Elastic Deformation of Polycrystals : Effects of Young's modulus, shear modulus and Poisson's ratio

Abstract

Elastic deformation of polycrystals under uniaxial and shear loadings is studied with the application of the idea of constraint ratio which represents the mode of deformation of polycrystals. Local deformation behavior of polycrystals is analysed using a plane rectangular model of polycrystals and the finite element method, where elastic constant of each grain is assumed to be represented by Young's modulus and Poisson's ratio. Discussions are made on the relation between the calculated local behavior and the overall deformation behavior of polycrystals. The value of constraint ratio of a grain in tension changes from constant stress to constant strain according to the changes of elastic constants of the neighbor grians. The change of constraint ratio is also affected by the aspect ratio of grains. The mean equivalent constraint ratio for polycrystals is defined when each grain in polycrystals has a different value of the mean constraint ratio. The effect of Poisson's ratio on deformation behavior of grains is found to be relatively small in general, while the effect of the transverse Young's modulus perpendicular to the stress axis is comparatively large. The mean constraint ratio in shear deformation takes its minimum value for a certain aspect ratio of grains. Discussions are dame on the relation between analytical and experimental values of elastic constants of polycrystals and those calculated from elastic constants of single crystal.