On the Inversion of Subsurface Residual Stresses from Surface Stress Measurements

  • P. Ballard
  • A. Constantinescu
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 66)


X-ray diffraction provides an efficient method to measure the stress tensor at a surface point of a polycrystalline body. When the stress at an interior point of the body is to be measured, it is common to remove matter in order to reach the considered point. However, this matter removal induces, in general, a stress redistribution so that the measured stress is different from the original residual stress. This paper addresses the problem of reconstructing the original stress field from the measurements. The problem is solved by a general method which leads to explicit inversion formulae for the case of simple geometries. Closed-form expressions are obtained for the two-dimensional and three-dimensional half-space. For bodies of arbitrary shape, an existence and uniqueness theorem is proved. The existence proof is constructive and a numerical algorithm may be derived.


Residual Stress Stress Field Surface Traction Residual Stress Field Curvilinear Coordinate System 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Moore, M.G. and Evans, W.P. (1958) Mathematical correction for stress in removed layers in X-ray diffraction residual stress analysis, SAE Trans., Vol. no. 66, pp 340–345.Google Scholar
  2. Ballard, P. and Constantinescu, A. (1994a) Sur l’inversion d’un champ de contraintes résiduelles en fonction des contraintes mesurées en surface, C. R. Acad. Sci. Paris, Série II, Vol. no. 318, pp. 859–863zbMATHGoogle Scholar
  3. Ballard, P. and Constantinescu, A. (1994b) Reconstruction d’un champ de contraintes résiduelles à partir des contraintes mesurées sur des surfaces successives. Existence et unicité, C. R. Acad. Sci. Paris, Série II, Vol. no. 319, pp. 1117–1122zbMATHGoogle Scholar
  4. Ballard, P. and Constantinescu, A. (1994c) On the inversion of subsurface residual stresses from surface stress measurements, J. Mech. Phys. Solids, Vol. no. 42, pp. 1767–1787MathSciNetADSCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • P. Ballard
    • 1
  • A. Constantinescu
    • 1
  1. 1.Laboratoire de Mécanique des SolidesEcole PolytechniquePalaiseau CedexFrance

Personalised recommendations