Coupling stress fields and vacancy diffusion in phase-field models of voids as pure vacancy phase

High vacancy concentrations in crystals may lead to formation and growth of voids, which is connected to swelling under irradiation and degradation of material properties. Recent experimental work suggests that vacancy condensation may also be involved in nucleation and evolution of porosity in early stages of ductile fracture. Mostly in the realm of irradiation effects, void formation and growth has been simulated with phase-field methods, where voids are treated as pure vacancy phases. Since vacancies induce an eigenstrain field, it is well-known that the evolution of vacancy concentrations is coupled to the elastic stress field. However, the few existing elastically coupled diffuse interface models of void growth seem to face a conceptual problem in the diffuse interface; in the center of which they predict the highest eigenstrains, which results in unrealistically high, fluctuating stresses. In the current work, we present a new model for coupling elastically driven vacancy diffusion with a diffuse interface model of void surfaces, which overcomes the named short-comings and closely reproduces the sharp interface solution. This is achieved by making the eigenstrain a function of the non-conserved order parameter used to distinguish the crystal and void phase. The model is verified for two-dimensional example problems by comparison to the analytical solution of the according sharp interface model. Eventually, the model is used to show the impact of elasto-diffusional coupling on void growth in mechanically loaded systems. We analyze the model with regard to the bi-stable energy landscape and discuss limitations and future prospects of the approach.