The anisotropy of Young's modulus, shear modulus and Poisson's ratio in cubic materials

Abstract

The directional behaviour of Young's modulus, shear modulus, and Poisson's ratio are expressed for a number of crystallographic planes for cubic materials. Their behaviour as a function of direction on a particular plane is shown to be a simple sum of sines and cosines of twice and sometimes of four times the angle. A general expression gives the coefficients for the sines and cosines and a table gives the coefficients for 19 planes on the standard triangle of the stereographic projection. Superposed on the stereographic projection are shown polar plots of the shear modulus Gprime12 (1prime direction normal to the plane) for silicon. Examples are also given showing G12prime for copper for some planes of zones [1bar above 00], [1bar above 10] and [2bar above 10].