Validating a mean-field theory via large-scale phase-field simulations for abnormal grain growth induced by nonuniform grain boundary properties

摘要

The mean-field theory proposed by Humphreys is widely used to predict or interpret abnormal grain growth induced by nonuniform grain boundary properties. Based on this theory, the abnormal growth conditions of a specific grain can be expressed as a function of only three parameters: the size ratio, boundary energy ratio, and mobility ratio between the specific grain and its surrounding matrix grains. However, quantitative and systematic validation of this theory is not yet reported neither in experiments nor simulations. In this study, to elucidate the validity of the mean-field theory, we perform large-scale phase-field simulations for two-dimensional and three-dimensional abnormal grain growth. The multi-phase-field numerical model and parallel graphics processing unit computing are employed, which enables the accurate analyses of abnormal growth in large-scale systems with several hundreds of thousands of grains while accounting for the nonuniformity in grain boundary properties. Systematic simulations are performed while varying the size ratio, boundary energy ratio, and mobility ratio between the specific grain and matrix grains. The simulated results and theoretical predictions on the abnormal grain growth behaviors, i.e., whether or not the abnormal growth occurs and the maximum size that can be reached by an abnormally growing grain, are compared in detail. The large-scale multi-phase-field simulations reveal for the first time the agreement between the mean-field theory and numerical simulation quantitatively, demonstrating that the mean-field theory is a versatile means for describing abnormal grain growth. GRAPHICS .