Theoretical analysis of strain- and stress-based forming limit diagrams

Abstract

Forming limit diagram is extensively used in the analysis of sheet metal forming to define the limit of deformation of materials without necking or fracture. This article contributes in construction of strain- and stress-based forming limit diagrams by theoretical analysis of several available instability criteria, including bifurcation analysis of diffuse and through-thickness neck formation, shear stress-based criteria onset of through-thickness necking, and so on, and comparative studies among different available theories are done with earlier published work on forming limit in different literatures. The scope of Tresca criterion in forming limit diagram is also investigated in this article. It is found that apart from stress-based forming limit diagram, conventional failure criterion equivalent failure strain versus triaxiality (η) plot is also strain path independent.