Asymptotic solution for mode III crack growth in J 2-elastoplasticity with mixed isotropic-kinematic strain hardening

Abstract

Mode III fracture propagation is analyzed in a J2-flow theory elastoplastic material characterized by a mixed isotropic/kinematic law of hardening. The asymptotic stress, back stress and velocity fields are determined under small-strain, steady-state, fracture propagation conditions. The increase in the hardening anisotropy is shown to be connected with a decrease in the thickness of the elastic sector in the crack wake and with an increase of the strength of the singularity. A second order analytical solution for the crack fields is finally proposed for the limiting case of pure kinematic hardening. It is shown that the singular terms of this solution correspond to fully plastic fields (without any elastic unloading sector), which formally are identical to the leading order terms of a crack steadily propagating in an elastic medium with shear modulus equal to the plastic tangent modulus in shear.

Mode III crack growth in linear hardening materials with strain gradient effects

“…The problem of mode III crack propagation within the classical J 2 -flow theory was first analysed by Amazigo and Hutchinson (1977) and Ponte Castañeda (1987) for materials which display linear and isotropic hardening and extended by Bigoni and Radi (1996) to mixed isotropic/kinematic hardening. These investigations found that the strength of the stress singularity turns out to be extremely weak for the typically small values of the strain hardening for ductile metals.…”

Effects of Characteristic Material Lengths on Ductile Crack Propagation

“…In fact, the solution obtained for conventional elastic-plastic response predicts a weak stress singularity for small strain-hardening, which becomes vanishing small in the limit case of elastic-perfectly plastic behavior of the material, namely for α = 0. The curves plotted in Figures 2b and 3b show that the displacements ahead and behind the crack-tip are opposite in sign, unlike the classical Mode III crack-tip fields in non-polar materials [19][20][21]. Similar results have been also obtained for a Mode III crack both for CS elastic [23] and CS elastic-plastic material behavior [26].…”

“…The problem of Mode III crack propagation in ductile materials was first analyzed within the classical J 2 -flow theory for linear and isotropic hardening [19,20] and extended to mixed isotropic/kinematic hardening [21]. These investigations found that the strength of the stress singularity turns out to be extremely weak for small strain hardening.…”