The Voigt model case

Abstract

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 Kroner models of elasticity. The latter model yields results very close to physical reality. The Reuss and Voigt models lead to two extreme solutions. The Kroner 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 Kroner 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 conformi...