Variational self-consistent estimates for texture evolution in viscoplastic polycrystals

Abstract

The variational self-consistent (V-SC) method is presented for simulating texture evolution in viscoplastic polycrystals undergoing large deformation. The theory is based on a recent non-linear homogenization procedure which makes use of estimates of the self-consistent type for the instantaneous response of a suitably chosen “linear comparison polycrystal” to generate corresponding estimates for the non-linear viscoplastic polycrystal. Making use of consistent estimates for the average strain rate and spin in the grains of the polycrystal, and of standard kinematical arguments, evolution equations are derived for the crystallographic and morphological textures. Applications to titanium polycrystals under uniaxial tension, compression and plane-strain compression performed at 750 °C are presented. The texture predictions and macroscopic stress–strain responses are compared with those given by earlier models, and with finite element (FEM) simulations and experimental measurements taken from the literature. Better overall agreement with FEM simulations is obtained for the V-SC estimate than for the other models. However, the comparison with the experimental results is not as good, especially for plane-strain compression, where additional effects due to friction cannot be ruled out.