Scaling of Monte Carlo simulations of grain growth in metals

The term microstructure defines many properties of metals that have practical significance. The final microstructure established during metal-forming processes is determined by the grain growth, recrystallization and recovery phenomena. Since these phenomena represent stochastic processes, they require a statistical treatment, and therefore, the Monte Carlo (MC) method is often used to simulate them. However, the MC method does not provide physical time and length scales, and thus a scaling procedure is required to map the simulation results to the physical material behavior. In this paper, we compare MC simulation results with theoretical models and experimental observations for grain growth of metals at different temperatures to obtain scaling relationships between physical time/length scales and the MC step/cell size. These scaling relationships can then be employed in multi-scale modeling of metal-forming processes.