Shear band spacing in gradient-dependent thermoviscoplastic materials

We study thermomechanical deformations of a viscoplastic body deformed in s imple shear. The strain gradients are taken as independent kinematic variab les and the corresponding higher order stresses are included in the balance laws, and the equation for the yield surface. Three different functional r elationships, the power law, and those proposed by Wright and Batra, and Jo hnson and Cook are used to relate the effective strain rate to the effectiv e stress and temperature. Effects of strain hardening of the material and e lastic deformations are neglected. The homogeneous solution of the problem is perturbed and the stability of the problem linear in the perturbation va riables is studied. Following Wright and Ockendon's postulate that the wave length whose initial growth rate is maximum determines the minimum spacing between adjacent shear bands, the shear band spacing is computed. It is fou nd that the minimum shear band spacing is very sensitive to the thermal sof tening coefficient/exponent, the material characteristic length and the nom inal strain-rate. Approximate analytical expressions for the critical wave length for heat conducting nonpolar materials and locally adiabatic deforma tions of gradient dependent materials are also derived.