Shear crack propagation along weak planes in solids: A finite deformation analysis incorporating the linear harmonic potential

B. Chen, Y. Huang*, H. Gao, P. D. Wu

*Corresponding author for this work

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

Recent molecular dynamics simulations of dynamic crack propagation have shown that a shear crack propagating at a sub-Rayleigh speed may have a finite crack opening, but the crack opening vanishes once the crack tip velocity exceeds the shear wave speed. This observation is at odds with classical linear elastic solutions which indicate that a pure shear crack should have zero opening. To understand this discrepancy, we develop in this paper a finite deformation continuum theory incorporating the linear harmonic potential to describe the deformation of a crack in a solid with triangular lattice structure. Using the asymptotic method of Knowles [Eng. Fract. Mech. 15 (1981) 469], we show that there is indeed a finite crack opening for a dynamic, sub-Rayleigh shear crack. This opening is on the order of the lattice constant, and is attributable to the geometric nonlinearity of finite deformation near the crack tip. We also show in another paper that, once the crack tip velocity exceeds the shear wave speed, Knowles' asymptotic method gives a vanishing crack opening. These conclusions based on the continuum analysis for sub-Rayleigh and super-shear cracks agree well with the molecular dynamics simulations.

Original languageEnglish (US)
Pages (from-to)1-14
Number of pages14
JournalInternational Journal of Solids and Structures
Volume41
Issue number1
DOIs
StatePublished - Jan 1 2004

Keywords

  • Crack opening
  • Dynamic crack propagation
  • Harmonic potential
  • Shear cracks

ASJC Scopus subject areas

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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