A Unified Representation for Fundamental Equations of Various X-Ray Stress Measurement Methods

Abstract:

The X-ray stress measurements by the sin²ψ method, the cos α method and the XRD² method are basically composed of the fundamental equations based on diffraction vectors and the calculation for determining X-ray stress. The fundamental equations are expressed differently, which are due to the fact that the measurement systems associated with the incident X-ray control device and the diffracted X-ray detector are different. Although the dependent variable that is the measured quantity is the same diffraction angle theta in the fundamental equations, the main independent variable is different like the tilt angle ψ in the sin² ψ method and the central angle α, γ of the Debye-Scherrer ring in the cos α method, the XRD² method, respectively. Therefore, the stress determination method has been devised based on each the fundamental equation. By clarifying the differences between each X-ray stress measurement method and making a relationship, a unified representation for the fundamental equations is formalized. Therefore, a comparison of each X-ray stress measurement method is expressed in the same Euler space, and a conversion method for each X-ray stress measurement method is presented.

• Periodical: Key Engineering Materials (Volume 968)
• Pages: 9-13
• DOI: https://doi.org/10.4028/p-M5eBl8
• Online since: December 2023
• Authors: Shoichi Ejiri*, Hiroaki Ohba, Toshihiko Sasaki
• Keywords: 2D Method, Cosα Method, Non-Destructive Inspection, Residual Stress, Sin²ψ Method, Two-Dimensional Detector, X-Ray Stress Measurement, XRD²

References

[1] H. H. Lester, R. H. Aborn, The behavior under stress of the iron crystals in steel, Army Ordnance, 6 (1925) 120-1274.

[2] G. Sachs, J. Weerts, Elastizitätsmessungen mit Röntgenstrahlen, Zeitschrift für Physik, 64 (1930) 344-358.

[3] R. Glocker, E. Osswald, Unique determination of the principal stresses with X-rays, Zeitschrift für Technische Physik, 161 (1935) 237-242.

[4] I.C. Noyan, J.B. Cohen, Residual Stress: measurement by diffraction and interpretation, Spring-Verlag, 1987.

[5] V.Hauk, Structural and Residual Stress Analysis by Nondestructive Methods, Elshevier, 1997.

[6] S. Taira, K. Tanaka, T. Yamazaki, A Method of X-ray Microbeam Measurement of Local Stress and Its Application to Fatigue Crack Growth Problem, J. Soc. Mater. Sci., 27 (1978) 251-256.

[7] T. Sasaki, Y. Hirose, Single Incidence X-Ray Stress Measurement for All Plane Stress Components Using Imaging Plate of Two-Dimensional X-ray Detector, J. Soc. Mater. Sci., 44 (1995) 1138-1143.

DOI: 10.2472/jsms.44.1138

[8] B. B. He, K. L. Smith, A New Method for Residual Stress Measurement Using An Area Detector, Proceedings of the Fifth International Conference on Residual Stresses (ICRS-5), (1997) 634-639.

[9] B. B. He, Two-Dimensional X-Ray Diffraction (2nd edition), Wiley (2018).

[10] T. Miyazaki, T. Sasaki, X-ray Stress Measurement From An Imperfect Debye-Scherrer Ring, J. Materials Research, 106 (2015) 237-241.

DOI: 10.3139/146.111179

[11] T. Miyazaki, T. Sasaki, A Comparison of X-ray Stress Measurement Methods Based on The Fundamental Equation, J. Appl. Cryst., 49 (2016) 426-432.

DOI: 10.1107/s1600576716000492

[12] H. Dölle, V. Hauk, Rontgenographische Spannungensemittlung für Eignnspannungs-systeme allgemeiner Orientierung, Härterei-Technische Mitteilungen, 31 (1976) 165-168.