FINITE-ELEMENT METHOD FOR SHEET FORMING BASED ON AN ANISOTROPIC STRAIN-RATE POTENTIAL AND THE CONVECTED COORDINATE SYSTEM

Abstract

A variational formulation and the associated finite element (FE) equations have been derived for general three-dimensional deformation of a planar anisotropic rigid-plastic sheet metal which obeys the strain-late potential proposed by Barlat et al. [Int. J. Plasticity 9, 1 (1993)]. By using the natural convected coordinate system, the effect of geometric change and the rotation of planar anisotropic axes were efficiently considered. In order to check the validity of the present formulation, a cylindrical cup deep drawing test was modeled for a 2008-T4 aluminum alloy sheet sample. Earing simulations were performed and planar anisotropic material properties were experimentally determined. Even though quantitative agreement was not fully achieved, reasonably good agreement was found between the FE simulation and the experiment in thickness strain distribution and earing. No numerical difficulty due to planar anisotropy was encountered, and the computational procedure was found to be very stable, requiring only moderate computational time. The results have shown that the present formulation for planar anisotropic deformation can provide a good basis for the analysis of sheet metal forming processes for planar anisotropic materials, especially for aluminum alloy sheets.