Young’s Modulus of Single Crystalline Iron and Elastic Stiffness

Abstract

Elastic stiffness c₁₁, c₁₂ and c₄₄ are key parameters in the analysis of elastic deformation behaviors. In order to determine the values of these parameters, Young’s modulus of single crystal; E₁₀₀, E₁₁₀ and E₁₁₁ are needed as well as Young’ modulus Ep and Poisson’s ratio ν in poly-crystal. In this paper, the values of Young’s modulus in single crystalline iron are summarized and then elastic stiffness was estimated for pure iron under the conditions; E_p=208.2 GPa and ν=0.291 that are reliable values for isotropic poly-crystalline iron. As a result, it is found that Young’s modulus of single crystalline iron should be as follows: E₁₀₀=127.8 GPa, E₁₁₀=214.3 GPa, E₁₁₁=276.6 GPa. From these values, elastic stiffness of iron is calculated at c₁₁=228.1 GPa, c₁₂=135.0 GPa, c₄₄=113.2 GPa. Diffraction Young’s modulus of iron can be estimated on the basis of Kröner model by applying the values of elastic stiffness. It is also confirmed that the average value of diffraction Young’s modulus agrees with the value of Young’s modulus E_p (208.2 GPa) of ideal poly-crystalline iron.