Coupled phase field finite element model for crack propagation in elastic polycrystalline microstructures

This paper is aimed at the development of a coupled finite element-phase field modeling framework for simulating fracture processes in anisotropic elastic materials under finite deformation conditions with tension-compression asymmetry of crack phase. A novel Helmholtz free energy density is proposed in terms of a phase field order parameter dependent elastic Green-Lagrange strain tensor. It accommodates anisotropy of the material and unilateral conditions of material damage. The paper also addresses numerical instabilities, which adversely affect computational fracture simulations. Solutions based on viscous stabilization are suggested to effectively overcome the convergence issues of nonlinear FE solvers. Numerical examples are carried out to highlight different aspects of the developed framework. Numerical results with the proposed model are successfully compared with experimental results for validation. The model admits the unilateral conditions of the crack phase and predicts the correct crack kinking in mode II fracture. Special attention is drawn to numerical details affecting the efficiency and accuracy of the phase field models.