A Boltzmann-type kinetic model for misorientation distribution functions in two-dimensional fiber-texture polycrystalline grain growth

Abstract For mathematical modeling of polycrystalline materials, it is critical to understand how the statistics of evolving grain boundary networks depend on the set of laws that govern the dynamics at a microscopic scale. Such rules describe the motion of grain boundaries and their junctions, as well as criteria for the corresponding topological transitions. Although these laws have been known for quite some time, their precise role in the development of the networks' mesoscopic properties is not sufficiently clear. A possible way to establish a connection between statistical features of the whole networks and fundamental rules for the evolution of individual grain boundaries is to conduct numerical experiments via generally recognized large-scale simulation approaches. Alternatively, it is possible to develop less computationally expensive techniques such as kinetic models based on partial differential equations, while preserving essential characteristics of grain boundary networks. The aim of this paper is to develop a novel kinetic modeling approach for estimating number- and length-weighted misorientation distribution functions in the particular technologically important case of polycrystalline thin films with fiber textures and with anisotropic grain boundary energy densities. Our approach is tested by comparing the numerical results, which it gives for two specific benchmark examples, with the corresponding large-scale simulation results from the related literature. One auxiliary benchmark example is also considered.