A general framework for generating convex yield surfaces for anisotropic metals
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The aim of this paper is to develop a general procedure to create yield surfaces (both isotropic and anisotropic) for elastic plastic metals with particular reference to sheet metal forming operations. Due to the fact that the forming limit of sheet metals requires a very accurate prediction of the yield limits and their normals, it is desirable to create yield functions that offer independent control of the yield points and the normal to the yield surface at a particular stress state without affecting its global convexity properties and the yield points at other states of stress. We achieve this by creating a class of yield surfaces that are obtained by the intersection of a number of elementary convex surfaces (such as planes and cylinders); the edges and corners that are a result of the intersection are smoothened by Lp-norm smoothing technique to give rounded comers. The yield surfaces generated by this procedure are centrosymmetric in nature and are thus limited in their applicability. We show that many of the standard yield surfaces can be recast into this form. We obtain a new yield surface that fits the experiments obtained for the 6022-T4 aluminum alloy as reported by Barlat et al. The same yield surface is also used to fit the results of the Taylor-Bishop-Hill polycrystal theory applied to a material with copper texture. The data were obtained from Choi et al.
