Elastic Constants in Ideal Poly-Crystalline Metals

Abstract

Metals have elastic anisotropy depending on the crystal orientation, so that Young’s modulus and Poisson’s ratio have different values depending on the crystal orientation. Diffraction analysis in poly-crystalline metals yields another type of Young’s modulus termed as “Diffraction Young’s modulus and diffraction Poisson’s ratio”. Generally, the elastic anisotropy is reduced in poly-crystal due to the interaction among crystal grains. This means that diffraction Young’s modulus and diffraction Poisson’s ratio reflect the elastic deformation behavior of each crystal grain in poly-crystalline metals. In the present investigation, an ideal poly-crystal model with isotropic crystal orientations is proposed and then the average values of diffraction Young’s modulus and diffraction Poisson’s ratio are estimated for poly-crystalline metals: Al, Cu, Ni, Fe(fcc), Fe(bcc), V, Mo and Cr. In ideal poly-crystalline metals, Poisson’s ratio and Young’s modulus were theoretically estimated as follows: Al(0.345, 71.0 GPa), Cu(0.340, 131.1 GPa), Ni(0.329, 196.1 GPa), Fe(fcc)(0.292, 199.3 GPa), Fe(bcc)(0.292, 204.7 GPa), V(0.355, 136.4 GPa), Mo(0.305, 316.5 GPa), Cr(0.214, 282.9 GPa).