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Why we should give up the sin2ψ method

Published online by Cambridge University Press:  06 March 2012

Balder Ortner
Balder Ortner
Affiliation:
University Leoben, Jahnstraße 12, A-8700 Leoben, Austria
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Abstract

The sin2ψ method can be formulated as a single system of simultaneous linear equations. Using this it is easy to show that the sin2ψ method is not a least-squares method. It further helps to compare the accuracies of the stress tensors obtained by the sin2ψ method and the method of least squares. Quantitative comparisons have been made for different fictitious measurements. It is shown that the unnecessary loss in accuracy by using the sin2ψ method is quite significant and by no means negligible. The same course of action has been applied to compare the so-called Dölle-Hauk method with a least-squares method; the result is similar. Some other methods for X-ray stress determination, most often similar to the sin2ψ method, and their shortcomings are also discussed briefly, together with the corresponding, more effective and more versatile least-squares method.

Keywords

X-ray stress measurementsin2 ψ methodX-ray elastic factorsleast-squares method
Type
Methods For Residual Stress Analysis
Information
Powder Diffraction , Volume 24 , Supplement S1 , June 2009 , pp. S16 - S21
Copyright
Copyright © Cambridge University Press 2009

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References

Ballard, B. L., Predecki, P. K., Watkins, T. R., Kozaczek, K. J., Braski, D. N., and Hubbard, C. R. (1997). “Depth profiling biaxial stresses in sputter deposited molybdenum films: Use of the cos2θ method,” Adv. X-Ray Anal.AXRAAA 39, 363–370.Google Scholar
Behnken, H., in Spiess, L., Schwarzer, R., Behnken, H., Teichert, G. (2005). Moderne Röntgenbeugung (Vieweg, Wiesbaden).Google Scholar
Cullity, B. D. (1956). Elements of X-Ray Diffraction (Addison-Wesley, Reading, MA).Google Scholar
Dölle, H. (1979). “The influence of multiaxial stress states, stress gradients, and elastic anisotropy on the evaluation of (residual) stresses by X-rays,” J. Appl. Crystallogr.JACGAR 12, 489–501.10.1107/S0021889879013169CrossRefGoogle Scholar
Dölle, H. and Hauk, V. (1978a). “Einfluss der mechanischen anisotropie des vielkristalls (texture) auf die rontgenographische spannungsermittlung,” Z. Metallkd. 69, 410–417.Google Scholar
Dölle, H. and Hauk, V. (1978b). “Röntgenographische Ermittlung von Eigenspannungen in texturierten Werkstoffen,” Z. Metallkd. 69, 682–685.Google Scholar
Hauk, V. (1997). Structure and Residual Stress Analysis by Nondestructive Methods (Elsevier, Amsterdam).Google Scholar
Hauk, V. and Vaessen, G. (1985). “Eigenspannungen in den Kristallitgruppen texturieter Stahle,” Z. Metallkd. 76, 102–107.Google Scholar
Lu, J. (1996). Handbook of Measurement of Residual Stresses (Fairmont Press, Lilburn).Google Scholar
Noyan, I. C. and Cohen, J. B. (1987). Residual Stress: Measurement by Diffraction and Interpretation (Springer-Verlag, New York).CrossRefGoogle Scholar
Ortner, B. (2005). “An analytic and generalized formulation of the sin2ψ-method,” Z. Metallkd. 96, 1049–1055.CrossRefGoogle Scholar
Ortner, B. (2006). “Symmetry properties and transformation behaviour of the X-ray stress factors,” J. Appl. Crystallogr.JACGAR 39, 401–409.10.1107/S0021889806011526CrossRefGoogle Scholar
Ortner, B. (2007). “A comparison of different distributions of azimuth angles in the sin2ψ-method,” Int. J. Mater. Res.IJMRFV 98, 87–90.CrossRefGoogle Scholar
Ortner, B., Antretter, T., Hofmann, M., and Werner, E. (2008). “Measurement of all six components of X-ray elastic factors,” Mater. Sci. ForumMSFOEP 571–572, 225–229.10.4028/www.scientific.net/MSF.571-572.225CrossRefGoogle Scholar
Peiter, H. (1992). Handbuch der Spannungsmesspraxis (Vieweg-Verlag, Wiesbaden).Google Scholar
Quaeyhaegens, C., Knuyt, G., and Stals, L. M. (1995). “Study of the residual macroscopic stress in TiN coatings deposited on various steel types (TuSA1),” Surf. Coat. Technol.SCTEEJ 74–75, 104–109.10.1016/0257-8972(95)08359-6CrossRefGoogle Scholar
Quaeyhaegens, C., Knuyt, G., and Stals, L. M. (1996). “Residual macroscopic stress in highly preferentially oriented titanium nitride coatings deposited on various steel types,” J. Vac. Sci. Technol. AJVTAD6 14, 2462–2468.10.1116/1.580037CrossRefGoogle Scholar
Taira, S., Tanaka, K., and Yamazaki, T. (1978). “A method of X-ray microbeam measurement of local stress and its application to fatigue crack growth problems,” J. Soc. Mater. Sci. Jpn 27, 251–256.CrossRefGoogle Scholar
Vermeulen, A. C. (2002). “Assumptions in thin film residual stress methods,” Mater. Sci. ForumMSFOEP 404–407, 35–42.10.4028/www.scientific.net/MSF.404-407.35CrossRefGoogle Scholar
Welzel, U., Ligot, J., Lamparter, P., Vermeulen, A. C., and Mittemeijer, E. J. (2005). “Stress analysis of polycrystalline thin films and surface regions by X-ray diffraction,” J. Appl. Crystallogr.JACGAR 38, 1–29.10.1107/S0021889804029516CrossRefGoogle Scholar
Winholtz, R. A. and Cohen, J. B. (1988). “Generalised least-squares determination of triaxial stress states X-ray diffraction and the associated errors,” Aust. J. Phys.AUJPAS 41, 189–199.CrossRefGoogle Scholar