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, image, of the perturbation that has the maximum initial growth rate gives the spacing, image, between adjacent shear bands, and (ii) image where image 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 image. The effect of varying the thermal conductivity, the strain-rate hardening exponent and the average axial strain rate on image has been delineated. It is found that image. However, for image, the value of image strongly depends upon the strain rate hardening exponent image. No scaling law is found between image and the Taylor–Quinney parameter. For image, the value of image depends upon the strain-rate hardening exponent image and increases monotonically with an increase in the value of image.