Effect of material parameters on shear band spacing in work-hardening gradient dependent thermoviscoplastic materials

We study thermomechanical deformations of a viscoplastic body deformed in s imple shear. The effect of material elasticity is neglected but that of wor k hardening, strain-rate hardening, thermal softening, and strain-rate grad ients is considered. The consideration of strain-rate gradients introduces a material characteristic length into the problem. A homogeneous solution o f the governing equations is perturbed at different values t(0) of time t, and the growth rate at time to of perturbations of different wavelengths is computed, Following Wright and Ockendon's postulate that the wavelength of the dominant instability mode with the maximum growth rate at time to dete rmines the minimum spacing between shear bands, the shear band spacing is c omputed, It is found that for the shear band spacing to be positive, either the thermal conductivity or the material characteristic length must be pos itive. Approximate analytical expressions for locally adiabatic deformation s of dipolar (strain-rate gradient-dependent) materials indicate that the s hear band spacing is proportional to the square-root of the material charat eristic length, and the fourth root of the strain-rate hardening exponent. The shear band spacing increases with an increase in the strain hardening e xponent and the thermal conductivity of the material, (C) 1999 Elsevier Sci ence Ltd. All rights reserved.