Initiation and propagation of localized deformation in elasto-plastic strips under uniaxial tension

Abstract

This paper deals with the evolution of inhomogeneous deformation in shape memory alloy strips and mild steel strips under uniaxial tension. New experiments on NiTi strips, which initially are in an austenitic phase, show that at a critical stress level martensite nucleates in sharp bands inclined at 55° to the axis of loading. Under prescribed end displacement martensite subsequently spreads either by steady-state propagation of inclined transition fronts or via a criss-cross pattern of finger-like features. Similar events have been reported in the literature regarding the evolution of Luders bands in fine grained steel strips and wires. The similarity of macroscopic events, despite the different mechanisms of instability at the micro-level, prompted us to approximate the material behavior as a finitely deforming elasto-plastic solid with a trilinear up-down-up nominal stress-strain response. Two such stress-strain responses were used in finite element simulations of strip tension tests. In the first the true stress-strain response maintains its stability and in the second the intermediate branch has a negative slope. While both material models produced inhomogeneous deformations with features similar to those of the experiments, the larger initiation peak associated with the second gave results which closely resembled specific experiments. The numerical simulations confirmed that the evolution of events seen in experiments on SMAs and mild steels is strongly influenced by overall geometric (structural) effects. Furthermore, the success of this simple continuum constitutive model strongly suggests that continuum level events remain dominant players in such fine grained materials.