An investigation of the strain path dependence of the forming limit curve

Abstract

The dependence of the forming limit curve on the deformation history is examined by considering two specific examples of sheet metal forming, representative of two classes of non-proportional strain path: one example is an axisymmetric punch stretching problem, which gives rise to a gradual variation in the strain path from a proportional path; the other example consists of a sheet with residual strains subjected to a proportional stretching so that the complete deformation history, if represented in the principal in-plane strain coordinates, takes a sharp turn. Results are presented for these examples for each of three plasticity theories: flow theory, J2-deformation theory and the recently proposed corner theory. By assuming a plastic potential increment dependent on the direction and magnitude of the incipient plastic strain increment the corner theory gives results which agree qualitatively with experimental observations and therefore seems to be favored for the bifurcation analysis of sheet metal forming problems involving significant strain path variations.