Phase field modeling of crack propagation

Abstract

Fracture is a fundamental mechanism of materials failure. Propagating cracks can exhibit a rich dynamical behavior controlled by a subtle interplay between microscopic failure processes in the crack tip region and macroscopic elasticity. We review recent approaches to understand crack dynamics using the phase field method. This method, developed originally for phase transformations, has the well-known advantage of avoiding explicit front tracking by making material interfaces spatially diffuse. In a fracture context, this method is able to capture both the short-scale physics of failure and macroscopic linear elasticity within a self-consistent set of equations that can be simulated on experimentally relevant length and time scales. We discuss the relevance of different models, which stem from continuum field descriptions of brittle materials and crystals, to address questions concerning crack path selection and branching instabilities, as well as models that are based on mesoscale concepts for crack tip scale selection. Open questions which may be addressed using phase field models of fracture are summarized.

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• A unified first order hyperbolic model for nonlinear dynamic rupture processes in diffuse fracture zones
• Fractographic aspects of crack branching instability using a phase field model
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• A Hybrid Phase Field Model for Fracture Induced by Lithium Diffusion in Electrode Particles of Li-ion Batteries
• Universality and stability phase-diagram of two-dimensional brittle fracture
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• Fracture as a pattern formation process
• Space-time formulation, discretization, and computational performance studies for phase-field fracture optimal control problems
• Modeling of grain boundary dynamics using amplitude equations
• Diffusion-Dependent Pattern Formation on Crystal Surfaces
• Study of three-dimensional crack fronts under plane stress using a phase field model
• Predicting high rate granular transition and fragment statistics at the onset of granular flow for brittle ceramics
• Elastic and plastic effects on heterogeneous nucleation and nanowire formation