Evaluation of the stress field around a notch tip using contour integrals

J. H. Chang, L. K. Kang

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


The mode I and mode II asymptotic stresses around a notch tip are in general governed by different orders of singularity. Direct computation of the mixed-mode near-tip stress field therefore appears to be difficult. In this paper, we propose a pair of contour integrals JkR. The integrals are shown to be path-independent in a modified sense and so they can be accurately evaluated with finite element solutions. As an aside, by defining a pair of generalized stress intensity factors (SIFs) (KI)β and (KII)β, the relationship between JkR and the SIFs is derived and expressed as functions of the notch angle β. Once the JkR-integrals are accurately computed, the generalized SIFs and, consequently, the asymptotic mixed-mode stress field can then be properly determined. The feasibility of our formulation is demonstrated in two numerical examples, where various instances with different notch angles are considered. No particular singular elements are used in this study.

Original languageEnglish
Pages (from-to)569-586
Number of pages18
JournalInternational Journal of Engineering Science
Issue number5
StatePublished - Mar 2002


  • Generalized SIFs
  • J-integrals
  • Mixed-mode stresses
  • Modified path-independence
  • Notch tip
  • Singular behavior


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