Anisotropy of Deformation and X-Ray Elastic Constants in Polycrystalline Metals

The states of stress and strain in grains were analyzed with a plane model of polycrystals in a uniaxial elastic deformation. The finite element method is adopted and the elastic constants of polycrystalline metals and X-ray elastic constants were calculated. The strain is nearly uniform in the region across the grain boundary parallel to the stress axis, while the stress is uniform when the grain boundary is perpendicular to the stress axis. It follows that, in the case of grains having a small value of Young's modulus, there is a stress concentration at the region near the grain boundary parallel to the stress axis. The elastic constants of polycrystals change under the condition of the restriction of grains, which is caused by the elastic anisotropy of the crystal. The X-ray elastic constants S₁ S₂/2 are close to those calculated by the Reuss model. In this case, S₂/2 is not much affected by the restriction of grains.