Computer simulation of normal grain growth in three dimensions

Abstract

Computer modelling has been carried out to study normal grain growth in three dimensions. The approach consists of digitizing the microstructure by dividing the polycrystalline material into small volume elements and storing the spatial location and crystallographic orientation of each element. An energy is assigned between each element and its neighbours, such that neighbours having unlike orientations provide weaker bonding than neighbours of like orientations. The annealing treatment during which grain growth occurs is simulated using a Monte Carlo technique in which elements are selected at random and thermally activated transitions to other orientations are attempted. With time, the system evolves so as to reduce the total grain interface area. The microstructures produced are in good correspondence to observations of pure metals and ceramics which have undergone grain growth. Power-law kinetics (Ř = ctn) are observed, with a growth exponent in three dimensions of n = 0.48 ± 0.04 in the long-time limit. It is found that the distribution of grain radii determined in terms of its most natural measure (radii calculated from volume) is best described by a log-normal function. In contrast, the distribution of grain radii data determined from cross-sectional area is best described by a generalization of the distribution function proposed by Louat. Good correspondence between simulation, experiment and Louat’s distribution is found when the distribution is determined from cross-sectional area. The simulation microstructure also exhibits well defined topical (e.g. faces, edges and corners) distributions. A linear relationship is obtained between the grain radius determined from volume and the number of faces, edges and corners per grain of that size. A similar topology-size relationship is found when grains are observed in cross-section. Good agreement between the three-dimensional topological properties and experiments is obtained. Finally, the effect of grain shape on stereological transformations is discussed. © 1989 Taylor & Francis Group, LLC.