On the third-order elastic constants of polycrystalline media

Expressions for the third-order elastic constants of polycrystalline media in terms of their single-crystal elastic constants are obtained by the direct method due to Voigt. For materials like Cu, Al, Fe, Nb, Mg and Al₂O₃, for which experimental data on third-order elastic constants of both polycrystalline and single-crystal forms are available, the calculated and experimental values are compared. It is found that the agreement is good in those cases in which the grains are uniform in size and nearly randomly oriented in the polycrystalline specimens. This raises the question whether it is meaningful to talk of uniform-strain (Voigt) and uniform-stress (Reuss) approximation for the third-order elastic constants of polycrystalline media. The present analysis may have some relevance to the recently synthesized nanophase materials.