A new analytical test case for anisotropic grain growth problems

摘要

Grain growth in polycrystals is one of the principal mechanisms that take place during heat treatment of metallic components. This work treats the single boundary simplification of the anisotropic grain growth problem. By applying the first principles of thermodynamics and mechanics, an expression for the velocity field of a migrating grain boundary with an inclination-dependent energy density is expressed. This result is used to generate the first, to the authors' knowledge, space-time analytical solution to the anisotropic grain growth problem. This new anisotropic benchmark is simulated in order to explore the convergence properties of the proposed level-set finite element numerical model. Convergence of the method being illustrated, another configuration, using a more general grain boundary energy density, is investigated in order to show the added value of the new formulation.