ANISOTROPIC PLASTIC POTENTIALS FOR POLYCRYSTALS AND APPLICATION TO THE DESIGN OF OPTIMUM BLANK SHAPES IN SHEET FORMING

Recently, some Potentials were proposed to analytically describe the plastic behavior of orthotropic metals. These potentials, when expressed in six-dimensional stress space, were called yield functions or, when expressed in six-dimensional strain-rate space, were called strain-rate potentials. It was shown that these phenomenological potentials provide good approximations of the plastic potentials calculated with polycrystal models. They can be used for any type of loading condition, and they can account for orthotropic anisotropy. In a parallel effort, called ideal forming theory, a forming design theory that optimizes processes and initial blank shapes in sheet forming was developed. This ideal forming theory was implemented in a finite element modeling code in order to design the blank shape directly from the final part shape. The main input to this model includes the final part geometry and the constitutive behavior of the material. In the present article, the constitutive equations describing the plastic behavior of metals as well as the main features of the ideal forming theory are briefly summarized. Then, application of the strain-rate potential to the design of a blank shape for a circular cup drawn from an anisotropic Al-Li sheet is presented. It is shown that the design code efficiently predicts the shape of the blank needed to obtain a cup with minimal earing from a highly anisotropic material.