A phase field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects
Abstract Phase field models have been a topic of much research in recent years. Results have shown that these models are able to produce complex crack patterns in both two and three dimensions. A number of extensions from brittle to ductile materials have been proposed and results are promising. To date, however, these extensions have not accurately represented strains after crack initiation or included important aspects of ductile fracture such as stress triaxiality. This work introduces a number of contributions to further develop phase field models for fracture in ductile materials. These contributions include: a cubic degradation function that provides a stress strain response prior to crack initiation that more closely approximates linear elastic behavior, a derivation of the governing equations in terms of a general energy potential from balance laws that describe the kinematics of both the body and phase field, introduction of a yield surface degradation function that provides a mechanism for plastic softening and corrects the non physical elastic deformations after crack initiation, a proposed mechanism for including a measure of stress triaxiality as a driving force for crack initiation and propagation, and a correction to an error in the configuration update of an elastoplastic return mapping algorithm for J 2 flow theory. We also present a heuristic time stepping scheme that facilitates computations that require a relatively long load time prior to crack initiation. A number of numerical results will be presented that demonstrate the effects of these contributions.