Rietveld-based energy-dispersive residual stress evaluation: Analysis of complex stress fields σij(z)

Daniel Apel*, Manuela Klaus, Martin Genzel, Christoph Genzel

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


A method for the evaluation of strongly inhomogeneous residual stress fields in the near-surface region of polycrystalline materials is introduced, which exploits the full information content contained in energy-dispersive (ED) diffraction patterns. The macro-stress-induced diffraction line shifts ΔE ψ hkl observed in ED sin2ψ measurements are described by modeling the residual stress state σ ij (z) in real space, based on Rietveld's data analysis concept. Therefore, the proposed approach differs substantially from currently used methods for residual stress gradient analysis such as the 'universal plot' method, which enable access to the Laplace stress profiles σ ij (τ). With the example of shot-peened samples made of either 100Cr6 steel or Al2O3, it is demonstrated that the simultaneous refinement of all diffraction patterns obtained in a sin2ψ measurement with hundreds of diffraction lines provides very stable solutions for the residual stress depth profiles. Furthermore, it is shown that the proposed evaluation concept even allows for consideration of the residual stress component σ33(z) in the thickness direction, which is difficult to detect by conventional sin2ψ analysis.

Original languageEnglish
Pages (from-to)511-526
Number of pages16
JournalJournal of Applied Crystallography
Issue number2
Publication statusPublished - 1 Jan 2014


  • depth gradients
  • energy-dispersive diffraction
  • residual stress analysis
  • Rietveld refinement
  • triaxial residual stress state


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