The effect of stress induced anisotropy on shear band formation

Abstract

This paper describes the effect of non-coaxiality arising from material anisotropy on bifurcation phenomena such as shear band formation. The elasto-plastic model originally proposed by Sekiguchi and Ohta [7] is one of the typical models which include anisotropy and it is used to examine the effect of anisotropy on shear band formation. First, we shall extend this elasto-plastic model for infinitesimal strain to a model for finite strain and discuss the mathematical structure of this model. The stress induced anisotropy is found to bring about a vertex-like effect, such as the non-coaxiality between the Cauchy stress tensor and a plastic stretching tensor, into the constitutive relation. Then, we shall examine the effect of this non-coaxiality on bifurcation conditions in relation to the material rigidity which changes with the angle of simple shear. Finally, it will be concluded that this non-coaxiality arising from the anisotropy does not contribute much to triggering instability by localization of the deformations which result in shear band formation, while on the other hand, the non-coaxiality due to the yield vertex effect is rather inclined towards instability by localization of the deformations.