In-plane bending fracture of a large beam containing a circular-arc crack

Y. C. Shiah, Jiunn Fang, Chin Yi Wei, Y. C. Liang

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In this paper, the crack problem of a large beam-like strip weakened by a circular arc crack with in-plane bending moments applied at both ends is approximately solved using the complex variable technique. Complex stress functions corresponding to the applied bending moments are superposed with those due to the disturbance of the crack to satisfy the governing boundary equation. The conformal mapping function devised to transform the contour surface of a circular arc crack to a unit circle is then substituted in the boundary equation to facilitate the evaluation of Cauchy integrals. In this way, the complex stress functions due to the crack disturbance are determined and the stress intensity factors are calculated through a limiting process to give their explicit forms. Eventually, the geometric functions for the variation of the stress intensity factors on account of the crack shape are plotted as a function of the curvature of a circular-arc crack.

Original languageEnglish
Pages (from-to)145-151
Number of pages7
JournalJournal of Mechanics
Issue number3
Publication statusPublished - 2002

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanical Engineering
  • Applied Mathematics


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