QUASI-STATIONARY THREE-DIMENSIONAL GRAIN SIZE DISTRIBUTION WITH TOPOLOGY DEPENDENCY OF GRAIN GROWTH
基于晶粒长大拓扑依赖性的准稳态三维晶粒尺寸分布

A new topology-related individual grain growth rate equation was derived under the assumption of the statistical grain model. It depicts that the changing rate of grains is related to the grain size and topological properties. The continuity equation from the particle coarsening theory was adapted to grain growth. Based on the grain growth rate equation and the continuity equation, an asymptotic solution was obtained. The solution is an one-parameter family of distributions other than a unique distribution function, which is supported by quasi-stationary grain size distributions obtained from simulations of vertex model, surface evolver, phase-field model and Monte Carlo method.