Instability analysis and shear band spacing in gradient-dependent thermoviscoplastic materials with finite speeds of thermal waves

Abstract

We analyze the stability of a homogeneous solution of coupled nonlinear equations governing simple shearing deformations of a strain-rate gradient-dependent thermoviscoplastic body in which thermal disturbances propagate at a finite speed. The homogeneous solution is perturbed by an infinitesimal amount and equations linear in the perturbation variables axe derived. Conditions for these perturbations to grow are deduced. The shear band spacing, L_s, is defined as L_s = inf_t0≥0 (2π/ξ_m(t₀)) where ξ_m is the wave number of the perturbation introduced at time t₀ that has the maximum growth rate at time t₀. It is found that the thermal relaxation time (i.e. the ratio of the coefficient of the second time-derivative of the temperature in the heat equation to that of the first time-derivative) significantly affects the shear band spacing and the value of t₀ for which ξ_m(t₀) is maximum.