Computing stress intensity factors for curvilinear cracks

Maurizio M. Chiaramonte, Yongxing Shen, Leon M. Keer, Adrian J. Lew

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


The use of the interaction integral to compute stress intensity factors around a crack tip requires selecting an auxiliary field and a material variation field. We formulate a family of these fields accounting for the curvilinear nature of cracks that, in conjunction with a discrete formulation of the interaction integral, yield optimally convergent stress intensity factors. In particular, we formulate three pairs of auxiliary and material variation fields chosen to yield a simple expression of the interaction integral for different classes of problems. The formulation accounts for crack face tractions and body forces. Distinct features of the fields are their ease of construction and implementation. The resulting stress intensity factors are observed converging at a rate that doubles that of the stress field. We provide a sketch of the theoretical justification for the observed convergence rates and discuss issues such as quadratures and domain approximations needed to attain such convergent behavior. Through two representative examples, a circular arc crack and a loaded power function crack, we illustrate the convergence rates of the computed stress intensity factors. The numerical results also show the independence of the method from the size of the domain of integration.

Original languageEnglish (US)
Pages (from-to)260-296
Number of pages37
JournalInternational Journal for Numerical Methods in Engineering
Issue number4
StatePublished - Oct 26 2015

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


  • Finite element methods
  • Hydraulic fracturing
  • Muskhelishvili


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