Strain burst phenomena in the necking of a sheet that deforms by non-associated plastic flow

Abstract

In non-close-packed crystalline lattices, e.g. bcc metals and intermetallics, the stress-state dependence of the Peierls barrier for the motion of a screw dislocation violates Schmid's law and leads to non-associated plastic flow in single crystals and polycrystalline aggregates (Bassani 1994 Adv. Appl. Mech. 30 191–258, Bassani et al 2001 Mater. Sci. Eng. A 319–321 97–101). Plasticity models based upon distinct yield and flow functions are proposed to describe polycrystalline behaviour and specialized to the case of isotropic response. Studies of sheet necking using both a Marciniak–Kuczynski analysis and finite elements predict that non-associated flow has a significant effect on the evolution of inhomogenieties in the sheet. For nearly rate-insensitive response, intermittent bursts of strain arise as a consequence of non-associated flow, particularly for deformations near the plane-strain state. These strain bursts, which are due to instantaneously unstable deformation behaviour, are observed to be sensitive to mesh refinement in the case of a purely local constitutive description. Strain-gradient effects are introduced, which significantly improves convergence.