On the identification of material hardening for anisotropic sheets via bulge tests

The hydraulic bulge test provides a useful tool to characterize the mechanical behavior of sheet metal under nearly equibiaxial loading, such as the material hardening response. However, the kinematic relationships during bulge tests of anisotropic sheets are still less understood and need further clarification. To this end, extensive numerical simulations of bulge tests are first performed, covering different die geometries and materials that exhibit distinct hardening features and Hill48 anisotropy. Based on the general scaling laws of the kinematic relationships, the numerical results are then used to establish an analytical model that explicitly relates the dome height, apex strain, and radii of curvatures in terms of the die ratio, material hardening parameter, and anisotropy. In addition, the general extraction procedure, which incorporates the analytical model to obtain the hardening responses of anisotropic sheets, is also provided. Finally, the effectiveness of the analytical model is confirmed based on representative results of AA6061 and DP600 sheet experiments and supplementary numerical simulations. The proposed model is expected to help facilitate the application of bulge tests in characterizing the plasticity and forming behavior of anisotropic sheet materials.