Recrystallization kinetics: A coupled coarse-grained dislocation density and phase-field approach

During recrystallization, dislocation-poor grains grow and invade the heavily deformed dislocation-rich matrix. In this work, we develop a coupled dislocation density and phase-field method to model the isothermal recrystallization process as a phase transformation, driven by the stored elastic energy. Dislocations are represented in two spatial dimensions in terms of a continuous Burgers vector field, and their contribution to the elastic energy density is explicitly incorporated. A key feature of our approach is that the driving force for grain growth becomes nonlocal in space due to the presence of long-ranged dislocation strain fields. We employ the model to examine the influence of various spatially heterogeneous dislocation distributions random, cellular, and algebraically correlated on the growth morphology of an isolated recrystallized grain. Our results show that grain growth can be highly anisotropic and irregular in cellular dislocation networks, in agreement with recent experiments. The source of this anisotropy is related to the anisotropy of the underlying dislocation network as well as the long-ranged dislocation stress fields. We also discuss how to extend this method to three spatial dimensions by invoking the full dislocation density tensor.