Microscopic Deformation Behavior and X-Ray Elastic Constants in Polycrystalline Metals (Influence of Grain Shape)

The influence of the grain shape on the microscopic deformation of polycrystalline metals was studied analytically by the finite element method in the uniaxial elastic deformation. In the present analyse, a plane model of polycrystals was used and the elastic constants of the polycrystals and the X-ray elastic constants were also calculated. The stress in individual grains became uniform when the grain was oblate in the direction of the applied stress, while the strain became uniform when it was prolate. The stress at the region across the grain boundary changed with the crystal orientation and the shape of the grains, and it was closely related to the deformation of the grain. The elastic constant was affected by the shape of the grains, indicating that the anisotropic properties in the polycrystals arose from the elongated grains. The influence of the grain shape on the X-ray elastic constants S1, S2/2 was dependent on the diffraction plane. In the case of α-iron, the influence on S1 was small for the reflection from the (211) planes.