Relation between Diffraction Young's Modulus Ratio and Elastic Anisotropy in Metals

Abstract

Elastic anisotropy of polycrystalline metals can be evaluated by the difference in diffraction Young's modulus of each crystal plane {hkl} and the values of Young's modulus are theoretically calculated applying the stiffness; C₁₁, C₁₂ and C₄₄ to the Reuss and Voigt model. In this paper, the values of diffraction Young's modulus E^*_hkl are calculated by the Reuss-Voigt average model for pure iron (bcc), austenitic steels (fcc), nickel (fcc), copper (fcc) and aluminum (fcc) and then the Young's modulus ratio ω_hkl=(E^*_hkl/E₀) is proposed to evaluate the relative elastic anisotropy. Here, E₀ denotes the value obtained by the Voigt model. The value of E₀ can be estimated from the experimentally obtained Young's modulus E_m for polycrystalline metals by the equation; E₀≒1.13E_m. It was also found that there is good correlation between the anisotropy parameter A_i (=2C₄₄/(C₁₁-C₁₂)) and ω_h00=(E^*_h00/E₀).