A hybrid approach for the efficient computation of polycrystalline yield loci with the accuracy of the crystal plasticity finite element method

Abstract

Direct experimental evaluation of the anisotropic yield locus (YL) of a given material, representing the zeros of the material’s yield function in the stress space, is arduous. It is much more practical to determine the YL by combining limited measurements of yield strengths with predictions from numerical models based on microstructural features such as the orientation distribution function (ODF; also referred to as the crystallographic texture). For the latter, several different strategies exist in the current literature. In this work, we develop and present a new hybrid method that combines the numerical efficiency and simplicity of the classical crystallographic yield locus (CYL) method with the accuracy of the computationally expensive crystal plasticity finite element method (CPFEM). The development of our hybrid approach is presented in two steps. In the first step, we demonstrate for diverse crystallographic textures that the proposed hybrid method is in good agreement with the shape of the predicted YL estimated by either CPFEM or experiments, even for pronounced plastic anisotropy. It is shown that the calibration of only two parameters of the CYL method with only two yield stresses for different load cases obtained from either CPFEM simulations or experiments produces a reliable computation of the polycrystal YL for diverse crystallographic textures. The accuracy of the hybrid approach is evaluated using the results from the previously established CPFEM method for the computation of the entire YL and also experiments. In the second step, the point cloud data of stress tensors on the YL predicted by the calibrated CYL method are interpolated within the deviatoric stress space by cubic splines such that a smooth yield function can be constructed. Since the produced YL from the hybrid approach is presented as a smooth function, this formulation can potentially be used as an anisotropic yield function for the standard continuum plasticity methods commonly used in finite element analysis.