The Voigt model case

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Abstract
Diffraction elastic constants connect residual or applied macro-stresses to measured diffraction elastic line-shift strains. They have the dimension of compliance and supply a means of determining unknown macro-stresses from measured strain data. For texture-free materials the diffraction elastic constants can be calculated for the Reuss, Voigt or Kröner models of elasticity. The latter model yields results very close to physical reality. The Reuss and Voigt models lead to two extreme solutions. The Kröner solution is in most cases very close to the arithmetic mean of the Reuss and Voigt solutions which conforms to the Hill approximation. For textured materials, use of the Kröner model (based on a self-consistent method) is not (yet) feasible. The diffraction elastic constants for textured materials according to the Voigt model are derived in this paper. It is shown that only three orientation distribution function (o.d.f.) series-expansion coefficients are necessary for the calculations conforming to earlier derivations. The Hill approximation can also be applied to the case of textured materials. The Reuss-model diffraction elastic constants have been derived earlier for these materials. Averaged with the Voigt-model data obtained in this paper they may lead to a realistic approximation of the diffraction elastic constants. Consequently, determination of unknown macro-stresses in textured materials may be performed to a higher degree of accuracy.