Boundary element modeling of thermo-fatigue processes under cyclic quasi-static thermal loading

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.