Hostname: page-component-6898cfcb55-kwdml Total loading time: 0 Render date: 2026-11-12T00:34:47.950Z Has data issue: false hasContentIssue false
  • English
  • Français

Counting Statistical Errors in Principal Stresses and Directions Determined by Diffraction

Published online by Cambridge University Press:  06 March 2019

D.A. Witte,
R.A. Winholtz and
S.P. Neal
Get access

Extract

The state of stress in a material, as represented by the stress tensor, can be measured using x-ray or neutron diffraction techniques. A stress tensor measured using diffraction represents an experimental estimate of the true state of stress in the material. The measured stress tensor will include both instrumental and counting statistical errors. With careful measurement techniques, instrumental errors can be minimized, and accurate results can be obtained. The errors in the measured stress tensor that are due to counting statistics can be estimated using well established error propagation techniques. Unfortunately, these errors cannot be analytically propagated through the solution to the eigenvalue problem which yields the principal stresses and directions. Without estimates of the errors associated with the principal stresses and directions, the values determined for these quantities are of limited value.

Information

Type
Research Article
Information
Advances in X-Ray Analysis , Volume 37: Forty-Second Annual Conference on Applications of X-ray Analysis, August 2-6, 1993 , 1993, pp. 265 - 278
Copyright
Copyright © International Centre for Diffraction Data 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1. Noyan, I.C. and Cohen, J.B., “Residual Stress: Measurement by Diffraction and Interpretation,“ Springer-Verlag, New York (1987).Google Scholar
2. Hutchings, M.T. and Krawitz, A.D., eds., “Measurement of Residual and Applied Stress Using Neutron Diffraction,” Kluwer, Dordrecht (1992).Google Scholar
3. James, M.R. and Cohen, J.B., Study of the precision of x-ray stress analysis, Adv. X-ray Anal., 20:291–307 (1977).Google Scholar
4. Winholtz, R.A. and Cohen, J.B., Generalised least-squares dclermi nation of triaxial stress states by x-ray diffraction and the associated errors, Aunt. J. Phys, 41-189 (1988).Google Scholar
5. Karasudhi, P., “Foundations of Solid Mechanics,” Kluwer, Boston (1991).Google Scholar
6. Schwartz, L.H. and Cohen, J.B., “Diffraction from Materials,” 2nd ed., Springer-Verlag, New York (1987).Google Scholar
7. Bevington, Philip R., “Data Reduction and Error Analysis for the Physical Sciences,” McGraw-Hill, New York (1969).Google Scholar
8. Winhoitz, R.A. and Krawitz, A.D., Methods for depth profiling complete stress tensors using neutron diffraction, this volume.Google Scholar
9. Krawitz, A.D. and Winhoitz, R.A., Use of position-dependent stress-free standards for diffraction strcsss measurements, Mater, Set. Engr., in press.Google Scholar