Multiscale modeling and simulation of grain boundary evolution

In this paper we discuss modeling and simulation of two dimensional grain boundary evolution at different scales, with emphasis on their relations. The motivation is the need to reduce the high computational complexity of detailed models on one hand, and the additional physical insight offered by multiscale representations on the other hand. Both are essential to our understanding of polycrystalline materials, facilitating the construction of new tools with predictive capabilities. The smallest scale model in this study is a Monte-Carlo Potts model which is followed by a curvature driven model, governed by the Mullins Equation together with the Herring Condition at triple junctions. Spatial coarse-graining results in a model that uses representation of the grain boundaries in terms of their end points and a constant curvature, that is able to capture size distribution function quite accurately at a fraction of the cost. Temporal coarse graining, in which grains are represented in terms of area and number of sides, is governed by a stochastic process, offering new statistical quantities that characterize evolution of large networks. The models are studied from coarse graining view point, facilitating the construction of tools with predictive capabilities which are essential for engineering applications.