An effective modeling approach based on the ALE and M-integral for simulating crack propagation under thermo-mechanical loadings

Abstract Traditional engineering materials suffer from the presence of internal cracks, originating either during production processes or usage, that tend to grow under the action of thermo-mechanical loading, thus compromising the overall integrity. A proper evaluation of fracture behavior is then essential to limit dramatic failures that may lead to unsafe conditions. The present work proposes an effective modeling strategy for simulating crack propagation mechanisms in linear elastic continuum media subjected to mechanical and thermal loadings. The model involves a classic FE framework enhanced by Moving Mesh (MM) techniques and Interaction Integral Method (M-integral). MM serves as a powerful tool for reproducing geometry evolution caused by crack advance. In particular, the MM uses the Arbitrary Lagrangian-Eulerian (ALE) formulation, which is effective to handle random cracks. In the proposed framework, the ALE moves the computational nodes around the crack front, starting from a referential coordinate system according to classic fracture criteria, which define crack advance conditions and propagation direction. Reliable movements depend upon proper values of Stress Intensity Factors (SIFs) at crack fronts. To this end, the method adopts the M-integral for extracting mixed-mode SIFs. Since the crack front moves during the propagation, the M-integral is expressed by using the ALE formulation, thus evaluating fracture variables on deformed elements without losing accuracy. The use of proper rezoning techniques ensures the consistency of the mesh motion, limiting mesh distortions and remeshing events. The reliability of the proposed model is assessed through comparisons with existing numerical strategies.