A Fundamental Study on the Evaluation and Applicability as a Mixed-mode Fracture Criterion of Crack Energy Density in an Arbitrary Direction

Takao Utsunomiya, Katsuhiko Watanabe

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3 Citations (Scopus)


It has previously been shown that crack energy density can be defined in any direction at a crack tip without any restrictions on constitutive equations. The crack energy density, εφ, in an arbitrary direction can be divided into the contributions of each mode (εφ= εI φII φIII φI φII φand εIII φ are the contributions of modes I, II and III, respectively), which can be evaluated by path-independent integrals corresponding to each. These are defined for a completely sharp crack as the limits where the notch root radius ρ approaches zero in a notch model. Therefore, it is necessary to use a notch model with a sufficiently small value of ρ in evaluations of the quantities through FEM. In this paper, εφ and εI φ are evaluated by path-independent integrals through elastic-plastic finite element analyses varying the value of ρ, and we discuss which of ρ should be adopted in evaluations of them. Moreover, by applying these results to an experimental result of ductile fracture under a mixed mode, we show that εI φ is a potential parameter for expressing elastic-plastic fracture criterion under a mixed mode.

Original languageEnglish
Pages (from-to)1832-1840
Number of pages9
JournalTransactions of the Japan Society of Mechanical Engineers Series A
Issue number516
Publication statusPublished - 1989 Jan 1



  • Crack Energy Density
  • Finite Element Method
  • Fracture Criterion
  • Fracture Mechanics
  • Mixed-mode Crack
  • Path-independent Integral

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering

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