PSI - Issue 81

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

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• the stage of dominant growth of a single crack under further cyclic loading (Stage 4).

The rules for combining adjacent semi-elliptical surface cracks (Wen et al., 2016; Lu and Li, 2017) (Fig. 1) into computational models differ among existing standards. In particular, when assessing the durability of structural components, ASME Code Section XI, BS 7910, and FITNET consider a calculation scheme in which each adjacent crack propagates independently up to the moment of their coalescence (Fig. 1, a). Subsequently, neglecting the crack coalescence period, the cracks are replaced by a single surface crack with the same depth a as the adjacent cracks and a total surface length of 2c 1 + 2c 2 . Other standards (API 579-1, GB/T 19624) (Fig. 1, b) adopt a more conservative approach.

a) standards ASME; BS 7910; FITNET

b) other standards

Fig. 1. Computational schemes for the coalescence of coplanar surface cracks.

The assessment of crack growth in structures is generally associated with the determination of the stress intensity factor (SIF), which characterizes the stress-strain state (SSS) in the vicinity of a crack tip. The calculation of the SIF in real structures is a complex problem due to geometry and boundary conditions, especially for three-dimensional bodies (Brighenti and Carpinteri, 2013). The problem of determining the SIF and assessing fracture processes becomes significantly more complicated under mechanical interaction (Stage 2) and coalescence (Stage 3) of two or more cracks under cyclic loading of structures (Pidgurskyi et al., 2022; Kikuchi, M., 2016). This is explained by the fact that, during interaction and coalescence, the internal segments of the contours of two cracks are subjected to a substantial influence, which leads to significant changes in the SIF. These changes depend on crack geometry, their relative positions, structural features of the specimens, and loading conditions. The above mentioned factors affecting the SIF values are usually taken into account in an integrated manner by means of additional influence factors (Patel, et al., 2010; Pidgurskyi et al., 2022). However, the results obtained predominantly by the finite element method (FEM) (Kikuchi, M., 2016; Azuma and Li, 2017) are insufficient to draw generalized conclusions in this field. This is due to the fact that errors in defining the crack-front configuration have a significant effect on the accuracy of SIF determination for cracks with a curved front and, consequently, on the assessment of the fatigue life of structural components at the crack propagation stage. This also explains the conservative nature of the approaches adopted in the above-mentioned standards for evaluating the structural integrity of components under the interaction of multiple cracks. In this regard, the objective of the present study is to develop a methodology and to evaluate the SIF using FEM when modeling the growth process of identical coplanar semi-elliptical surface cracks that have not yet coalesced in structural components and, on this basis, to develop statistical models. 2. Research Methodology The solution of solid mechanics problems using the finite element method in the presence of a surface crack in a solid body (Ariatedja and Mamat, 2011) involves the following main stages (Fig. 2): • first, a generalized problem formulation (type of analysis, general model definition, applied loads, etc.); • second, the creation of geometry model suitable for FEM analysis; • third, the generation of a finite element mesh for the constructed geometry; • fourth, the creation of a surface crack of a prescribed configuration and its integration into the model at the mesh level; • fifth, the specification of boundary conditions and loads for the mode with a crack; • sixth, the numerical solution of the problem; • seventh, the analysis of the SIF along the front of the semi-elliptical surface crack and visualization of the results.