Polycrystal elastic constants for triclinic crystal and physical symmetry

Abstract

The problem of obtaining the Voigt average for the elastic stiffnesses with texture-describing weight functions has been solved for triclinic crystal and physical symmetries. The average is obtained by expanding theTijklmnpq, which relate the elastic stiffnesses in the rotated reference frame, c^{\,\prime}_{ijkl}, to those of the principal elastic stiffnesses,cmnpq, in generalized spherical harmonics, multiplying by the orientation distribution function and integrating over all orientations. The condition imposed to assure a unique expansion results in the absence of terms with oddL, so that the results are completely determinable from conventional X-ray pole figures. This is the most general case, from which all higher-symmetry solutions may be obtained by application of symmetry operations. The Reuss average for elastic compliances may be obtained in a similar fashion.