PSI - Issue 81

Oleh Yasniy et al. / Procedia Structural Integrity 81 (2026) 244–250

248

In the second part of the main cycle, the damage values of the microcrack nucleation nuclei were computed using Eq. (1) for the number of cycles obtained during the crack growth step. In each nucleus for which condition (3) was satisfied, a crack with an initial length of 0.2 mm was initiated. The crack surface was oriented along the plane corresponding to the maximum principal stresses. Subsequently, a BEM analysis was performed for the problem with the newly formed geometry of the crack system, and the main cycle was repeated until all nuclei were destroyed or the dimensionality of the problem exceeded the prescribed limit. 3. Numerical results The numerical simulation was carried out to investigate the evolution of thermally induced cracking and the associated stress – intensity characteristics under cyclic thermal loading. The crack system was generated and propagated according to the previously described damage accumulation and growth model, combined with the dual boundary element method for stress and SIF evaluation. Particular attention was paid to the spatial distribution of cracks and the corresponding background field of von Mises equivalent stress at different stages of the fatigue process. Two representative numbers of cycles, N =8 256 and N =23 256, were selected to illustrate the intermediate and more advanced stages of damage development (Fig. 2).

(a)

(b)

Fig. 2. Crack network at N=8 256 (a) and N=23 256 (b) cycles.

At N =8 256 cycles, a relatively sparse network of short cracks is observed. Most cracks remain isolated or weakly interacting, and their lengths are still limited by the early stage of growth. The von Mises stress field exhibits pronounced concentration zones near the crack tips, while large regions of the domain retain comparatively moderate stress levels. Stress redistribution due to the presence of cracks is local, and the overall pattern of stresses still reflects the initial thermal loading configuration. The spacing between neighboring cracks at this stage remains relatively large, indicating limited coalescence and interaction effects. At N =23 256 cycles, the crack configuration becomes significantly more complex and denser. Individual cracks have grown in length, and several zones of interacting cracks can be clearly distinguished. The von Mises stress background shows more heterogeneous and fragmented patterns, with extended regions of stress concentration associated with clusters of cracks. The interaction between nearby cracks intensifies, resulting in noticeable shielding and amplification effects in various parts of the domain. Some cracks exhibit deviations in their growth direction, reflecting the influence of mixed-mode loading conditions and mutual interaction. The overall damage state at this stage corresponds to an advanced phase of thermal fatigue, where the structural integrity is notably degraded. The evolution of the overall (mean) stress intensity factor (Fig.3) under increasing equivalent thermal stress demonstrates a clear increasing trend. As the level of equivalent thermal stress rises, the average SIF for the entire crack system becomes higher, indicating a growing driving force for crack propagation. This behavior is consistent with the increasing severity of the thermal loading and the progressive accumulation of damage. The plot of the overall mean crack length (Fig. 4) shows a monotonic increase with the number of cycles, reflecting the continuous growth of the initiated cracks. At the same time, the overall mean distance between cracks decreases, which is a direct consequence of both crack initiation in new nuclei and the extension of existing cracks. The decrease in the mean distance between cracks highlights the transition from isolated crack behavior to a more collective and interactive cracking regime. As cracks approach each other, their stress fields increasingly overlap, enhancing local stress concentrations and accelerating further growth. This interaction contributes to a positive feedback mechanism, where higher SIF values promote faster crack extension and the formation of new cracks. The numerical results clearly demonstrate that the structural