ASYMPTOTIC SOLUTION FOR MODE-III CRACK-GROWTH IN J(2)-ELASTOPLASTICITY WITH MIXED ISOTROPIC-KINEMATIC STRAIN-HARDENING

Mode III fracture propagation is analyzed in a J(2)-flow theory elasto plastic material characterized by a mixed isotropic/kinematic law of h ardening. The asymptotic stress, back stress and velocity fields are d etermined under small-strain, steady-state, fracture propagation condi tions. The increase in the hardening anisotropy is shown to be connect ed 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 secon d order analytical solution for the crack fields is finally proposed f or the limiting case of pure kinematic hardening. It is shown that the singular terms of this solution correspond to fully plastic fields (w ithout 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 shea r.