PSI - Issue 81

Ivan Pidgurskyi et al. / Procedia Structural Integrity 81 (2026) 47–53

50

(b) provision of an additional minimum distance between the projections of the “tubes” to form a transition zone for merging the local meshes of each surface crack with the global mesh of the model (Fig. 3, b). This distance primarily depends on the cross- sectional dimensions of the “tubes” surrounding the contours of adjacent surface cracks and on their configuration. It should be noted that the transverse cross- section of the “tube” enveloping the crack front can be minimized by reducing the number of contours forming the “tube” (while maintaining result accuracy) and by decreasing the size of the minimum finite element. Considering the above limitations in finite element mesh construction, models of bodies with surface cracks were developed using the proposed methodology. The distribution of stress intensity factors (SIFs) along the fronts of interacting surface cracks was obtained using the finite element method (FEM). The research methodology is described in studies Pidgurskyi, 2018 and Pidgurskyi et al., 2022. The specialized software package ANSYS Workbench (ANSYS, Inc., 2022) was employed. Semi-elliptical surface cracks in a plate of finite dimensions subjected to tensile stresses were modeled. Three-dimensional models of the specimens were created, comprising a global finite element mesh and a local mesh in the crack region. Tetrahedral finite elements were used. The element size of the global mesh was 2.75 mm, while that of the local mesh was 0.1 mm. Specimens with thicknesses of t = 20 mm and t = 30 mm and widths of 80 mm, 120 mm, and 160 mm were modeled. The material was low-alloy steel 09 Г2С with a yield strength σ y = 380 MPa and an ultimate tensile strength σᵤ = 530 MPa, subjected to an applied nominal stress σ n = 200 MPa. The Poisson’s ratio under elastic deformation was ν = 0.3. As a result of the computations, SIF values were obtained along the contour of the surface crack for φ = 0 … 2π. The determination of the SIF along the contour of two identical coplanar cracks was performed for different relative configurations of coplanar cracks (Fig. 4). In the first case, the mutual interaction of two cracks with a constant crack depth a and a variable surface length 2 c ᵢ was investigated (Fig. 4, a). In the second case, the surface crack length 2 c remained constant, while the crack depth a ᵢ varied (Fig. 4, b). In addition, the specimen thickness t and the distance between the innermost points of the two interacting cracks t s were considered as variable parameters. ).

Fig. 4. Modeling of identical semi-elliptical surface cracks in a plate of finite dimensions.

3. Research Results When an object is influenced by a significant number of factors – namely, a / c (the crack aspect ratio of identical cracks), a / t (the crack depth-to-thickness ratio), and t s / c (the spacing-to-surface-length ratio of adjacent cracks) – it is important to obtain the combined effect of these factors within a statistical mathematical model. Such a model makes it possible to evaluate the interrelationships among the above-mentioned factors and to obtain quantitative estimates of the influence of each factor on the processes under investigation. In this regard, a block diagram of simulation modeling of the mutual interaction of two identical coplanar surface cracks approaching each other is proposed, indicating the input and output factors (Fig. 5).