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Grinfeld instability on crack surfaces.

R Spatschek1, E A Brener

  • 1Institut für Festkörperforschung, Forschungszentrum Jülich, D-52425 Jülich, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 3, 2001
PubMed
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Crack surfaces become unstable and wavy beyond a critical length, reducing their energy. This instability, driven by surface diffusion, modifies crack tip conditions, requiring chemical potential matching instead of stress intensity factor considerations.

Area of Science:

  • Materials Science
  • Solid Mechanics
  • Fracture Mechanics

Background:

  • Propagating cracks exhibit morphological instability due to nonhydrostatic stresses, known as the Asaro-Tiller-Grinfeld instability.
  • Understanding crack surface morphology is crucial for predicting material failure and designing robust structures.

Purpose of the Study:

  • To numerically investigate the morphological instability of crack surfaces.
  • To determine the critical crack length for the onset of this instability.
  • To analyze the dynamic evolution and implications of crack surface waviness.

Main Methods:

  • Numerical simulations of crack propagation.
  • Analysis of surface diffusion and condensation-evaporation driven dynamics.
  • Investigation of stress intensity factors and chemical potentials at crack tips.

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Main Results:

  • Crack surface waviness reduces crack energy below a critical length (L(c) = 5.18 L(G)).
  • Instability evolution shows divergent curvature near crack tips.
  • The condition for crack tip stability shifts from K(II) disappearance to chemical potential matching.

Conclusions:

  • Crack surface morphology is inherently unstable, influencing fracture behavior.
  • The critical length and dynamic evolution of this instability are quantified.
  • A generalized condition for crack tip stability is established, applicable to various loading scenarios.