Abstract
In the present paper, the elastic deformation of polycrystalline metals under uniaxial stress was studied microscopically using a plane model of polycrystals. The stress and strain in a round crystal embedded in a homogeneous medium were analyzed by the finite element method, and the elastic constants of the bulk specimen and the lattice strains in grains reflecting X-rays were calculated.
The results obtained are summarized as follows.
(1) The stress in a grain calculated with the present model changes from that of a uniform local stress model to that of a uniform local strain model according to the change of crystal orientation in regard to the direction of applied stress.
(2) The elastic constants of polycrystalline metals are affected by the condition of restriction of grains, and it is closely related to the extent of elastic anisotropy of crystal whether the influence is large or not.
(3) The influence of restriction of grains on the mean value εψ of lattice strain for the grains reflecting X-rays is relatively small and the εψ/σ-sin2ψ relation and X-ray elastic constant (-ν/E)X-ray based on the present model are comparatively close to those of a uniform local stress model.
