Strain-gradient effects on steady-state crack growth in linear hardening materials

摘要

Steady-state rectilinear crack propagation is analysed in couple stress elastic-plastic solids, displaying linear isotropic hardening. The flow-theory version of couple stress plasticity is adopted for the constitutive description of the material. A higher order asymptotic analysis of crack-tip fields is performed under mode Ⅰ and mode Ⅱ loading conditions, both for plane strain and plane stress problems. In particular, the stress and couple stress fields are assumed to display distinct strengths of their singularity, so that, although the most singular term of the velocity field turns out to be irrotational, the leading order terms of couple stress and rotation gradient fields do not vanish, but couple with higher order terms of the strain and velocity fields. It follows that, under mode Ⅰ crack propagation, the rotation gradients produce a substantial increase of the stress singularity and, thus, of the traction level ahead of the crack-tip, with no need to invoke stretch gradients, whereas an increase in the shear traction ahead of the crack-tip is observed under mode Ⅱ loading conditions. These results may contribute to explaining the occurrence of cleavage fracture in ductile metals from the point of view of atomistic fracture mechanics.