Variational eigenstrain analysis of residual stresses in a welded plate

Alexander M. Korsunsky, Gabriel M. Regino, David Nowell

Research output: Contribution to journalArticlepeer-review

88 Citations (Scopus)


We present the formulation for finding the distribution of eigenstrains, i.e. the sources of residual stress, from a set of measurements of residual elastic strain (e.g. by diffraction), or residual stress, or stress redistribution, or distortion. The variational formulation employed seeks to achieve the best agreement between the model prediction and some measured parameters in the sense of a minimum of a functional given by a sum over the entire set of measurements. The advantage of this approach lies in its flexibility: different sets of measurements and information about different components of the stress-strain state can be incorporated. We demonstrate the power of the technique by analysing experimental data for welds in thin sheet of a nickel superalloy aerospace material. Very good agreement can be achieved between the prediction and the measurement results without the necessity of using iterative solution. In practice, complete characterisation of residual stress states is often very difficult, due to limitations of facility access, measurement time or specimen dimensions. Implications of the new technique for experimental analysis are all the more significant, since it allows the reconstruction of the entire stress state from incomplete sets of data.

Original languageEnglish
Pages (from-to)4574-4591
Number of pages18
JournalInternational Journal of Solids and Structures
Issue number13
Publication statusPublished - 15 Jun 2007
Externally publishedYes


  • Diffraction
  • Eigenstrain
  • Fatigue
  • Finite element method
  • Residual stress


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