Influence of strain-rate sensitivity on necking and instability in sheet metal forming

Abstract

Analytical closed form solutions based on a linear perturbation analysis are obtained to predict limit strains for rate sensitive materials. A closed form solution, independent of the choice of yield criterion, is first obtained for the negative minor strain regime of the forming limit diagram (FLD). The Von Mises yield criterion is invoked next, and the limit strains corresponding to the positive minor strain regime of the FLD are obtained. Predictions from the analytical model are then compared to experimental observations. It is noted that the effective limit strain is enhanced by strain rate sensitivity of the material. It is also observed that the effective limit strain is not influenced by the prior strain path, but rather by the instantaneous strain rate ratio in the final stage of the quasi-stable deformation.