Numerical prediction of the limiting draw ratio for aluminum alloy sheet

The numerical prediction of limiting draw ratio (LDR) using an explicit dynamic finite element code, LS-DYNA, is presented. A series of 10 different tooling geometries were modelled for a cylindrical-cup-drawing process, with the differences being variations in the die and punch profile radii. Three phenomenological yield criteria incorporating rolling-induced crystallographic texture effects (the Lankford coefficient and the yield exponent) are considered and their effect on the predicted strain distributions within drawn cups is assessed through comparison with measured strains. In general, transverse anisotropy is shown to have a large influence on the predicted strains whereas the influence of in-plane anisotropy is small. Reasonable agreement with measured strains is obtained using the Barlat-89 non-quadratic yield criterion. The LDR is predicted based on two methods: (i) proximity to the forming limit as characterized by a forming limit ratio (FLR) parameter calculated using predicted principal strains; and (ii) attainment of the peak punch force (PPF) corresponding to the maximum blank size that can be drawn into the die cavity without necking. The predicted LDR was in good agreement with that from experiment for tooling profile radii greater than 3 mm; however, the PPF method was less sensitive to variations in punch profile radius than were the FLR-based predictions. For the sharp 3 mm die radius tooling, the model over-predicts the LDR (unconservative) which suggests a change in the failure mechanism to a bending failure, since the bend radius-to-thickness ratio approaches the bendability limit for AA5754-O.