On fast fracture in an elastic-(plastic)-viscoplastic solid – 1. Stress and velocity fields with loading and unloading processes

An asymptotic analysis of the near-tip field is given for fast crack propagation in an elastic-plastic-viscoplastic solid. The plasticity of the material is characterised by power law hardening, and the visco-plasticity covers primary, secondary and tertiary creep depending on a parameter q being smaller, equal to and larger than zero, respectively. The yield condition used is Von Mises criterion. Explicit results are given for the order of the crack-tip singularity, the angular position at which unloading occurs, and the angular variations of stresses and velocities in the near crack-tip fields. In particular, it is shown that the eigenvalue, which determines the order of stress singularity, relates only to the viscoplastic parameters but is independent of the crack-tip speed, boundary and loading conditions. Also, it is found that the plasticity effect cannot explicitly enter the asymptotic stress field. Otherwise, additional assumptions would be required.