Effect of Strain Gradient on Formation of Shear Band under Kinematic Hardening Rule

Abstract

In the present work, the formation of shear band under simple shear loading is investigated using the rate-independent elastic-plastic constitutive relations. A small initial perturbation representing material imperfection is introduced into the work piece to develop the post-localization behaviors. Since kinematic hardening rule assumed under a finite deformation regime, the stress rate is co-rotated with respect to the spin of substructure using the plastic spin concept. Moreover, the strain gradient terms are incorporated into the yield function to obtain a non-local plastic constitutive relation and its results are compared with a conventional plasticity model. It is noted that the shear band formation is accompanied by decrease in the magnitude of spatial increment within the regime of localization. Moreover, the strain gradient affects the shear localization behavior significantly such that the intensity of shear band increases as the strain gradient coefficient increases when the J₂ flow theory is employed. The effect of strain gradient on the deformation localization is, however, almost negligible for a material deformed accord with the J₂ deformation theory.