Mechanical field fluctuations in polycrystals estimated by homogenization techniques

The fluctuation of mechanical fields arising in polycrystals is investigated. These materials are viewed as composites of the Hashin–Shtrikman type with a large number of anisotropic phases and a ‘granular’ topology. We show that the estimation of the intra–phase stress and strain (rate) second moments comes down to the resolution of a linear system of equations. Applied to a linear viscous face–centred cubic (FCC) polycrystal, it is observed that significant local slip rates are estimated even when the corresponding Schmid factor vanishes, due to the intergranular interactions. For the application to viscoplastic polycrystals, the secant and affine nonlinear extensions of the self–consistent scheme are compared. At large stress sensitivity (n = 30), it is observed that the secant linearization leads to almost uniform slip rates for all slip systems in every phase, whereas the affine approach predicts a much larger spread. Furthermore, there is no one–to–one relation between the phase–average stress (or strain rate) and the corresponding second moment. It is emphasized that intra–phase strain–rate heterogeneities should be accounted for when dealing with microstructure evolution.