Journal of Materials Science

, Volume 51, Issue 11, pp 5343–5355 | Cite as

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

  • J. Ramirez-Rico
  • S.-Y. Lee
  • J. J. Ling
  • I. C. Noyan
Original Paper


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.


Ferrite Residual Stress Area Detector Residual Stress Measurement Sample Rotation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

10853_2016_9837_MOESM1_ESM.docx (1.3 mb)
Supplementary material 1 (DOCX 1373 kb)


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • J. Ramirez-Rico
    • 1
  • S.-Y. Lee
    • 2
  • J. J. Ling
    • 2
  • I. C. Noyan
    • 2
  1. 1.Fisica de la Materia Condensada-ICMSUniversidad de Sevilla-CSICSevillaSpain
  2. 2.Applied Physics and Applied MathematicsColumbia UniversityNew YorkUSA

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