Instability strain and shear band spacing in simple tensile/compressive deformations of thermoviscoplastic materials

We analyze the stability of homogeneous simple tensile/compressive deformations of an isotropic heat-conducting thermoviscoplastic bar by studying the growth of infinitesimal perturbations superimposed upon a homogeneous deformation. The smallest axial strain at which the superimposed perturbation has a positive initial growth rate is called the instability strain. Two criteria are used to determine the shear band spacing; (i) the wave number, ξmξm, of the perturbation that has the maximum initial growth rate gives the spacing, Ls=2π/ξmLs=2π/ξm, between adjacent shear bands, and (ii) Ls=inft0⩾02π/ξm(t0)Ls=inft0⩾02π/ξm(t0) where t0t0 is the time when the homogeneous solution is perturbed. It is found that the geometric softening/hardening significantly affects the instability strain and the value of LsLs. The effect of varying the thermal conductivity, the strain-rate hardening exponent and the average axial strain rate on LsLs has been delineated. It is found that Ls∝(nominal axial strain rate)-0.757Ls∝(nominal axial strain rate)-0.757. However, for Ls∝(thermal conductivity)χ¯, the value of χ¯ strongly depends upon the strain rate hardening exponent mm. No scaling law is found between LsLs and the Taylor–Quinney parameter. For Ls∝(specific heat)χLs∝(specific heat)χ, the value of χχ depends upon the strain-rate hardening exponent mm and increases monotonically with an increase in the value of mm.