A continuum model of deformation-twin dominant crack growth in fcc metals

Abstract

A continuum model is proposed to address the effects of deformation twinning on ductile versus brittle fracture behaviour of low strain-hardening fcc metals after exhaustion of work hardening. Instead of discrete twin nucleation, a number of partial dislocations ahead of the tip exhibit themselves as twins at the final stage of failure. The crack-tip plasticity is amended for deformation twinning and the constitutive form for the flow strength of arrays of twins of the same sign is expressed as a second gradient of microrotation for their coupling. The twins not only shield the crack tip but also inhibit further dislocation emission to form a dislocation-free zone (DFZ) in the immediate vicinity of the tip. The stress fields induced by deformation twinning lead to fracture branching under Mode I loading. The model is borrowed from the conceptual model presented by Beltz et al. [Acta Mater. 44 3943 (1996)], based on the equivalence of the stresses derived from twin-based crack-tip plasticity, macroscopic plasticity and elasticity on the DFZ boundary. The DFZ size and the crack-tip shielding ratio are obtained, as well as the branching angle. The branching angle is noteworthy for low strain-hardening metals. A strong dependence of the toughness on intrinsic surface energy and hardening index is examined. The toughness reduction due to crack-tip constraints and in the ductile-to-brittle transition (DBT) temperature region is revisited and found to be in agreement with experimental observations and available predictions.