Effective Elastic Properties of Textured Cubic Polycrystals

Mityushov, E. A.; Berestova, S. A.; Odintsova, N. Yu.

doi:10.1080/0730330021000000227

Cited by 7 publications

(1 citation statement)

References 18 publications

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“…The problem of relating micro and macro elastic stress and strain fields has been treated by Voigt (1887), Reuss (1929), Hill (1952), Eshelby (1957Eshelby ( , 1959, Krö ner (1958Krö ner ( , 1977, Hashin & Shtrikman (1963), Kneer (1964Kneer ( , 1965, Morris (1969Morris ( , 1970Morris ( , 1971, Hirsekorn (1990), Humbert et al (1991), Shermergor et al (1991), Kiewel & Fritsche (1994), Park et al (1995), Kiewel et al (1995Kiewel et al ( , 1996 and Mityushov et al (2002). Eshelby (1957Eshelby ( , 1959 used an ingenious sequence of hypothetical cutting, straining and rejoining operations to calculate the elastic properties of an isotropic matrix, containing a dispersion of ellipsoidal shaped isotropic inclusions having elastic properties different from those of the matrix.…”

Section: Introductionmentioning

confidence: 99%

Polycrystal elastic constants for triclinic crystal and physical symmetry

Morris¹

2006

J Appl Cryst

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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.

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