Towards a Statistical Theory of Texture Evolution in Polycrystals

Most technologically useful materials possess polycrystalline microstructures composed of a large number of small monocrystalline grains separated by grain boundaries. The energetics and connectivity of the grain boundary network plays a crucial role in determining the properties of a material across a wide range of scales. A central problem in materials science is to develop technologies capable of producing an arrangement of grains—a texture—that provides for a desired set of material properties. One of the most challenging aspects of this problem is to understand the role of topological reconfigurations during coarsening. Here we propose an upscaling procedure suitable for large complex systems. The procedure is based on numerical experimentation combined with stochastic tools and consists of large-scale numerical simulations of a system at a microscopic level, statistical analysis of the microscopic data, and formulation of the model based on stochastic characteristics predicted by the statistical analysis. The procedure promises to be valuable in establishing the effective model of microstructural evolution in realistic twoand three-dimensional systems. To test these ideas we use our upscaling procedure to study the mesoscopic behavior of a reduced one-dimensional network of grain boundaries. Despite the simplicity of its formulation, this model exhibits highly nontrivial behavior characterized by both growth and disappearance of grain boundaries and develops probability distributions similar to those observed in higher-dimensional simulations. Here we focus on the grain deletion events which are common to all coarsening systems.