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 (${\sigma }_{\mathrm{T}}/{\tau }_{\mathrm{Y}}$>$\sqrt{3}$), 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 (${\sigma }_{\mathrm{T}}/{\tau }_{\mathrm{Y}}$<$\sqrt{3}$), 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).

一般认为，用于描述各向同性金属材料塑性行为的屈服准则的选择对成形操作预测的准确性没有太大影响。出于这个原因，von Mises 屈服准则用于对塑性行为进行建模。然而，根据 von Mises 屈服准则，无论材料如何，简单剪切和单轴拉伸下的屈服应力之比是相同的。在本文中，提出了一项数值研究，该研究表明，即使是最简单的深拉工艺之一，即圆柱形杯的成型，屈服描述也会影响塑性应变的预测和零件的最终轮廓。对于屈服的描述，使用了允许区分各向同性材料的各向同性屈服准则。具体而言，该屈服准则涉及参数 α，该参数仅用剪切屈服应力和单轴拉伸屈服应力之间的比值表示；对于 α = 0，它简化为 von Mises 屈服准则。数值研究的结果具有启发性，并被认为在考虑拉拔性能的材料要求和用于预测深拉工艺塑性行为的模型时提供了新的观点。从对材料在杯子成型过程中所经历的加载路径的分析来看，似乎应该重新考虑屈服面的张力-张力象限中的屈服特性决定最终轮廓的普遍看法。确实，${\sigma }_{\mathrm{吨}}/{\tau }_{\mathrm{是}}$>$\sqrt{3}$)，杯子高度大于 von Mises 材料 (α = 0)，高于 α < 0 (${\sigma }_{\mathrm{吨}}/{\tau }_{\mathrm{是}}$<$\sqrt{3}$)，即剪切屈服应力和单轴拉伸屈服应力之间的比值越低，杯子高度越大。结果表明，这主要与最初位于法兰区域的材料的塑性变形有关，这取决于压缩-拉伸象限中屈服面的形状（即垂直于单轴之间的区域中的屈服面）。压缩和纯剪应力状态）。