Analytical procedures for the determination of the anisotropy parameters of the non-quadratic orthotropic Yld91 yield function for extruded materials

Abstract

For extrusion materials, generating data for various orientations is very challenging, so the parameters involved in anisotropic yield criteria must be estimated using limited data. Except for Hill (1948)model, parametrization of anisotropic models is done numerically, and the quality of the predictions is strongly dependent on the quality of the parametrization. Recently, Cazacu (2018) has demonstrated that the 3-D anisotropic yield criterion Yld91 can be rewritten as a polynomial in terms of the stress components. In this paper we specialize and use the Yld91 criterion and associated flow rule to model the behavior of extruded materials. Specifically, we provide analytical procedures for identification of the Yld91 criterion using only yield stresses or only Lankford coefficients. In either case, the datapoints used as input are the same as those required for Hill (1948)'s identification. First, illustration of the approach is provided for an extruded AA6060 material for which data is available only in a single plane. Next, we consider an extruded AA 7079, for which data is available in all the symmetry planes. For both materials, the influence of data subset used for parameterization on the quality of the predictions and the material response for multiaxial loadings is discussed.