Three-dimensional large-scale grain growth simulation using a cellular automaton model

Abstract

The mechanical properties of metallic materials are highly dependent on the average and distribution of the grain size. Therefore, it is important to accurately understand grain growth behavior, and numerical simulations play an important role in this regard. Accordingly, in this study, a three-dimensional cellular automaton (3DCA) grain growth model was developed using a simple grain boundary curvature model and the stochastic transition rule as a CA algorithm. To validate this model, a large-scale 3DCA simulation of the ideal grain growth was performed, and the obtained results were compared with those of the ultra-large-scale phase-field (PF) simulation and other analytical models. The grain coarsening during the simulation followed a parabolic law, and the distributions of the normalized grain radius and number of grain faces were transformed to steady-state distributions over time. Moreover, the relationship between the normalized grain size and the normalized growth rate was in good agreement with the Hillert theory for the normalized grain sizes of 0.2–2.2. The simulation results were similar to the ultra-large-scale PF simulation data, in which grains remained in the steady state on a statistically reliable scale. Finally, the established relationships between the normalized growth rate, the normalized grain size, and the number of grain faces were in good agreement with the analytical model. Our results indicate that the grain growth behavior can be quantitatively predicted by the proposed 3DCA model. The calculation time required for this simulation (15000 steps with 10003 grids) was about 2.4 d using a personal desktop computer with 1 CPU. From the comparison with ultra-large scale PF simulations, we estimated that this 3DCA model has the potential to calculate >10 times faster than the PF method.