Prediction of Fracture Limit for Backward Extrusion of Cup by Instability Condition to Cleaving Action on Localized Bifurcation Zone

Abstract

We investigated a method of determining the geometry of the die and punch, which are not allowed to fracture in the forming process of backward extrusion of cup. On the basis of the localized bifurcation theory, it is suggested that final fracture, which is recognized as the separation of a continuum material, may occur in the shear band zone with cleavage. A newly proposed instability condition to the cleaving action in the shear band zone is applied to predict the fracture limit on the forming process. Finite element analysis of the forming process is performed to know the stress state, which is required in the theory. The experimental observation using an optical microscope is also conducted to recognize fracture occurrence during the forming process. Results show that the combination of the punch shoulder radius and the die shoulder radius ensures forming without fracture.