Asymptotic fields for dynamic crack growth in non-associative pressure sensitive materials

Abstract

Asymptotic near-tip fields are analyzed for a plane strain Mode I crack propagating dynamically in non-associative elastic-plastic solids of the Drucker-Prager type with an isotropic linear strain hardening response. Eigen solutions are obtained over a range of material parameters and crack speeds, based on the assumption that asymptotic solutions are variable-separable and fully continuous. A limiting speed, beyond which a tendency to slope discontinuity in angular distributions of stresses and velocities is detected, is found to deviate from the associative models. At low strainhardening rates, the onset of the plastic potential corner zone ahead of the crack-tip imposes another limit to the crack speed. Correspondingly, those limits imply the limits to the degree of non-associativity at a given crack speed. In addition, a tendency to slope discontinuity in the angular radial stress distribution sets another limit on the nonassociativity at vanishing hardening rates.