Influence of bulk free energy density on single void evolution based on the phase-field method

Abstract

Phase-field models are widely adopted to study the void evolution problem, overcoming difficulties and drawbacks of the sharp boundary approach and rate theory. This paper focuses on improving the performance of the phase-field model of which the vacancy concentration is used as the single conserved order parameter. Following recent developments in these phase-field models, the void dynamic, or more precisely the void growth rate which plays a vital role in characterizing the microstructural evolution of irradiated materials, cannot be accurately reproduced. Moreover, the interfacial energy or the void-matrix interface modeled by the Ginzburg-type gradient energy term is usually characterized by an empirical coefficient that is quite difficult to determine. For these reasons, a general relation of the bulk free energy density, the coefficient of the gradient energy term and the interface width is analytically derived from the planar interface case, and then validated by the numerical simulation example of a single void evolution in molybdenum (Mo). The obtained void growth rate agrees well with the prediction of rate theory while the interface width is smaller than a critical value in the considered cases regardless of the shape of the free energy density. This study will not only help to construct the appropriate formulation of the bulk free energy density, but will also provide an easy method of calculating the corresponding gradient energy coefficient and selecting the grid size according to the pre-estimated interface width.