A thermodynamically consistent theoretical framework for the thermomechanically coupled phase-field fracture model and its application to thermal shock in ceramics

Abstract

This work presents a thermodynamically consistent framework for a thermomechanically coupled phase-field fracture model to simulate crack evolution in ceramics subjected to thermal shock. The model systematically incorporates temperature-dependent material properties and a temperature-dependent damage initiation threshold derived from a force-heat equivalence energy density principle. This threshold effectively suppresses spurious damage accumulation during elastic loading, a common limitation in standard phase-field models. The fully coupled governing equations are derived variationally and implemented in a finite element framework using a staggered scheme in finite element software. Simulations of thermal shock in alumina and zirconia demonstrate that temperature-dependent properties critically govern crack initiation, propagation paths, and network topology. The model captures complex phenomena including stress shielding, competitive crack growth, and transformation-induced crack deflection, showing good quantitative agreement with experimental observations.