Near-tip field for steady dynamic crack growth in a compressible elastic-plastic material

Abstract

The influence of compressibility on the stress and deformation fields near the tip of a mode I dynamic crack growing steadily in an elastic-perfectly-plastic material under plane strain conditions is studied. The material is characterized by the von Mises yield criterion and J 2 flow theory of plasticity. This solution has the properties that the angular variation of stress and particle velocity around the crack tip is continuous, and the stress and strain are bounded at the crack tip. It is found that a parameter θ 0, which can not be determined by asymptotic analysis, may characterize the effect of the far field. When the material is nearly incompressible, a perturbation solution in the small parameter ϵ = 1 2 − v (v is Poisson's ratio) is constructed. As ϵ → 0, the solution tends to that for the incompressible case obtained by Leighton et al. (1987). Asymptotic analysis of steady dynamic crack growth in an elastic-plastic material. J. Mech. Phys. Solids 35, 541–563.