Phase field modeling of directional fracture in anisotropic polycrystals

A phase field theory for modeling deformation and fracture of single crystals, polycrystals, and grain boundaries is developed. Anisotropies of elastic coefficients and fracture surface energy are addressed, the latter enabling favorable cleavage on intrinsically weak planes in crystals. An order parameter increases in value as damage accumulates in an element of material. The shear elastic coefficients deteriorate with cumulative damage regardless of local strain state, while the effective bulk modulus degrades only under tensile volumetric deformation. Governing equations and boundary conditions are derived using variational methods. An incremental energy minimization approach is used to predict equilibrium crack morphologies in finite element simulations of deforming polycrystals. Thin layers of material, representative of glassy second phases near grain boundaries, are assigned possibly different properties than surrounding crystals. Results of simulations of polycrystals subjected to tensile loading are reported, with base properties representative of silicon carbide or zinc. Key findings include (i) a tendency for intergranular over transgranular fracture as the grain boundary surface energy is reduced or as cleavage anisotropy is increased and (ii) an increase in overall ductility and strength, the latter similar to Hall-Petch scaling, as the absolute size of the polycrystal is reduced while holding the ratio of phase field regularization length to grain size fixed. Published by Elsevier B.V.