Three-dimensional finite-element method simulations of stamping processes for planar anisotropic sheet metals

摘要

A three-dimensional finite-element method (FEM) was developed to simulate forming processes with arbitrarily shaped tools for planar anisotropic sheet metals. An implicit, updated Lagrangian formulation based on an incremental deformation theorywas employed along with a rigid-viscoplastic constitutive equation. Contact and friction were considered using the mesh-normal scheme which compatibly describes arbitrary tool surfaces and FEM meshes without depending on the explicit spatial derivativesof tool surfaces. The consistent full set of governing relationships, which includes the equilibrium equation and mesh-normal geometric constraints was appropriately linearized. Based on membrane approximation, linear triangular elements were used todescribe formed sheets. The non-quadratic strain-rate potential previously developed by Barlat et al. was employed to account for the in-plane, anisotropic properties of sheets. Numerical simulations were performed for the deep drawing of a cylindricalcup and the stamping of an automotive front fender panel to test the planar anisotropic finite element code. In the cup-drawing analysis of a 2090-T3 aluminium alloy sheet sample, the predicted earing profile and cup height were compared with experiments. The predicted and experimental thickness strains were in relatively good agreement, even though thinning trends between rolling and transverse directions were reversed. In the fender stamping analyses of both the aluminum alloys and a mild steel sheet,the numerical stability, accuracy, and usefulness of the formulation were confirmed for automotive applications. In-plane, anisotropic effects on the forming limit curves are also discussed.