Natural frequencies of stable Griffith cracks

A. Jagota, P. Rahul-Kumar, S. Saigal

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

A quasi-statically growing stable crack, if perturbed from its equilibrium position, will accelerate back towards it. Within quasi-static, ideal, Griffith fracture theory, vibrations of the crack and the structure have characteristic natural frequencies. We explore this feature of Griffith fracture theory in two simple geometries: a crack between a bar and a substrate, and a crack in a double-cantilever beam (DCB) specimen. For small perturbations about the stable quasi-static configuration, the dynamic equations of motion reduce to simple eigenvalue problems, leading to exact expressions for natural frequencies and mode shapes. An interesting feature of the mode shapes is that they correspond to force-free or moment-free conditions at the crack tip. Using an extended form of Hamilton's principle, we have developed a variable-length finite element technique to calculate natural frequencies and mode shapes of deformations perturbed from the stable equilibrium state. Its accuracy is demonstrated by application to the two problems analyzed previously. The possibility of crack tip oscillations in real brittle materials with irreversibility in crack tip decohesion is discussed in light of Rice's generalization of the Griffith theory.

Original languageEnglish (US)
Pages (from-to)103-120
Number of pages18
JournalInternational Journal of Fracture
Volume116
Issue number2
DOIs
StatePublished - Jul 2002
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Modeling and Simulation
  • Mechanics of Materials

Keywords

  • Dynamic fracture
  • Free oscillations
  • Griffith fracture
  • Natural frequencies
  • Perturbation analysis
  • Stability

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