Elastic constants in ideal poly-crystalline metals

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).