Anisotropic yield function of hexagonal materials taking into account texture development and anisotropic hardening

Because of twinning and texture evolution, the yield surface for hexagonal close-packed (hcp) metals significantly changes its shape with accumulated plastic deformation. Traditional hardening laws cannot accurately model these phenomena. In this paper, an anisotropic model that captures the influence of evolving texture on the plastic response of hcp metals is proposed. Initial yielding is described using a recently developed analytical yield function that accounts for both anisotropy and strength differential effects. To describe the change of the shape of the yield surface during monotonic loading, the evolution of the anisotropic coefficients involved in the expression of the yield function is considered. The evolution laws for the anisotropic coefficients are obtained based on experimental data and crystal plasticity theory, together with a macroscopic-scale interpolation technique. This approach is further applied to the description of the mechanical behavior of high-purity zirconium at room temperature. Validation of the proposed model is provided by applying it to the simulation of the three-dimensional deformation of a beam subjected to four-point bending along different directions with respect to the hard-to-deform 〈c〉-axis predominant orientation of the material. Comparison between predicted and measured macroscopic strain fields and beam sections shows that the proposed model describes very well the difference in response between the tensile and compressive fibers and the shift of the neutral axis.