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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 second-order GDP may be successfully applied in simulation of
the shear displacement distribution of material points at flow lines in the
ASBs.
