Inverse identification of the Swift law parameters using the bulge test

An inverse methodology is proposed for determining the work hardening law of metal sheets, from the results of pressure vs. pole height, obtained from the bulge test. This involves the identification of the parameters of the Swift law. The influence of these parameters as well as the sheet anisotropy and the sheet thickness on the results of pressure with pole height is studied following a forward analysis, based on finite element simulation. This allows understanding that the overlapping of the pressure vs. pole height curves of different metal sheets is possible, provided that the hardening coefficient has the same value, whatever the values of the remaining parameters of the Swift law, the sheet anisotropy and the initial sheet thickness. The overlapping of the curves is performed by multiplying the values of the pressure and the pole height using appropriate factors, which depend on the ratios between the yield stresses and the thicknesses of the sheets, and also on their anisotropy. Afterwards, an inverse methodology is established, consisting of the search for the best coincidence between pressure vs. pole height of experimental and reference curves, the latter being obtained by numerical simulation assuming isotropic behaviour with various values of the Swift hardening coefficient in the range of the material under study. This methodology is compared with a classical strategy and proves to be an efficient alternative for determining the parameters of the Swift law. It aims to be simple from an experimental point of view and, for that purpose, only uses results of the load evolution during the test. The methodology is limited to materials with the hardening behaviour adequately described by the Swift law.