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, xm, of the perturbation that has the maximum initial growth rate gives the spacing, Ls 1⁄4 2p=xm, between adjacent shear bands, and (ii) Ls 1⁄4 inf t0X02p=xmðt0Þ where t0 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 Ls. The effect of varying the thermal conductivity, the strain-rate hardening exponent and the average axial strain rate on Ls has been delineated. It is found that Ls / ðnominal axial strain rateÞ . However, for Ls / ðthermal conductivityÞ, the value of w̄ strongly depends upon the strain rate hardening exponent m. No scaling law is found between Ls and the Taylor–Quinney parameter. For Ls / ðspecific heatÞ, the value of w depends upon the strain-rate hardening exponent m and increases monotonically with an increase in the value of m. r 2005 Elsevier Ltd. All rights reserved.