A study of the Yld2004 yield function and one extension in polynomial form: A new implementation algorithm, modeling range, and earing predictions for aluminum alloy sheets

As shown recently in (Soare and Barlat, 2010. Convex polynomial yield functions. J. Mech., Phys. Solids, 58, 1804–1818), the principal values based yield function Yld2004, proposed in (Barlat et al., 2005. Linear transformation based anisotropic yield function. Int. J. Plast., 21, 1009–1039), is polynomial for integer exponents. Based on this observation, a new algorithm is proposed for implementing symmetric yield functions formulated in terms of principal values. The algorithm is tested here by simulating with a commercial FE code the cylindrical deep drawing of two aluminum sheets. It is found that the classical description of the in-plane directional properties of the sheet (uniaxial r-values and yield stresses), even if modeled correctly by the yield function, is not sufficient for a unique characterization of the predicted earing profile. For certain combinations of the directional properties the r-value in biaxial stressing has to be considered for a correct calibration of the material model. This in turn requires a finer detail in yield surface modeling and, to achieve it, an ad-hoc extension of Yld2004 is constructed. In combination with the proposed implementation algorithm, the extension is shown to be a useful research tool, having some interesting modeling capabilities and satisfactory FE runtime.