Self-similar crack expansion method for three-dimensional cracks under mixed-mode loading conditions

Yonglin Xu, B. Moran, T. Belytschko

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Three-dimensional planar cracks under mixed-mode loading conditions are investigatedby using the self similar crack expansion method with the boundary integralequation technique. For a planar crack under general loading (tensile and shear)conditions, the normal displacement and tangential displacements on the crack surfaceexhibit uncoupled characteristics. However, the tangential displacements in thetwo directions are generally coupled. In this paper, two coupled boundary integralequations for a crack subject to shear loading are solved using the analyticallynumerical method, where the integrals on elements" are estimated by using the explicitexpression of the close form of the integrals. Combination of the self-similar crackexpansion method and the analytically numerical method results in good accuracy, with errors in stress intensity factors of penny-shaped cracks and elliptical cracksless than one percent. This numerical analysis is applicable to the analysis of crackswith arbitrary geometry.

Original languageEnglish (US)
Pages (from-to)557-565
Number of pages9
JournalJournal of Applied Mechanics, Transactions ASME
Issue number3
StatePublished - Sep 1998
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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