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Selfconsistent Evaluation of Non-Uniform Stress Profiles and X-Ray Elastic Constants from X-ray Diffraction Experiments

Published online by Cambridge University Press:  06 March 2019

H. Wern and
L. Suominen
H. Wern
Affiliation:
Hochschule fur Technik und Wirtschaft des Saarlandes GoebenstraBe 40 D-66117 Saarbrucken, Germany
L. Suominen
Affiliation:
American Stress Technologies, Inc., Pittsburgh, PA
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Abstract

A method to obtain the triaxial depth profiles of strains and stresses as a function of the depth below the surface is described. Instead of using inverse Laplace transforms to extract the z-profiles from the measured τ-profiles, a numerically stable inverse formalism with trigonometric basis functions is used. The formalism has already been applied with great success to the hole-drilling method for the determination of residual stresses. It requires no prior knowledge of the stress state and is suitable even for strongly non-linear stress fields. This is demonstrated by experimental data sets for the conventional Ω-, ѱ- and modified ѱ goniometers. Furthermore this method enables in situ determination of Poisson's ratio as well as the stress free lattice spacing using a selfconsistency criterion for isotropic materials. It is now possible to find a proper normalization of the residual strains and residual stresses. Because of the formulation as an inverse problem, analytical expressions for the beam path integrals could be derived even for curved surfaces. Inverse problems are often extremely ill-conditioned. Therefore the uniqueness of the solution is discussed in terms of a spectral shift of the corresponding eigenvalues.

Information

Type
Research Article
Information
Advances in X-Ray Analysis , Volume 39: Forty-Fourth Annual Conference on Applications of X-ray Analysis, July 31 - August 4, 1995 , 1995, pp. 339 - 352
Copyright
Copyright © International Centre for Diffraction Data 1995

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