Grain growth simulation of steels during heat treatment with statistically modeled discrete neighborhood

A new grain growth model is proposed that extends classical mean-field models to include the local neighborhood of grains. The theoretical basis of the approach is the equilibrium angle of grain boundaries at triple junctions, which is estimated to be 120°considering 2 dimensions, in the case of isotropic grain boundary energy. Based on this fact and a size comparison of individual grains, an algorithm is developed that assigns a discrete neighborhood relationship to all grains, resulting in the generation of an artificial microstructure. For validation, samples of a CMn steel were examined in different states after heat treatments and the microstructure was characterized using deep learning approaches to extract grain boundaries from etched samples with excellent statistics and reliability. The properties and statistical characteristics of the artificial and real microstructures are presented and compared. It is shown that simple topological approaches, such as the linear relationship between the number of grain neighbors and the relative grain size, are good only in a first approximation, but collapse in detail. The proposed model is able to resemble these small deviations of a real microstructure from topological models. Furthermore, the grain growth behavior of such an artificial microstructure is compared with real grain growth experiments. The comparison shows that by implementing the discrete neighborhood of grains, behaviors such as abnormal grain growth seem to be covered to a certain extent without additional treatment as required in other models.