[SY-I11] The effect of strong anisotropic grain boundary energy and mobility on microstructure formation and evolution: mesoscale modeling and simulation
Invited
Nanocrystalline materials have exceptional mechanical properties. Because of their small microstructural length scale, their macroscopic properties are dramatically influenced by grain boundaries (GBs). In this work we develop an algorithm for constructing the Allen-Cahn equation for grain boundary migration including an orientation-dependent, nonconvex, anisotropic boundary energy. The energy minimizing morphology for boundaries with nonconvex energy is faceted, but lacks a lengthscale, resulting in unstable solutions in phase field gradient flow. It is therefore necessary to include a second-order regularization to penalize corners To compute the variational derivative of this complex free energy, we simplify by transforming into the eigenbasis of the Hessian. This reduces the computation of principal curvatures to second derivatives with respect to the second and third principal axes, which preserves computational efficiency.To incorporate realistic boundary behavior, the lattice-matching model is used to calculate boundary energy for arbitrary orientations, on-the-fly. Simulations are conducted for microstructure evolution in a real-space implementation using adaptive mesh refinement. Finally, we propose a continuum understanding of GB motion as a shear transformation goverened by compatibility. Optimal boundary transformations are determined using a systematic process for shear identification, and by computing the minimum energy barrier for each. Such transformations typically require an atomic “shuffle” meaning that they atoms do not transform in the Cauchy-Born sense. The resulting optimal transformation can then be incorporated at the mesoscale by modeling the elastic energy as a multiwell potential. This provides a continuum context for understanding disconnections and faceted boundary migration.