XXXIV. The correction of elasticity measurements on slightly anisotropic materials

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Abstract
Expressions are derived for the average elastic constants of a poly-crystalline bar, having circular symmetry about its principal axis, and composed of material with cubic crystal symmetry. It is shown that the differences between these and the corresponding constants obtained for a material with completely random orientation depend in each case on the same function of the crystal orientation distribution, and therefore the complete elastic behaviour of the material may be determined from measurements of three independent quantities. In particular, it is shown how the true elastic constants of an isotropic specimen may be determined from the results of a series of longitudinal and torsional resonance tests, or from three measurements of travel-time of high-frequency pulses of mechanical energy through the material. When the orientation distribution is expressed in terms of zonal harmonics it is found that elastic anisotropy is caused solely by the presence of the component P 4 (cos θ). Stereographic charts are included showing the texture corresponding to this and three higher harmonics, thereby establishing a relation between the elastic behaviour of cubic materials and the results of x-ray measurements.

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