Comparison of the Identifiability of Flow Curves from the Hydraulic Bulge Test by Membrane Theory and Inverse Analysis

Abstract

In the hydraulic bulge test, flow curves are determined by applying a hydrostatic pressure to one side of a clamped sheet metal specimen, which bulges freely into a circular cavity under the pressure. The pressure and various data such as bulge height, curvature and equivalent strain at the pole are recorded and used to calculate the flow curve of the specimen material using analytical equations based on membrane theory. In the determination of the flow curve, the elastic behavior of the specimen, the elastic-plastic transition and bending effects are neglected, and the flow curves calculated this way are affected by these simplifications. An alternative to this procedure is an inverse analysis, which proceeds by searching for a flow curve that minimizes the difference between computed and measured data, e.g. bulge height vs. pressure. An inverse analysis based on a finite element model takes into account elastic and bending effects but since it involves the solution of an optimization problem, it is not clear whether it yields more accurate results than membrane theory. The objective of this paper is to compare the ‘identifiability’ of a given flow curve from the bulge test by direct identification based on membrane theory and by inverse analysis with different objective functions to be minimized. Using a re-identification procedure, it is shown that an inverse analysis can improve the results of the direct identification if a suitable objective function is chosen.