Forming Analysis on the Effect of Ultra-Thinning of Sheet Metals Based on a Stress Rate Direction-Dependent Constitutive Model

In formability evaluation, it is important to accurately predict the onset timing and morphology of fracture in a workpiece from a physical point of view. The authors have developed a material model based on the stress rate direction-dependent constitutive equation, which is a non-normality law model, and applied it to forming analyses. The authors have also developed a forming limit prediction method based on the three-dimensional local bifurcation theory, which can theoretically predict the forming limits of arbitrary sheet and bulk metals. In this study, these methods are applied to evaluate the formability of thin and ultra-thin metallic sheets. The proposed model was applied to a square cylinder drawing analysis, and the accurate evaluation of the local necking allowed us to capture the transition of the fracture zone in response to changes in the amount of corner cut. In addition, appropriate forming parameters for ultra-thin sheets were also investigated. These analyses demonstrated the validity and usefulness of the proposed stress rate direction-dependent constitutive model.