Inverse identification of the work hardening law from circular and elliptical bulge tests

An inverse identification strategy is proposed to characterize the hardening behaviour of metal sheets up to high strains, regardless of the material anisotropy. The Levenberg-Marquardt method is used to minimize the gap between the experimental and numerical, pressure vs. pole height curves, of bulge tests with circular and elliptical dies, by iteratively updating the work hardening and the Hill'48 parameters of the numerical model. The optimization of the Hill'48 parameters is used only to ensure that the yield surface is conveniently described in a region close to the stress paths that occur in the circular and elliptical bulge tests, in order to improve the identification of the hardening parameters. The strategy aims to be accurate and simple from an experimental point of view, using only the results of pressure vs. pole height. The results are compared with those of the membrane theory procedure standardized in ISO 16808 (2014) and experimentally validated for two materials, DP600 steel and Al5754 aluminium alloy. For anisotropic materials, the proposed methodology represents a clear improvement when compared to the membrane theory procedure since it avoids the equibiaxial stress state assumption.