PSI - Issue 81

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ScienceDirect

Procedia Structural Integrity 81 (2026) 244–250

VIII International Conference “In - service Damage of Materials: Diagnostics and Prediction“ (DMDP 2025) Boundary element modeling of thermo-fatigue processes under cyclic quasi-static thermal loading Oleh Yasniy a , Iaroslav Pasternak b , Dmytro Tymoshchuk a, *, Iryna Didych a , Olha Malyshevska c a Ternopil Ivan Puluj National Technical University, Ruska Str 56, Ternopil, Ukraine b Lesya Ukrainka Volyn National University, Voli Avenue 13, Lutsk, Ukraine c Ivano-Frankivsk National Medical University, Galytska Str. 2, Ivano-Frankivsk, Ukraine Abstract This work applies boundary element modeling to study thermo-fatigue crack initiation and growth under cyclic quasi-static thermal loading in plane thermoelastic problems. An accurate boundary element implementation with analytical integration on quadratic elements is used, with special treatment of singular stress fields near cracks. The model considers a plate subjected to cyclic thermal loading with randomly distributed initial micro-cracks representing stochastic defect initiation. Crack nucleation is modeled probabilistically at grid nodes when local stress exceeds a critical threshold that decreases over time due to material degradation. Fatigue crack growth in existing cracks is governed by the Paris law, with propagation direction determined by the maximum hoop stress criterion. The framework combines probabilistic nucleation and deterministic crack growth into a unified multiscale scheme for thermo-fatigue simulation. Numerical experiments analyze the influence of degradation parameters, thermal loading modes, and Paris law parameters on crack evolution. Results show that crack networks are highly sensitive to both mechanical and probabilistic factors, with practical relevance for assessing thermo-fatigue in components such as mill rolls.

© 2026 The Authors. Copy from the contract: Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of DMDP 2025 organizers Keywords: boundary elements; thermal fatigue; fatigue crack; Paris law; probabilistic approach

1. Introduction One of the fundamental factors that significantly affects the structural integrity and strength of structural elements is the thermal fatigue of materials. It remains an important and still insufficiently studied issue, characteristic of many branches of engineering such as aircraft engineering (Mansoor et al., 2007; Rémy et al., 2007) , electronics (Liu & Plumbridge, 2007; Ubachs et al., 2007), automotive engineering (Beck et al., 2007; Firouzdor et al, 2007), thermal and nuclear power engineering (Ahmadi & Zenner, 2005; Yasniy et al., 2017; Kamaya & Taheri, 2008; Maruschak et al. 2014; Malesys et al., 2009; Taheri, 2007; Tohgo et al., 2009), metallurgy, and others. Thermal fatigue is accompanied by surface cracking of structural elements, with the formation of a network of surface cracks being typical even under relatively small temperature fluctuations. It is known that thermo-fatigue cracks stop growing once they reach a certain depth (and corresponding length) due to a decrease in temperature and, consequently, thermal stresses. This phenomenon is observed during the operation of power plant structural components (Taheri, 2007) and has been experimentally confirmed (Malliot et al., 2005). However, if additional tensile mechanical stresses act in the immediate vicinity of

* Corresponding author. Tel.: +380352519700. E-mail address: dmytro.tymoshchuk@gmail.com

2452-3216 © 2026 The Authors. Copy from the contract: Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of DMDP 2025 organizers 10.1016/j.prostr.2026.03.042