Dynamic crack-tip field for tensile cracks propagating in power-law hardening materials

Abstract

The near-tip field of a dynamically propagating crack in an incompressible power-law hardening material is studied using the asymptotic method as an extension of Leighton et al. (Journal of the Mechanics and Physics of Solids, 1987, Vol.35, pp.541–563). The crack is subjected to tensile loads and propagates steadily under plane strain conditions. The material deformation is described by the J ₂ flow theory of plasticity with infinitesimal displacement gradients. Results show that, in the present crack-tip field, (a) the angular variations of stresses, strains and particle velocities around the crack tip are fully continuous; (b) the stresses and strains at the crack tip are bounded; (c) there is a free parameter σ_eq0 which cannot be determined in the asymptotic analysis. Comparisons indicate that the present asymptotic solution matches well with full-field numerical results, and the parameter σ_eq0 can characterize the effects of the far field on the crack-tip field. Furthermore, the present solution approaches that of Leighton et al. (1987) in the limit as the material hardening exponent goes to infinity, but does not reduce to the accepted solution for quasi-statically growing cracks in the limit as the crack speed goes to zero.