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A Method for Studying the Temperature Dependence of Dynamic Fracture and Fragmentation
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The transition from subsonic to supersonic cracks.

Chris Behn1, M Marder2

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|February 26, 2015
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Supersonic cracks in brittle materials are physically possible, contrary to continuum fracture theory. Analytical solutions reveal distinct atomic motion patterns for subsonic versus supersonic crack propagation.

Keywords:
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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Computational Physics

Background:

  • Continuum fracture theory posits limitations on crack propagation speeds.
  • Lattice dynamics offer a microscopic perspective on fracture phenomena.
  • Previous models struggled to reconcile supersonic crack behavior.

Purpose of the Study:

  • To derive a full analytical solution for steady-state in-plane crack motion in a brittle triangular lattice.
  • To investigate atomic motion around crack tips across subsonic and supersonic speeds.
  • To compare lattice-based crack dynamics with continuum fracture predictions.

Main Methods:

  • Developed a full analytical solution for crack motion in a triangular lattice.
  • Performed numerical evaluations for large-scale systems.
  • Analyzed atomic displacement fields and oscillations near the crack tip.

Main Results:

  • Analytical solutions enable efficient evaluation for large systems, aiding comparison with continuum theory.
  • Supersonic cracks, faster than Rayleigh wave speed, are demonstrated to exist in lattice systems.
  • Subsonic cracks exhibit stress intensity factors, while supersonic cracks do not.
  • Distinct oscillation patterns characterize subsonic (small-amplitude, high-frequency) and supersonic (large-amplitude, low-frequency) crack motion.

Conclusions:

  • Supersonic cracks are physically valid phenomena in lattice systems, challenging continuum theory.
  • The disappearance of the stress intensity factor for supersonic cracks necessitates a revised understanding of their behavior.
  • Microscopic atomic motion provides crucial insights into macroscopic crack propagation, particularly for supersonic speeds.