1. Introduction

Plastic deformation in anisotropic sheet-metal consists of four distinct phases, namely, uniform deformation, diffuse necking, localized necking and final failure. The last three phases are commonly known as non-uniform deformation. New sheet-metals such as aluminium alloys, titanium alloys and Ni-based super-alloys, display from experimental evidence necking-failure behaviour where localised thinning is hardly visible. Plastic instability of these sheet-metals has been found to suffer material degradation which confirmed the need to properly characterize their forming limit using a theory of damage mechanics. Coupling the incremental theory of plasticity with damage and a plastic instability criterion, the enhanced criterion proposed in this paper can be used to predict not only the forming limit but also the fracture limit under proportional or non-proportional loading and is suitable for sheet-metal forming simulation by finite-element analysis.

Another case is the sheet bending process where the outer layer of the bending sheet is unstable but the sheet as a whole is not unstable. So the formation of a neck is impossible, and the boundary in bending is the strain to fracture. This important phenomenon is not related in the FLD predicted using the conventional approaches based only on plastic-instability theories. In view of these shortcomings, a new unified approach to predict the FLD is presented. This approach enables the prediction of the three stages which lead to final rupture: diffuse, localized necking and failure. In addition, the new...