Fluctuation effects in grain growth

Abstract

In this study, we attempted to clarify the roles of fluctuation effects in grain growth. To capture the persistent nature in both space and time of fluctuations due to variations in the local surroundings of individual grains, we developed a local mean-field model. The fluctuation strength in this model is arbitrarily controlled by employing an artificial number, , of nearest neighbor grains. Large-scale numerical computations of the model for various values and initial GSDs were carried out to follow transient behaviors and determine the steady states. This study reveals that, in the classical mean-field model with no fluctuation effects, the steady state is not unique but is strongly dependent upon the initial GSD. However, a small fluctuation drives the mean-field model to reach the Hillert solution, independent of the fluctuation strength and initial GSD, as long as the fluctuation strength is sufficiently small. On the other hand, when the fluctuation is sufficiently strong, the fluctuation pushes the steady state of the mean-field model out of the Hillert solution, and its strength determines a unique steady state independent of the initial GSD. The strong fluctuation makes the GSD more symmetric than the Hillert distribution. Computations designed to mimic actual 2 and 3D grain growth were carried out by taking the number of nearest neighbors of each grain as a function of the scaled grain size. The resultant GSDs in two and three dimensions were compared with the direct simulations of ideal grain growth.