On the effect of the ratio between the yield stresses in shear and in uniaxial tension on forming of isotropic materials

Abstract

It is generally believed that the choice of the yield criterion used to describe the plastic behaviour of isotropic metallic materials does not affect much the accuracy of the predictions of forming operations. For this reason, the von Mises yield criterion is used for modelling the plastic behaviour. However, according to the von Mises yield criterion, irrespective of the material, the ratio between the yield stresses in simple shear and in uniaxial tension is the same. In this paper, it is presented a numerical study which reveals that even for one of the simplest deep drawing processes, namely the forming of a cylindrical cup, the yielding description influences the predictions of the plastic strains and the final profile of the part. For the description of yielding, an isotropic yield criterion which allows to differentiate between isotropic materials was used. Specifically, this yield criterion involves a parameter α which is expressible solely in terms of the ratio between the yield stresses in shear and in uniaxial tension; for α = 0 it reduces to the von Mises yield criterion. The results of the numerical study are revealing and are believed to provide a new point of view when considering material requirements for drawing performance and models to be used for prediction of the plastic behaviour in deep-drawing processes. From the analysis of the loading paths that the materials experience during the forming of the cup, it appears that the prevalent belief that the yielding properties in the tension-tension quadrant of the yield surface dictate the final profile should be reconsidered. Indeed, the simulations results indicate that for isotropic materials characterized by α > 0 (σT/τY> √ 3), the cup height is greater than for a von Mises material (α = 0), which is higher than the one obtained for materials with α < 0 (σT/τY< √ 3), i.e. lower values of the ratio between the yield stresses in shear and in uniaxial tension lead to greater cup heights. It is shown that this is mainly related to the plastic deformation of the material initially located in the flange region, which is dictated by the shape of the yield surface in the compression-tension quadrant (i.e. normal to the yield surface in the region between uniaxial compression and pure shear stress states).