Cellular automata simulations of grain growth in the presence of second-phase particles

In this article, we studied the grain growth kinetics in the presence of second-phase particles by using a 2D cellular automata (CA) model with deterministic rules. The curvature-driven grain growth mechanism was adopted in the CA model and an expanded method for the computation of curvature along a grain boundary was used. Simulations in real time and space were performed for various particle sizes, volume fractions of particles, and initial grain sizes, and their effects on the microstructure evolution and final limiting grain size were discussed. A modified Zener relation was proposed to predict the limiting grain size by introducing two items: one describes the effect of initial grain size and the other describes the effect of the ratio of initial grain size to particle size. The proposed relation shows a good fit to the simulated limiting grain sizes for different cases.