INVARIANTS IN ELASTIC PROPERTIES OF METAL SINGLE CRYSTALS OF CUBIC SYMMETRY

Abstract

The equations of the elastic compliance matrix components are derived for arbitrary crystallographic directions determined by the Euler angles for cubic single crystals using the approach [4] developed by the authors which consists in transformation of the elastic compliance tensor in the principal axes into an arbitrary coordinate system with subsequent use of the Euler angles. Euler’s angles are applied in the following format: rotation around the hexagonal axis z (azimuth angle α), inclination of the hexagonal axis to an arbitrary position z’ (polar angle β), rotation around the new position of z’ axis (shear direction angle γ). Analysis of the equations derived for the components of elastic compliance matrix for cubic single crystals revealed invariant combinations of the components which, in turn, revealed relations between technical characteristics of the elastic properties of cubic single crystals: Young’s modulus along an arbitrary crystallographic direction, shear modulus and Poisson’s coefficients in a plane perpendicular to the selected crystallographic direction, shear modulus under torsion around this direction, and others. The validity of the obtained relations is verified in the calculations done for arbitrary crystallographic directions and various cubic single crystals. Calculations for single crystals of copper and nickel are presented.