Phase field modeling of void nucleation and growth in irradiated metals

Motivated by the need to develop a spatially resolved theory of irradiation-induced microstructure evolution in metals, we present a phase field model for void formation in metals with vacancy concentrations exceeding the thermal equilibrium values. This model, which is phenomenological in nature, is cast in the form of coupled Cahn-Hilliard and Allen-Cahn type equations governing the dynamics of the vacancy concentration field and the void microstructure in the matrix, respectively. The model allows for a unified treatment of void nucleation and growth under the condition of random generation of vacancies, which is similar to vacancy generation by collision cascade in irradiated materials. The basic features of the model are illustrated using two-dimensional solutions for the cases of void growth and shrinkage in supersaturated and undersaturated vacancy fields, void-void interactions, as well as the spontaneous nucleation and growth of a large population of voids.