Simulation of multi-field coupled multiple crack interactions based on the fracture phase-field method

Abstract

Crack propagation and multi-crack interaction under multi-field coupling conditions constitute a central problem in material failure research, and conventional fracture mechanics approaches are generally inadequate for capturing such complex behavior. This work develops a phase-field fracture framework for simulating multi-field coupled multi-crack interaction, with particular emphasis on crack growth driven by coupled temperature/concentration and displacement fields. In the theoretical formulation, cracks are represented in a diffuse manner through the phase-field variable, and the degradation of thermal conductivity and diffusivity due to fracture damage is explicitly incorporated. Governing equations are established for thermo-mechanical coupling and for electrochemical concentration-displacement coupling, and the coupled system is solved numerically using an implicit finite element scheme. The model is first validated against mode I crack propagation and three-point bending fracture problems, where the numerical results agree closely with analytical solutions and previously reported data. The framework is then extended to multi-crack interaction scenarios, including parallel crack interaction and discharge processes in lithium electrodes. The results indicate that: (1) as the crack spacing decreases, the initial propagation angle increases and the interaction effect between cracks becomes more pronounced; (2) during glass quenching, thermally induced crack propagation exhibits a hierarchical pattern consistent with experimental observations; (3) during discharge in lithium electrodes, concentration gradients drive crack nucleation and growth, with crack propagation near the notch affected by a shielding effect. The proposed model is capable of effectively capturing multi-crack interaction and propagation behavior under multi-field coupling conditions, thereby offering a theoretical basis and a computational tool for multi-field fracture analysis of engineering structures.