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Universality in fragmentation

Astrom1, Holian, Timonen

  • 1Department of Physics, University of Jyvaskyla, P.O. Box 35, FIN-40351 Jyvaskyla, Finland.

Physical Review Letters
|October 6, 2000
PubMed
Summary
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This study reveals critical fragmentation behaviors in brittle solids and fluids under impact and explosion. Fragment size distributions exhibit scaling laws distinct from percolation universality classes, with energy balance predicting a specific correlation length exponent.

Area of Science:

  • Physics of fragmentation phenomena
  • Statistical mechanics and critical phenomena
  • Materials science and fracture mechanics

Background:

  • Fragmentation processes in solids and fluids are fundamental to various scientific and engineering disciplines.
  • Understanding the scaling laws and universality classes governing fragment size distributions is crucial for predicting material behavior under extreme conditions.
  • Previous studies have explored fragmentation but lacked a unified critical analysis across different impact and explosion scenarios.

Purpose of the Study:

  • To investigate the critical behavior of fragmentation in two-dimensional brittle solids subjected to impact.
  • To analyze the critical dynamics of fluid fragmentation induced by explosion.
  • To compare the scaling properties of fragment size distributions with established models like percolation theory.

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Main Methods:

  • Theoretical analysis of fragmentation dynamics under impact and explosion conditions.
  • Identification of critical points associated with nonzero impact velocity and infinite explosion duration.
  • Application of scaling theory to analyze fragment-size distributions and comparison with percolation cluster-size distributions.
  • Utilizing energy balance arguments to derive correlation length exponents.

Main Results:

  • Critical fragmentation phenomena were identified for both solid impact and fluid explosion.
  • Fragment-size distributions within critical regimes display scaling behavior qualitatively similar to percolation, yet belonging to a different universality class.
  • Energy balance calculations yield a correlation length exponent precisely half that of the percolation value.
  • In the slow-fracture limit, fragmentation is dominated by a single crack.

Conclusions:

  • Fragmentation processes in brittle solids and fluids exhibit critical behaviors governed by distinct universality classes.
  • The observed scaling laws and derived exponents provide new insights into the fundamental mechanisms of fracture and fragmentation.
  • The findings offer a theoretical framework for understanding and predicting fragment size distributions in diverse physical systems.