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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
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Affiliations:
1 IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
J. Appl. Phys. 113, 153509 (2013)
/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

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. ) can be found in Table .

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. ; (b) linear fit of weighted Reuss-Voigt fraction values for A < 5.

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.

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. .

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

Table I.

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

/content/aip/journal/jap/113/15/10.1063/1.4801917
2013-04-18
2014-04-23

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