A continuum model was proposed for the effects of deformation twinning upon the ductile versus brittle fracture behaviour of low strain-hardening face-centered cubic metals following the exhaustion of work-hardening. Instead of discrete twin nucleation, a number of partial dislocations ahead of the tip exhibited themselves as twins in the final stage of failure. The crack-tip plasticity was amended for deformation twinning, and the constitutive form for the flow-strength of arrays of twins of the same sign was expressed as a second gradient of micro-rotation for their coupling. The twins not only shielded the crack tip, but also inhibited further dislocation emission; thus forming a dislocation-free zone in the immediate vicinity of the tip. The stress fields introduced by deformation-twinning led to fracture branching under mode-I loading. The model was adapted from the conceptual model of Beltz et al. (1996); based upon the equivalence of the stresses derived from twin-based crack-tip plasticity, macroscopic plasticity and elasticity on the dislocation-free zone boundary. The dislocation-free zone-size and the crack-tip shielding ratio were obtained, as well as the branching angle. The branching angle was notable in low strain-hardening metals. A strong dependence of theupon intrinsic surface energy and hardening index was examined. The toughness reduction due to crack-tip constraints and reduction in the ductile-to-brittle transition temperature region was found to be in agreement with experimental observations and available predictions.

A Continuum Model of Deformation-Twin Dominant Crack Growth in FCC Metals. X.Zhang: Philosophical Magazine Letters, 2008, 88[1], 55-65toughness