Keywords: plasticity, hardening, yield curve, shear test, identification, finite element method.

Nowadays, sheet metal forming processes are far more complex than they were in the past and consequently the role of the corresponding computer simulations, based on physical, mathematical and numerical modelling of those processes, has become very important. There are many products in sheet metal forming, where during the production process, the limits of the material capability are almost exhausted. It is therefore very important that the sheet response is accurately described in constitutive models also at large plastic strains. The latter is the subject of this paper, which deals in particular with the identification of the hardening behaviour of the sheet metal at large plastic strains. A well known and frequently used test for the determination of the hardening behaviour is the standard tensile test. Unfortunately, the occurrence of plastic instability at relatively low plastic strains referred frequently as neck occurrence or necking destroys the uniformity of stresses and strains. Thus, determination of hardening after the onset of necking with the use of tensile tests becomes very complicated. In engineering practice a more or less appropriate extrapolation technique with different hardening laws (Swift, Voce, Gosh, etc.) are frequently used, but they often fail to predict the hardening behaviour of sheet metal at large plastic strains. To overcome such experience this paper presents a reliable identification of the hardening curve of sheet metal after the onset of necking using the shear test developed, for which no further development of the experimental equipment regarding standard tensile test is required. The only modification of standard tensile test is a particularly designed symmetric shear specimen, which enables the achievement of large shear strains during the stable loading condition. Two main advantages originate from the use of such a specimen. First, such a test reveals the hardening behaviour of the sheet metal beyond the plastic strains, at which instability (necking) in the case of tensile test occurs, and second, the test provides the information about yielding in shear affected regions. In order to take advantage of the shear test, computer-aided identification of the material data parameters are required for the optimization procedure employed. In addition, the paper presents the hardening curve approximation based on the cubic spline techniques. Such an approach is very convenient for use, because splines are smooth and are able to approximate accurately local curvatures without the global estimation being influenced. The main conclusion of this paper is, that the characterization of the hardening at large strain by applying the analytical continuation of a respective functional relationship established prior to necking, (i.e. upon performed tensile tests only), is seriously flawed as a result of the large differences between the curves obtained.

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