Viscoelastic-perfectly-plastic field at the tip of mode III steadily propagating crack

Under the assumption that the artificial viscosity coefficient at the propagating crack tip is inverse proportion to power law of the plastic strain rate, a rate-sensitive constitutive relationship is derived for elastic-perfectly-plastic materials. It is presumed that both the stress and strain possess the power law singularity, then the stress and strain fields are investigated asymptotically at a steadily propagating crack-tip. By means of dimension analyses, the matching conditions among the elasticity, plasticity and viscosity are discussed. Analyses and numerical computations are carried out for mode III dynamically propagating crack, and the variations of solution are discussed according to each parameter. The corresponding quasi-static problem is investigated asymptotically, which is shown to be a special case of dynamic one through comparison with it when the crack growing speed approaches zero. Thus the contradiction is resolved that the dynamical solution can not degenerate to a quasi-static one in non-viscosity analyses. The analytical and computational results indicate that the viscosity effect is an important factor in propagating crack-tip fields.