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Stress measurement using area detectors: a theoretical and experimental comparison of different methods in ferritic steel using a portable X-ray apparatus

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Abstract

Using area detectors for stress determination by diffraction methods in a single exposure greatly simplifies the measurement process and permits the design of portable systems without complex sample cradles or moving parts. An additional advantage is the ability to see the entire or a large fraction of the Debye ring and thus determine texture and grain size effects before analysis. The two methods most commonly used to obtain stress from a single Debye ring are the so-called \(\cos \alpha \) and full-ring fitting methods, which employ least-squares procedures to determine the stress from the distortion of a Debye ring by probing a set of scattering vector simultaneously. The widely applied \(\sin ^2\psi \) method, in contrast, requires sample rotations to probe a different subset of scattering vector orientations. In this paper, we first present a description of the different methods under the same formalism and using a unified set of coordinates that are suited to area detectors normal to the incident beam, highlighting the similarities and differences between them. We further characterize these methods by means of in situ measurements in carbon steel tube samples, using a portable detector in reflection geometry. We show that, in the absence of plastic flow, the different methods yield basically the same results and are equivalent. An analysis of possible sources of errors and their impact in the final stress values is also presented.

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References

  1. Heindlhofer K (1948) Evaluation of residual stress. McGraw-Hill Book Co., New York

    Google Scholar 

  2. Barrett CS (1952) Structure of metals. McGraw-Hill Book Co., New York

    Google Scholar 

  3. Taylor A (1961) X-ray metallography. Wiley, New York

    Google Scholar 

  4. Homicz RJ (1967) Fundamentals and basic techniques of residual stress measurements with a portable x-ray diffraction unit. Soc Automot Eng Trans 76(s1):912–917

    Google Scholar 

  5. James MR, Cohen JB (1978) The measurement of residual stresses by x-ray diffraction techniques. Treatise on materials science and technology, vol 19A. Academic, New York, pp 1–62

    Google Scholar 

  6. Gelfi M, Bontempi E, Roberti R, Depero L (2004) X-ray diffraction debye ring analysis for stress measurement (DRAST): a new method to evaluate residual stresses. Acta Mater 52(3):583–589

    Article  Google Scholar 

  7. He BB (2011) Two-dimensional X-ray diffraction. Wiley, Hoboken

    Google Scholar 

  8. Noyan IC, Cohen JB (1987) Residual stress. Springer, New York

    Book  Google Scholar 

  9. Hauk V (1997) Structural and residual stress analysis by nondestructive methods: evaluation-application-assessment. Elsevier, Amsterdam

    Google Scholar 

  10. Ling J, Lee S-Y (2015) Characterization of a portable x-ray device for residual stress measurements. Adv X-ray Anal 59:153–161

    Google Scholar 

  11. Boyce B, Furnish T, Padilla H II, Van Campen D, Mehta A (2015) Detecting rare, abnormally large grains by x-ray diffraction. J Mater Sci 50:6719–6729. doi:10.1007/s10853-015-9226-3

    Article  Google Scholar 

  12. Ramirez-Rico J, Stolzenburg F, Almer J, Routbort J, Singh D, Faber K (2013) In situ imaging and strain determination during fracture in a sic/sic ceramic matrix composite. Scripta Mater 69(7):497–500

    Article  Google Scholar 

  13. Harder BJ, Ramirez-Rico J, Almer JD, Lee KN, Faber KT (2011) Chemical and mechanical consequences of environmental barrier coating exposure to calcium-magnesium-aluminosilicate. J Am Ceram Soc 94:s178–s185

    Article  Google Scholar 

  14. Sasaki T, Hirose Y, Sasaki K, Yasukawa S (1997) Influence of image processing conditions of debye Scherrer ring images in x-ray stress measurement using an imaging plate. Adv X-ray Anal 40:588–594

    Google Scholar 

  15. Sasaki T, Kobayashi Y (2009) X-ray multiaxial stress analysis using two debye rings. Adv X-ray Anal 52:248–255

    Google Scholar 

  16. Sasaki T, Maruyama Y, Ohba H, Ejiri S (2014) Two-dimensional imaging of debye-Scherrer ring for tri-axial stress analysis of industrial materials. J Instrum 9:C07066

    Article  Google Scholar 

  17. Kampfe A, Kampfe B, Goldenbogen S, Eigenmann B, Macherauch E, Lohe D (2000) X-ray stress analysis on polycrystalline materials using two-dimensional detectors. Adv X-ray Anal 43:54–65

    Google Scholar 

  18. Behnken H, Hauk V (2001) Determination of steep stress gradients by x-ray diffraction-results of a joint investigation. Mater Sci Eng A 300(1):41–51

    Article  Google Scholar 

  19. Marques M, Dias A, Gergaud P, Lebrun J (2000) A methodology development for the study of near surface stress gradients. Mater Sci Eng A 287(1):78–86

    Article  Google Scholar 

  20. Dolle 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 12(6):489–501

    Article  Google Scholar 

  21. Taira S, Tanaka K, 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(294):251–256

    Article  Google Scholar 

  22. Chidambarrao D, Song Y, Noyan I (1997) Numerical simulation of the x-ray stress analysis technique in polycrystalline materials under elastic loading. Metall Mater Trans A 28(12):2515–2525

    Article  Google Scholar 

  23. Noyan I, Nguyen L (1988) Oscillations in interplanar spacing vs. sin2\(\psi \) a fem analysis. Adv X-ray Anal 31:191–204

    Google Scholar 

  24. Noyan I, Nguyen L (1989) Effect of plastic deformations on oscillations in \(d\) vs. \(\sin ^2\psi \) plots. Adv X-ray Anal 32:355–364

    Google Scholar 

  25. Noyan I, Cohen J (1983) Determining stresses in the presence of nonlinearities in interplanar spacing vs. \(\sin ^2\psi \). Adv X-ray Anal 27:129–148

    Google Scholar 

  26. Hounkpati V, Fréour S, Gloaguen D, Legrand V (2014) Influence of morphologic texture on stress analysis by x-ray and neutron diffraction in single-phase metallic materials. J Mater Sci 49(20):7049–7065. doi:10.1007/s10853-014-8410-1

    Article  Google Scholar 

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Acknowledgements

Loading experiments were performed at the Robert W. Carleton Strength of Materials Laboratory, Columbia University. Dr. A. Brügger’s assistance with the loading setup is gratefully acknowledged. The X-ray portable stress measurement device was kindly supplied by Pulstec Industrial Co., Ltd. The authors would like to thank Toshikazu Suzuki and Yoshinobu Teramoto for installation and technical support. J. Ramirez-Rico gratefully acknowledges the support from the Universidad de Sevilla Research Fund (V Plan Propio).

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Ramirez-Rico, J., Lee, SY., Ling, J.J. et al. Stress measurement using area detectors: a theoretical and experimental comparison of different methods in ferritic steel using a portable X-ray apparatus. J Mater Sci 51, 5343–5355 (2016). https://doi.org/10.1007/s10853-016-9837-3

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  • DOI: https://doi.org/10.1007/s10853-016-9837-3

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