Effect of out-of-plane stress on the forming limit strain of sheet metals

Abstract

In press forming of sheet metals, the material sheet is usually subjected to very large plastic strain under in-plane stressing. Moreover, the sheet also very often is subjected to out-of-plane compressive force between tools such as the upper and lower dies, the blank holder and the die, and so forth. However, the forming limit strain of sheet metals has been investigated so far only for the plane stress state without the effect of such out-of-plane force both theoretically and experimentally. In this paper, it is clearly demonstrated theoretically that out-of-plane stress (even as small as one tenth of the yield stress) may notably raise the forming limit strain and thus it can be effectively utilized to avoid earlier fracture of the sheet in press forming. The classical Swift's or Hill's criterion of instability, Storen & Rice's condition together with the J2G plasticity constitutive equation (previously proposed by one of the authors, Gotoh) for localized necking, and the numerical simulation of plane-stress and plane-strain tension of a sheet by the finite-element method (FEM) are applied here to discuss this problem, all leading us to the same conclusion.