A Novel Approach to Grain Shape Factor in 3D Hexagonal Cellular Automaton

Cellular automata (CA) modeling is a powerful and efficient tool for simulating the dynamic evolution of polycrystalline microstructures in modern materials and metallurgy studies, such as solidification, plastic deformation and recrystallization. We propose a novel model to calculate the shape factor of grains in three-dimensional hexagonal grid (3D-HEX) CA, which overcomes the disadvantages of 3D-HEX CA, such as complex algorithms and a long computation time. The shape factor is a quantitative measure of grain morphology based on the ratio of the surface area of the grain to its volume-equivalent-sphere and volume-equivalent-chain. It indicates how the shape of a grain or phase affects its mechanical properties, such as stiffness, deformation and fracture. Our model can easily calculate the shape factor for any grain by counting its surface cells and volume cells. We test our model on 1000 grains with different shapes (equiaxed, irregular and chain-like) by Monte Carlo (MC) methods. MC methods evaluate the validity of a calculation model by comparing the simulated outcomes with the observed or expected outcomes. The results show that our model can accurately describe the grain morphology and has a good comparability and generality.