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Equivalence of Kröner and weighted Voigt-Reuss models for x-ray stress determination
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10.1063/1.4801917
/content/aip/journal/jap/113/15/10.1063/1.4801917
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/15/10.1063/1.4801917

Figures

Image of FIG. 1.
FIG. 1.

Plot of ½S2 under Reuss, Voigt, Neerfeld and Kröner limits for Cu as a function of Γ. xKr is depicted graphically as the ratio of to . All of these XEC intersect at approximately Γ = 0.276, corresponding to the vertical dotted line. The single crystal elastic constants of Cu (from Ref. 22 ) can be found in Table I .

Image of FIG. 2.
FIG. 2.

(a) Weighted Reuss-Voigt fraction values, xKr, for various materials possessing cubic elastic symmetry plotted as a function of the anisotropy factor, A = 2 CC 1212/(CC 1111-CC 1122). Single crystal elastic constants were obtained from Ref. 22 ; (b) linear fit of weighted Reuss-Voigt fraction values for A < 5.

Image of FIG. 3.
FIG. 3.

Weighted Reuss-Voigt fraction values, xKr, for various materials possessing cubic elastic symmetry plotted as a function of the dimensionless parameter, Q = (CC 1111-CC 1122)/(CC 1111 + 2CC 1122). The asymptote 5/9 corresponds to the case of Q → ∞ and C2 ≪ C1.

Image of FIG. 4.
FIG. 4.

Plot of the weighted Reuss-Voigt fraction, xKr, of ½S2 for Ti as a function of the orientation parameter, η2, where squares correspond to specific (hkil) reflections. The continuous curve corresponds to values calculated using Eq. (23) .

Image of FIG. 5.
FIG. 5.

Plot of the Voigt, Reuss and Kröner limit ½S2 values for Ti as a function of η2, where the shaded portion delineates the range of η2 in which the Kröner XEC lies inside those under the Voigt and Reuss limits.

Tables

Generic image for table
Table I.

Single crystal elastic constants 22 and weighted Voigt-Reuss fraction corresponding to the Kröner limit, xKr, for several cubic materials.

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/content/aip/journal/jap/113/15/10.1063/1.4801917
2013-04-18
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Equivalence of Kröner and weighted Voigt-Reuss models for x-ray stress determination
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/15/10.1063/1.4801917
10.1063/1.4801917
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