Adiabatic shear banding in elastic-viscoplastic nonpolar and dipolar materials

Abstract

Simple shearing deformations of a block made of an elastic-viscoplastic material are studied. The material of the block is pressumed to exhibit strain hardening, strain-rate hardening and thermal softening. The effect of modeling the material of the block as a dipolar material in which the strain gradient is also taken as an independent variable has been investigated. The uniform fields of temperature and shear stress in the block are pertubed by superimposing a temperature bump at the center of the block, and the resulting initial-boundary-value problem is solved by the Galerkin-Gear method. It is found that for simple materials as the shear stress within the region of localization begins to collapse, an unloading shear wave emanates outwards from the edges of the shear band. For dipolar materials, the localization of the deformation is considerably delayed as compared to that for nonpolar materials, the shear stress does not collapse suddenly by decreases gradually, there is no unloading wave traveling outwards from the edges of the band, and the region of localized deformation is wider as compared to that for nonpolar materials.