Microstructure evolution influenced by dislocation density gradients modeled in a reaction–diffusion system

Abstract

Macroscopic properties of metallic materials are to a large extent dictated by the grain size and the presence and arrangement of grain boundaries. Plastic slip deformation will lead to the formation of dislocation pile-ups at grain boundaries, causing a heterogeneous distribution of dislocation density. This will on the macroscale manifest itself as a grain size dependence of the yield stress. Considering dynamic recrystallization, new grains will nucleate at sites of high stored energy. The existence of such favored nucleation sites is also largely due to a heterogeneous dislocation density distribution. To properly account for processes such as these in microstructure modeling, dislocation density gradients and grain boundary influence need to be considered. In the present contribution, the evolution of dislocation density is viewed as a reaction–diffusion system, involving mobile and immobile dislocations. Gradient effects are introduced by making the immobilization of mobile dislocations sensitive to the distance to grain boundaries. Through simulations in both single grains and polycrystals, it is shown that the present model provides a macroscopic yield stress behavior of Hall–Petch type, without explicitly incorporating a yield stress dependence on the grain size. In addition, the model is employed in a cellular automaton algorithm, allowing a polycrystalline microstructure to evolve due to dynamic recrystallization. It is shown that the introduced gradients provide important additions to recrystallization modeling.