A model for the shear displacement distribution of a flow line in the adiabatic shear band based on gradient-dependent plasticity

Abstract

Based on second-order gradient-dependent plasticity (GDP), we establish the shear displacement distribution of material points of a flow line beyond the occurrence of the adiabatic shear band (ASB) at a position on a thin-walled tubular specimen in dynamic torsion. In the ASB, the shear displacements of a material point include two parts caused by homogeneous and inhomogeneous strain components, respectively. The former is assumed to be a linear function of the material point coordinate, while the latter is found to be a sinusoidal function of the coordinate due to the microstructural effect. For the Ti-6Al-4V alloy and two kinds of steels, the coefficients of the constant, linear, and nonlinear terms in the expression for the shear displacement distribution are determined by least-squares fitting for different widths and positions of the ASB. During the localized shear process, the coefficients of the linear and nonlinear terms are found to have increasing tendencies, while the deformed ASB width (which is larger than the width of the ASB central region) is slightly decreased. This investigation shows that secondorder GDP may be successfully applied in simulation of the shear displacement distribution of material points at flow lines in the ASBs.