Theoretical Prediction of Shear-Band-Type Strain Localization and Discussion on Its Relation to Fracture

Abstract

It was previously reported by the author that the limit to ductility of a thin sheet is well predicted theoretically by the use of the J2G constitutive equation with the localized necking condition as the critical condition under the assumption of a plane stress state, where the J2G stands for the J2-Gotoh's corner theory which was previously proposed by the author. In this paper, the critical conditions for the vertical and oblique types of shear band bifurcation in a block subjected to severe compression are deduced by the use of the J2G constitutive equation. It is concluded that the vertical type shear band is followed almost immediately by fracture, whereas the oblique-type shear band does not necessarily induce an immediate fracture and it corresponds rather to the "oblique shear-band like patterns" which appear in the materials under severe compressive plastic deformation such as in rolling. If an additional condition (e.g., the critical value of the circumferential stress to overcome) is satisfied before the oblique type shear band bifurcation, then this bifurcation will induce the immediate fracture, whereas if the additional condition is satisfied after the bifurcation, then fracture will occur at this point. These conclusions are derived from the comparision of the theory with the corresponding experiments reported by other investigators.