Phase field modeling of fracture and crack growth

Abstract

Predicting crack growth in structural components is a computationally intensive process. Phase field models of crack growth reduce the computational complications associated with singularities, and allow finite element predictions of crack propagation without remeshing. A novel approach to derive governing equations based on a Lagrangian density is proposed and the phase evolution is shown to be governed by a diffusion type equation with a source term. We correlate the phase to the micromechanical response. The model was incorporated in a finite element code and used to predict crack growth phenomena including (1) values of critical stress, (2) crack path, and (3) crack bifurcation. It was shown that the values of the critical stresses can be accurately estimated by the change in the phase field crack tip velocity or by the use of energy contour integral. The phase field crack analysis is compared against LEFM results.