Modeling of Instability at the Tip of a Shear Band

Abstract

The present work focusses on the tip of the shear band, and assumes that the critical phenomena dictating the propagation or arrest of a shear band occur at the tip. This approach is analogous to fracture mechanics in which the crack tip is the region where the relevant processes are taking place, while the crack surfaces are merely the product. The driving energy for the extension of the tip comes from an increase of the imposed displacement, which generates shear stresses and strains. In the analysis presented in this paper the plastic deformation ahead of a shear band is calculated as a function of imposed displacement. A number of assumptions are required to render the problem tractable. The principal assumptions are given and justified below.