In this study, we developed a multi-order, phase field model to compute the stress distributions in anisotropically elastic, inhomogeneous polycrystals and study stress-driven grain boundary migration. In particular, we included elastic contributions to the total free energy density and solved the multicomponent, nonconserved Allen–Cahn equations via the semi-implicit Fourier spectral method. Our analysis included specific cases related to bicrystalline planar and curved systems as well as polycrystalline systems with grain orientation and applied strain conditions. The evolution of the grain boundary confirmed the strong dependencies between grain orientation and applied strain conditions and the localized stresses were found to be maximum within grain boundary triple junctions.

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