Fracture in distortion gradient plasticity

Abstract

In this work, distortion gradient plasticity is used to gain insight into material deformation ahead of a crack tip. This also constitutes the first fracture mechanics analysis of gradient plasticity theories adopting Nye's tensor as primal kinematic variable. First, the asymptotic nature of crack tip fields is analytically investigated. We show that an inner elastic region exists, adjacent to the crack tip, where elastic strains dominate plastic strains and Cauchy stresses follow the linear elastic stress singularity. This finding is verified by detailed finite element analyses using a new numerical framework, which builds upon a viscoplastic constitutive law that enables capturing both rate-dependent and rate-independent behaviour in a computationally efficient manner. Numerical analysis is used to gain further insight into the stress elevation predicted by distortion gradient plasticity, relative to conventional J2 plasticity, and the influence of the plastic spin under both mode I and mixed-mode fracture conditions. It is found that Nye's tensor contributions have a weaker effect in elevating the stresses in the plastic region, while predicting the same asymptotic behaviour as constitutive choices based on the plastic strain gradient tensor. A minor sensitivity to X, the parameter governing the dissipation due to the plastic spin, is observed. Finally, distortion gradient plasticity and suitable higher order boundary conditions are used to appropriately model the phenomenon of brittle failure along elastic-plastic material interfaces. We reproduce paradigmatic experiments on niobium-sapphire interfaces and show that the combination of strain gradient hardening and dislocation blockage leads to interface crack tip stresses that are larger than the theoretical lattice strength, rationalising cleavage in the presence of plasticity at bi-material interfaces