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Crack propagation as a free boundary problem.

D Pilipenko1, R Spatschek, E A Brener

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

Physical Review Letters
|March 16, 2007
PubMed
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This study models crack propagation as a phase transition, using a multipole expansion to find steady-state solutions. Elastodynamics reveal velocity saturation below Rayleigh speed and tip instabilities with increasing force.

Area of Science:

  • Physics
  • Materials Science
  • Solid Mechanics

Background:

  • Crack propagation is a critical phenomenon in material failure.
  • Modeling cracks as phase transitions offers a novel perspective.
  • Free boundary problems in fracture mechanics are computationally challenging.

Purpose of the Study:

  • To develop a numerical model for crack propagation using a sharp interface approach.
  • To investigate the influence of elastodynamic effects on crack behavior.
  • To identify steady-state solutions for crack velocity and shape.

Main Methods:

  • A sharp interface model for crack propagation.
  • Numerical solution of the free boundary problem via multipole expansion.
  • Inclusion of elastodynamic effects in the model.

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Main Results:

  • Steady-state crack solutions with self-consistently determined velocity and shape.
  • Observed saturation of crack velocity below the Rayleigh speed.
  • Identified tip blunting with increasing driving force and tip splitting instability above a critical force.

Conclusions:

  • The phase transition model successfully captures key aspects of crack propagation.
  • Elastodynamic effects are crucial for predicting crack velocity limits and instabilities.
  • The model provides insights into fracture behavior under varying stress conditions.