Anisotropic plastic potentials for polycrystals and application to the design of optimum blank shapes in sheet forming
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INTRODUCTION
C O M M O N practices for optimizing forming processes are based on trial and error methods wherein various combinations of process parameters are evaluated experimentally and analytically. Because of the indirect nature of experimental and analytical methods, it usually takes a significant number of iterations to obtain optimal processes. To overcome the indirect nature of analytical and experimental methods, a direct design theory called ideal forming theory was developed previously by Chung and Richmond tl-4~ to obtain optimum process parameters. This theory provides direct information regarding the optimum parameters in the design stage of processes. A major difference between this design theory and an analytical theory is that, in the former case, material elements are prescribed to deform along minimum plastic work paths. It is assumed that such paths provide optimum formability. Then, the optimum forming processes are obtained so as to have the most uniform strain distributions in final products. Besides the optimum strain distribution, this design theory provides the optimum initial blank shape as well as intermediate shapes of products and boundary traction histories that are the ideal forming process parameters. One important input to this theory is the plastic behavior of the material to be formed. Modeling of forming processes requires a good description of the constitutive behavior of materials, tSj At room temperature, the plastic flow of metals can be described with a plastic potential and its associated flow rule. This potential can be obtained from polycrystal F. BARLAT and K. CHUNG, Scientific Associates, and O. RICHMOND, Corporate Fellow, are with Alcoa Technical Center, Alcoa Center, PA 15069-0001. Manuscript submitted September 1, 1993. METALLURGICAL AND MATERIALS TRANSACTIONS A
models that are based on the microscopic mechanisms of plastic deformation. However, the use of such a potential, which is described by an array of points, is not efficient for practical numerical simulations of metal forming. Phenomenological descriptions of the plastic behavior of textured polycrystals seem to be more suitable for this purpose. Recently, some potentials were proposed to describe the plastic behavior of orthotropic metals analytically, t6-1~ One of these potentials, a yield function, was expressed in six-dimensional stress space, tTj whereas another one, a strain rate potential, was expressed in six-dimensional strain-rate space, t9j 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 incorporate the effects of orthotropic anisotropy. In this work, a brief description of both the phenomenological potentials and the ideal forming design theory is given. Then, the design theory is used along with the strain-rate potential as the material description. For demonstration purposes, an application to the design of the blank shape for minimal earing cup drawing
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