Anisotropic elasto-plastic finite element analysis using a stress–strain interpolation method based on a polycrystalline model

This paper describes a stress–strain interpolation method to model the macroscopic anisotropic elasto-plastic behavior of polycrystalline materials. Accurate analytical descriptions of yield loci derived from crystallographic texture [Int. J. Plasticity 19 (2003) 647; J. Phys. IV France 105 (2003) 39] are an interesting alternative to finite element models, where the macroscopic stress is provided by an averaging of microscopic stresses computed on a set of representative crystallites [Acta Metal 22 (1985) 923; Int. J. Plasticity 5 (1989) 67]. The parameters of the analytical functions modeling the yield locus are identified by comparison with a high number of stress tensors computed, for instance, by the well-known Taylor model [J. Inst. Metal 62 (1938) 307]. This identification method depends on the crystallographic texture and should be applied each time that the plastic strain has induced a significant texture evolution. The stress–strain interpolation method accurately describes the anisotropic material behavior in a narrow stress direction defined by only five stress points. The cost of texture updating is then greatly reduced compared to a full analytical function of the yield locus. After the mathematical description of the stress–strain interpolation method, its validity is demonstrated on two non-radial strain paths. The simulations of a deep drawing experiment allow comparing model predictions and measurements. Accuracy and CPU time of the interpolation stress–strain method are judged against two other models, respectively based on a complete analytical yield locus and on the averaging of crystallite stresses.