Some Recent Results in Viscoplastic Crack Propagation

We summarize here some recent results for the steadily-propagating viscoplastic crack in antiplane strain. We outline the effects of the inclusion of a zone of elastic unloading upon the near-tip field. The properties of the next higher-order term in the asymptotic expansion are then described. In contrast to the dominant term, the next higher-order term contains an undetermined constant which must be specified by the remote boundary conditions. Finally, we demonstrate how the lower-order problem may be cast in the form of a second-order integro-differential equation. This formulation yields an unexpected constraint upon the solution.