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X -Ray Elastic Constants and Their Meaning for Al and Fe

Published online by Cambridge University Press:  06 March 2019

Rui Mei Zhong ,
I. C. Noyan  and
J. B. Cohen
Rui Mei Zhong*
Affiliation:
Department of Materials Science and Engineering The Technological Institute Northwestern University Evanston, IL 60201
I. C. Noyan
Affiliation:
Department of Materials Science and Engineering The Technological Institute Northwestern University Evanston, IL 60201
J. B. Cohen
Affiliation:
Department of Materials Science and Engineering The Technological Institute Northwestern University Evanston, IL 60201
*
*Currently at Beijing Research Institute of Mechanical and Electrical Technology, Beijing, China
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Abstract

In the measurement of residual stresses via diffraction (using x-rays or neutrons) it is strains that are actually determined, by employing the interplanar spacing (dhkl) of the ﹛hkl﹜ planes as an internal strain gauge. The change in this spacing is measured from the shift of diffraction peaks (and Bragg's law) at several orientations of the sample to the incident beam, and the resultant strains are converted to stresses with the “diffraction elastic constants”, S1 (hkl) and S2 (hkl)/2. While these take on the values (- v/E) and (1 + v )/E respectively for an isotropic solid, in anisotropic materials their values depend on marry factors: preferred orientation, shape and orientation of second phases, interaction between grains. In fact there are reports of variation these constants with plastic deformation and theory predicts variations with morphology. While it is possible to calculate approximate values for these constants from theory and the single crystal elastic constants , Si and S2/2 are really not elastic constants in the strictest sense because or these other factors, and it is best to measure them. One of us (I. C. Noyan) has recently examined this problem in some detail , and we summarize his results here.

Type
Research Article
Information
Advances in X-Ray Analysis , Volume 29: Thirty-Fourth Annual Conference on Applications of X-ray Analysis, August 5-9, 1985 , 1985 , pp. 17 - 20
Copyright
Copyright © International Centre for Diffraction Data 1985

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References

1. Hilley, M.E., Larson, J.A., Jactzak, C.F. and Rickefs, R.E. (eds), “Residual Stress Measurement by X-ray Diffraction”, SAE Information Report, J. 784a, (2nd edition), SAE. Inc, New York (1971).Google Scholar
2. Marion, R.H. and Cohen, J.B., The Need for Experimentally Determined Xray Elastic Constants, Adv. in X-ray Analysis, 20: 355 (1977).Google Scholar
3. Wu, T.T., The Effect of Inclusion Shape on the Elastic Moduli of a Two- Phase Material, Int. J. Solids and Structures, 2: 1 (1966).Google Scholar
4. Dölie, H., Influence of Multiaxial Stress States, Stress Gradients and Elastic Anisotropy on the Evaluation of (Residual) Stresses by X-rays, J. Appl. Cryst., 12: 489 (1979).Google Scholar
5. Ncyan, I.C., Determination of the Elastic Constants of Inhomogeneous Materials with X-ray Diffraction, Mat. Sci & Eng., in press.Google Scholar
6. Dölie, H. and Hauk, V., Einfluss der Meehanischen Anisotrcpie des Vielkristails (Textur)auf die Rontgenographische Spannungser Mittlung, Z. Metallk., 69: 410 (1978).Google Scholar
7. Noyan, I.C. and Cohen, J.B., Determining Stress in the Presence of Nonlinearities in Interplanar Seeing vs. Sin2, Adv. in X-Ray Analysis. 27: 129 (1934).Google Scholar
8. Marion, R.H. and Cohen, J.B., Anomalies in Measurement of Residual Stress by X-ray Diffraction, Adv. in X-ray Analysis, 18: 446 (1975).Google Scholar
9. Perry, K., Noyan, I.c., Rudnik, p.J. and Cohen, J.B., The Measurement of Elastic Constants for the Determination of Stresses by X-rays, Adv. in X-Ray Analysis. 27: 159 (1984).Google Scholar
10. Dölie, H. and Cohen, J.B., Evaluation of (Residual) Stresses in Textured Cubic Metals, Met. Trans., 11A:831(1980).Google Scholar
11. Noyan, I.C. and Cohen, J.B., The Use of Neutrons to Measure Stresses, Scripta Metall., 18: 627 (1984).Google Scholar
12. Hauk, V.M. and Vaessen, G.J.H., Residual Stress Evaluation with Xrays, Met. Trans., 15A: 1407 (1984).Google Scholar