carried out to confirm the correctness of the problem formulation. As a result, a load-displacement diagram was obtained and compared with the experimental diagram (Fig. 4.a). As can be seen from the comparison, the numerical results show satisfactory agreement with experimental data, which confirms the reliability and physical correctness of the calculation model. The next stage of the study involved analyzing the influence of each parameter of the CZM and performing their subsequent iterative manual calibration. The objective was to achieve the best possible agreement between the numerical and experimental results by specifically fitting the peak load and the post-peak softening behavior.