Shear band spacing in thermoviscoplastic materials

A closed-form expression for shear band spacing in strain-hardening, strain-rate-hardening and thermally softening thermoviscoplastic materials is derived by studying the stability of a homogeneous solution of equations governing its simple shearing deformations. The wavelength of the perturbation that maximizes its initial growth rate is assumed to determine the shear band spacing, Ls: The dependence of Ls upon various material parameters and the nominal strain rate, _ e; is delineated. When written as Ls 1⁄4 A1k1 or A2_ e w 2 where A1 and A2 are parameters and k is the thermal conductivity, it is found that w2 ’ 0:787 and w 1 depends upon the strain-rate hardening exponent m; w 1 ’ 0:5 for m ’ 10 6 and n ’ 0:011; decreases rapidly to 0:21 for m ’ 10 4 and n ’ 0:011; and then increases slowly to 0:25 for m ’ 0:05 and n ’ 0:011: However, for m 1⁄4 0 and na0; w 1 1⁄4 1: r 2004 Elsevier Ltd. All rights reserved.