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. (C) 2011 Elsevier Masson SAS. All rights reserved.X1156sciescopu