X-ray and Mechanical Elastic Constants of Polycrystalline Metals

Abstract

The values of mechanical and X-ray elastic constants of polycrystalline metals are closely related with the condition of restriction of grains during deformation. The idea of constraint ratio which is introduced to express the condition of mutual restriction and deformation behavior of grains in polycrystals quantitatively is now extended to a three-dimensional case. General relation between an arbitrary condition of three-dimensional restriction of grains and elastic constant of polycrystals in derived. Numerical discussion is made on the relation between deformation of grains and elastic constant of polycrystals for several metals with cubic lattice. The mean values of constraint ratio calculated from experimental values of elastic constant of the polycrystalline metals are 0.50-0.74. Based on three-dimensional constraint, discussion in also made on X-ray elastic constant which is necessary for X-ray stress measurement, especially on the restriction of surface grains as well as interior grains in specimen. It is concluded from the comparison with experimental data that the influence of specimen surface on X-ray elastic constant is relatively small.