Random grid, three-dimensional, space-time coupled cellular automata for the simulation of recrystallization and grain growth

A new three-dimensional, random grid based cellular automaton model for the simulation of the evolution of a materials microstructure during recrystallization and grain growth is presented. The paper describes how the model can be linked to space and time coordinates and illustrates how theoretical analytical models describing grain boundary motion under the influence of a driving force can be used to control the cellular automaton. Simulation experiments illustrate the random grid base of the automaton eliminates the dependence of the model on the grid symmetry as observed in conventional cellular automata. Examples illustrating the correctness of the approach and its implementation are presented in the form of different verification experiments, including growth kinetics of a two different theoretical recrystallization processes, the shrinkage of a spherical grain driven by the curvature of its boundary and the evolution of the grain size distribution during grain growth in a polycrystalline microstructure.