Study of the elastic properties of hexagonal metal single crystals

Hexagonal metals (e.g., Be, Zr, Ti) are widely used in the nuclear industry, space and aircraft engineering (in manufacturing of the structural elements operating under extreme conditions). A promising way to improve the quality of products made of them is to improve the physical properties of materials using the natural anisotropy of metal single crystals. The results of studying anisotropy and a comparative analysis of the technical characteristics of the elastic properties of single crystals of hexagonal metals are presented. The equations of the elastic compliance matrix components are derived in the explicit form for arbitrary crystallographic direction proceeding from transformations of the elastic compliance tensor in the principal axes to a new arbitrary coordinate system with a subsequent use of Euler angles. Analytical expressions are presented for the technical characteristics of the elastic properties (shear and Young's moduli, Poisson's ratio) of the single crystals of 10 hep metals for an arbitrary crystallographic direction. The axial symmetry of the characteristics about the hexagonal axis is revealed. The sums of the elastic compliance coefficients which determine the shear moduli and the Poisson's ratios in two mutually perpendicular directions are constant in any crystallographic plane of the single crystal. A comparative analysis of the anisotropy of the elastic properties of single crystals of the studied group of metals revealed auxetic properties of Zn and Be single crystals and the region of crystallographic directions of uniaxia tension, leading to an auxetic effect The auxetic effect in Zn was observed under tension in the directions of the plane perpendicular to the hexagonal axis of the single crystal. The planes of the auxetic effect manifestation in Be single crystals are perpendicular to the directions making an angle of 45° with the hexagonal axis.