Phase field microelasticity theory and simulation of multiple voids and cracks in single crystals and polycrystals under applied stress

The phase field microelasticity theory of a three-dimensional elastically anisotropic single crystal with multiple voids and cracks is developed. It is extended to the case of elastically isotropic polycrystal. The theory is based on the exact equation for the strain energy of the equivalent continuous elastically homogeneous body presented as a functional of the phase field. This field is the equivalent stress-free strain. It is proved that the equivalent stress-free strain minimizing the strain energy of the elastically homogeneous body fully determines the elastic strain and displacement of the body with voids/cracks. The geometry and evolution of multiple voids and cracks are described by the phase field, which is a solution of the stochastic time-dependent Ginzburg-Landau equation. Other stress-generating defects, such as dislocations and precipitates, are trivially integrated into this theory. The proposed model does not impose a priori constraints on the configuration of multiple voids and cracks or on possible configurations and evolutions of cracks along their propagation paths. Examples of computations of the elastic equilibrium of systems with voids and/or cracks, the evolution of cracks in single crystals and polycrystals, and material toughening due to second-phase obstacles are considered. (C) 2002 American Institute of Physics.