Effect of strain rate sensitivity on FLDs—An instability approach

Linear instability method has been adopted in this analysis to predict the Forming Limit Diagrams (FLDs), and the traditional instability analysis has been modified to account for strain rate effect. The initiation and growth of instability have been considered by examining the role of material work-hardening and strain rate sensitivity in affecting the limit strains. It is found that the initiation of the deformation instability is independent of the strain rate-sensitivity, while it affects the quasi-static stage of deformation. After the initiation of the deformation instability, the perturbation growth rate is different for different deformation conditions. For strain rate independent materials, the perturbation can grow into an observable neck just after the critical strain is reached when the strain ratio is negative; while the perturbation growth rate decreases with the increase of the strain ratio for the right hand side of forming limit diagrams. Material strain rate sensitivity reduces this perturbation growth rate, and it is expected that the deformation has longer quasi-stable deformation with strain rate sensitivity. For the left hand side of forming limit diagrams, the predicted angle is in the zero extension direction which coincides with that obtained by Hill in 1952; while the instability will take place along the minor strain direction for the positive strain ratio. The present predictions correlate well with experimental observations.