A plane stress yield function for anisotropic sheet material by interpolation of biaxial stress states

An anisotropic plane stress yield function based on interpolation by second order Bézier curves is proposed. The parameters for the model are readily derived by four mechanical tests: a uniaxial, an equi-biaxial and a plane strain tensile test and a shear test. In case of planar anisotropy, this set of tests must be repeated for a number of directions. An arbitrary number of directions can be incorporated in the model. This flexibility can be used to describe, e.g., the yield stress and R-value as a function of the loading direction more accurately than with other common analytical yield functions. The relevance of an accurate description of the yield locus and the flexibility of the proposed yield function are demonstrated by the prediction of forming limit diagrams. It is demonstrated that the sensitivity of the FLD to small changes in the yield locus can also be used to determine some of the material parameters by inverse analysis.