Identification of the post-necking hardening behaviour of sheet metal by comparison of the internal and external work in the necking zone

The most common way to evaluate the stress–strain relation of sheet metal is by performing standard tensile tests. However, those tests only allow the identification of the hardening behaviour up to the point of maximum uniform elongation, at least when using standard measuring equipment and simple analytical formulas to derive the relation between force and stress, and, elongation and strain. Usually the hardening behaviour beyond this point is estimated by extrapolation of the hardening behaviour before the point of maximum uniform elongation. Such procedure may yield very different results, depending on the hardening law which is fitted to the available experimental data. Other methods which deal with the problem of extended yield curve identification have been proposed and the most applied among them are finite-element based inverse approaches. This paper presents an alternative method to identify the post-necking hardening behaviour of sheet metal without using a finite element model. The key point in the presented method is the minimization of the discrepancy between the internal and external work in the necking zone during a tensile test. The main focus of this paper is on the presentation of the method, the underlying assumptions and the experimental validation. In addition, the method was applied to identify two common hardening laws for DC05, which is a mild deep drawing steel, using experimental data from the pre- and post-necking region.