Analysis of Shear Band Development in a Viscoplastic Double Slip, Single Crystal in Tension

Abstract

Using an idealized planar single crystal model undergoing symmetrical double slip in tension, the effect of rate sensitivity on shear band initiation and on shear band development is analysed. The behavior of the crystal is assumed to be rigid-viscoplastic. By analysing the kinematics and statics of shear banding, the deformation modes involving shear banding pattern are formulated. By a linearized stability analysis, the critical condition for shear band initiation is obtained. To study shear band development, the formulated constitutive equations are numerically solved, and the maximum value of the localized shear is predicted. The results show three different stages of shear band development. The first corresponds to a slow progression of shear localization in the band, the second to a rapid shear localization accompanied with an unloading of surrounding material, and the third to a resumption of deformation in the surrounding material and to a progressive saturation of the shear band. All three stages depend strongly on rate sensitivity, especially the first stage which does not exist in the rigid-plastic case. Even very small rate sensitivity can delay significantly or even preclude the shear band formation. Finally a discussion of the results illustrates how a macroscopic shear band forms and propagates.