Nonlocal orientation field phase-field model for misorientation- and inclination-dependent grain boundaries

We propose to incorporate grain boundary (GB) anisotropy in phase-field modeling by extending the standard partial differential equations (PDEs) formulation to include a nonlocal functional of an orientation field. Regardless of the number of grains in the simulation, the model uses a single orientation field and incorporates grain misorientation and inclination information obtained from sampling the orientation field at optimized locations in the vicinity of the GB. The formalism enables simple and precise tuning of GB energy anisotropy while avoiding an extensive fitting procedure. The functional includes explicit GB functions to control the GB energy as a function of both misorientation and inclination. The model is validated by reproducing the linear grain growth rate, Wulff shapes with varying misorientations and anisotropic coefficients, and analytical equilibrium dihedral angles at triple junctions. Polycrystalline simulations further demonstrate grain growth, coalescence, triple junction behavior, and the influence of anisotropy on grain morphology.