Strain-rate-dependent forming limit diagrams for sheet metals

Abstract

Forming limit diagrams (FLDs) appear as one of the most applicable methods used for prediction of the instability in sheet metal forming. In this paper, the effects of strain rate on FLDs are analytically investigated over a wide range of strain rate (0.01/s—500/s). In order to obtain the strain-rate-dependent FLDs with the aid of imperfection concept, the motion equations (instead of equilibrium equations) are employed. Furthermore, in this study the critical strains, in plane strain loading, are numerically determined with respect to the principal strain rates at different material constants. For materials following the widely used Johnson—Cook constitutive law, the thermal softening due to the adiabatic conditions is taken into account. The results show that after a certain critical strain rate, by increasing the strain rate, localized necking is retarded and formability of sheet improves monotonically because of inertia effects. Finally, the comparison between numerical and available experimental FLDs for oxygen-free high conductivity (OFHC) copper is presented. This comparison shows that the theoretical results are in good agreement with the experimental observations.