Analysis of three-dimensional edge cracks under tensile loading

Yonglin Xu*, Brian Moran, Ted Belytschko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Three-dimensional edge cracks are analyzed using the Self-Similar Crack Expansion (SSCE) method with a boundary integral equation technique. The boundary integral equations for surface cracks in a half space are presented based on a half space Green's function (Mindlin, 1936). By using the SSCE method, the stress intensity factors are determined by the crack-opening displacement over the crack surface. In discrete boundary integral equations, the regular and singular integrals on the crack surface elements are evaluated by an analytical method, and the closed form expressions of the integrals are given for subsurface cracks and edge crakes. This globally numerical and locally analytical method improves the solution accuracy and computational effort. Numerical results for edge cracks under tensile loading with various geometries, such as rectangular cracks, elliptical cracks, and semi-circular cracks, are presented using the SSCE method. Results for stress intensity factors of those surface breaking cracks are in good agreement with other numerical and analytical solutions.

Original languageEnglish (US)
Pages (from-to)174-187
Number of pages14
JournalActa Mechanica Solida Sinica
Issue number2
StatePublished - 1999
Externally publishedYes


  • Boundary integral equation
  • Self-similar crack expansion

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Computational Mechanics


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