On Rate Dependence and Anisotropy in Phase Field Modeling of Polycrystalline Fracture

A phase field theory of fracture incorporating rate dependence (i.e., kinetic viscosity) and anisotropic elasticity is implemented to study strength and failure modes in polycrystalline materials. After presentation of the constitutive framework, a new analytical solution is derived for one-dimensional (1D) homogeneous loading at constant strain rate, wherein crack viscosity is enabled. The three-dimensional (3D) theory is implemented in a finite element (FE) context, with static and dynamic solutions verified up to peak loading for homogeneous microstructures. Extensive simulations of heterogeneous polycrystalline microstructures follow, where baseline material properties correspond to either boron carbide (B4C) or titanium diboride (TiB2). Results quantify effects of loading rate, elastic anisotropy, cleavage energy anisotropy, and grain boundary surface energy on tensile strength. Notable are effects of strong basal texture, which influences average strength via both elastic anisotropy and basal cleavage plane orientation. Effects of loading rate are naturally more prominent for materials that fail mostly intergranularly rather than transgranularly, in agreement with experimental observations.