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Assessing the Validity of Diffraction Stress Data with the Goodness-Of-Fit Statistic

Published online by Cambridge University Press:  06 March 2019

Thomas A. Lohkamp and
R. A. Winhoitz
Thomas A. Lohkamp
Affiliation:
Research Reactor Center and Mechanical & Aerospace Engineering University of Missouri-Columbia
R. A. Winhoitz
Affiliation:
Research Reactor Center and Mechanical & Aerospace Engineering University of Missouri-Columbia
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According to the standard model, strain in polycrystalline materials transforms like a tensor when measured with diffraction in different directions. This model predicts linear variation of d-spacing with sin2ѱ if the stresses σ13 and σ23 are absent or predicts ѱ-splitting if they are present. In diffraction stress measurements, d vs. sin2ѱ plots often exhibit behavior that cannot be predicted from this model. When such discrepancies are observed, stresses calculated from the data will not always be valid. Current practice is to determine the validity of data by visually inspecting d vs. sin2ѱ plots and subjectively assessing the goodness-of-fit. This paper proposes the χ2statistic as a tool for quantitatively determining goodness-of-fit, and it presents experimental results from the application of the statistic.

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Type
Research Article
Information
Advances in X-Ray Analysis , Volume 39: Forty-Fourth Annual Conference on Applications of X-ray Analysis, July 31 - August 4, 1995 , 1995, pp. 281 - 289
Copyright
Copyright © International Centre for Diffraction Data 1995

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References

Bevington, Philip R. (1969), Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York.Google Scholar
Courtney, S. B., Tricard, M. J.. and Hendricks, R. W. (1993), “PC-Based Management and James, M. R. and Cohen, J. B.. (1977), ”Study of the Precision of X-ray Stress Analysis”, Adv. X-ray Anal, 20:291-307. Google Scholar
Noyan, I. C. and Cohen, J. B.. (1987), Residual Stress: Measurement by Diffraction and Interpretation, Springer-Veriag, New York.Google Scholar
Noyan, I. C. and Cohen, J. B.. (1984), “Determining Stress in the Presence of Nonlinearities in Interplanar Spacing vs. Sin2Ψ”, Adv. in X-ray Anal, 27; 159. Google Scholar
H., William Flannery, Brian P., Teukolsky, Saul A., and Vetterling, William T. (1986), Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambrige.Google Scholar
Winholtz, R. A. (1995), “Corrections to Equations for Estimating the Counting Statistical Errors in Diffraction Stress Measurements”, /. Appl. Cryst, in Press.Google Scholar
Winholtz, R. A. and Cohen, J. B.. (1988), “Generalised Least-Squares Determination of Triaxial Stress States by X-Ray Diffraction and the Associated Errors”, Aust. J. Phys. 41:189. Google Scholar