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The Measurement of Elastic Constants for the Determination of Stresses by X-Rays

  • K. Perry (a1), I.C. Noyan (a1), P.J. Rudnik (a1) and J.B. Cohen (a1)


Residual and applied stresses (σij) are often measured via X-ray diffraction, by calculating the resultant elastic strains (ϵij) from the measured change in interplanar spacing (“d”). This method is non-destructive, reasonably reproducible (typically ±14 MPa), can be carried out in the field, and is readily automated to give values to an operator-specified precision , Let Li represent the axes of the measuring system with L3 normal to the diffracting planes, and Pi represent the sample axes. These axes are illustrated in Figure 1. In what follows, primed stresses and strains are in the laboratory system, while unprimed values are in the sample system.



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1. James, M.R. and Cohen, J.B., “PARS“-A Portable X-ray Analyzer for Residual Stresses, J. of Testing and Evaluation, 6:91 C1978).
2. James, M.R. and Cohen, J.B., Study of the Precision of X-Ray Stress Analysis, Adv. in X-Ray Anal., 20:291 (1977).
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5. Dolle, H. and Cohen, S. B., Residual Stresses in Ground Steels, Met. Trans. A, 11A:159 (1980).
6. Neerfeld, H., The Calculation of Stress from X-Ray Elongation Measurements, Mitt. KWI Eisenforsch., 24:61 (1942).
7. Kroner, E., Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls, Z. Physik, 151:504 (1958).
8. Brakman, C.M., Residual Stresses in Cubic Materials with Orthorhombic or Monoclinic Specimen Symmetry:Influence of Texture on ψ-Splitting and Non-linear Behaviour, J. Appl. Crystall., 16:325 (1983).
9. Noyan, I.C. and Cohen, J.B., Determining Stresses in the Presence of Non-linearities in Interplanar Spacing vs. sin2ψ-this volume.
10. Volk, W., “Applied Statistics for Engineers”, McGraw-Hill Book Co., New York City (1958).
11. James, M.R. and Cohen, J.B., The Measurement of Residual Stresses by X-Ray Diffraction Techniques, Treatise on Materials Science and Technology, 19A:1 (1980).
12. Society of Automotive Engineers,Residual Stress Measurement by X-Ray Diffraction”, SAE Handbook J784a, 2nd. ed., Soc. Auto. Eng., Inc., New York City (1978).
13. Kolb, K. and Maaherauch, E., Der Anisotropie einfluss rontgenographische Gitterdehnungsmessungen an Nickel, Z. Physik, 162:119 (1961).
14. Esquivel, A.L., X-Ray Diffraction Study of the Effects of Uniaxial Plastic Deformation on Residual Stress Measurements, Adv. in X-Ray Anal., 12:269 (1969). 15-Marion, R.H. and Cohen, J.B., The Need for Experimentally Determined X-Ray Elastic Constants, Adv. in X-Ray Anal., 20:355 (1977).
16. James, M.R. and Cohen, J.B., The Application of a Position Sensitive X-Ray Detector to the Measurement of Residual Stresses, Adv. in X-Ray Anal., 19:695 (1976).


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