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, LsLs. The dependence of LsLs upon various material parameters and the nominal strain rate, ɛ˙, is delineated. When written as Ls=A1kχ1Ls=A1kχ1 or A2ɛ˙χ2 where A1A1 and A2A2 are parameters and k   is the thermal conductivity, it is found that χ2≃-0.787χ2≃-0.787 and χ1χ1 depends upon the strain-rate hardening exponent m  ; χ1≃0.5χ1≃0.5 for m≃10-6m≃10-6 and n≃0.011n≃0.011, decreases rapidly to 0.210.21 for m≃10-4m≃10-4 and n≃0.011n≃0.011, and then increases slowly to 0.250.25 for m≃0.05m≃0.05 and n≃0.011n≃0.011. However, for m=0m=0 and n≠0n≠0, χ1=1χ1=1.