Fatigue crack growth reliability by probabilistic finite elements

Glen H. Besterfield*, Wing Kam Liu, Mark A. Lawrence, Ted Belytschko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

60 Scopus citations


Failure of components due to fatigue crack growth is a major problem in industry. The failure process initiates with the presence of small cracks which can cause catostrophic fracture or slow crack growth. When treating a problem of this type, many aspects of the problem should be treated as random variables. The probabilistic finite element method (PFEM) has been shown to be a practical approach for solving problems of this type. In this paper, the fusion of the PFEM and reliability analysis for probabilistic fatigue crack growth is presented. A comprehensive method for determining the probability of fatigue failure for mixed-mode cyclic loading is also presented. The loading is mixed-mode with randomness in the initial and final crack lengths, initial crack angle and position, material properties, crack growth law, crack direction law and loading. The methodology consists of calculating the reliability index via an optimization procedure, which is used to calculate the probability of fatigue failure. Performance of the methodology presented is demonstrated on a classical mode I fatigue problem.

Original languageEnglish (US)
Pages (from-to)297-320
Number of pages24
JournalComputer Methods in Applied Mechanics and Engineering
Issue number3
StatePublished - Apr 1991

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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