A general treatment of crack tip contour integrals

B. Moran*, C. F. Shih

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

402 Scopus citations


Given a general balance statement we derive an expression for the associated crack tip flux integral. The conditions under which the integral is physically meaningful and yields a non-trivial result are outlined. To illustrate the approach a number of well known integrals in use in fracture mechanics are derived. It is demonstrated that complementary analogues to these integrals can be derived in a similar fashion and a result indicating the equality of dual integrals under quite general conditions is presented. We discuss the domain integral method as an alternative means of representing crack tip integrals and we show that the method may be interpreted as a particular form of Signorini's theorem of stress means. A discussion of some associated integral identities is presented.

Original languageEnglish (US)
Pages (from-to)295-310
Number of pages16
JournalInternational Journal of Fracture
Issue number4
StatePublished - Dec 1987
Externally publishedYes

ASJC Scopus subject areas

  • Computational Mechanics
  • Modeling and Simulation
  • Mechanics of Materials


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