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Universal dynamic fragmentation in D dimensions.

J A Aström1, F Ouchterlony, R P Linna

  • 1Centre for Scientific Computing, P.O. Box 405, FIN-02101 Esbo, Finland.

Physical Review Letters
|July 13, 2004
PubMed
Summary
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A new model explains brittle fragmentation, revealing a two-part fragment-size distribution. This research on crack branching and Poisson processes is validated by simulations and real-world experiments.

Area of Science:

  • Physics of Materials
  • Geophysics
  • Computational Science

Background:

  • Brittle fragmentation is a complex phenomenon observed in various geological and material science contexts.
  • Understanding fragment-size distributions is crucial for predicting material behavior under stress.

Purpose of the Study:

  • To introduce a generic model for brittle fragmentation in D dimensions.
  • To analyze the resulting fragment-size distribution and its underlying mechanisms.
  • To validate the model using numerical simulations and experimental data.

Main Methods:

  • Development of a generic D-dimensional model for brittle fragmentation.
  • Analysis of crack branching-merging processes for small fragments.
  • Application of Poisson processes to model larger fragments and introduce a cutoff.

Related Experiment Videos

  • Numerical simulations in D=2.
  • Laboratory-scale experiments and large-scale quarry blastings in D=3.

    • Main Results:

    • The model predicts a two-component fragment-size distribution: scale-invariant at small sizes and exponential at larger sizes.
    • Numerical simulations confirm the distribution for D=2.
    • Experimental data for D=3 (granitic gneiss) validate the model.
    • Nonzero grain size in experiments causes deviations in the small-fragment limit.
    • The cutoff size appears to diverge at the minimum fragmentation energy; the scaling exponent is not universal.

    Conclusions:

    • The generic fragmentation model accurately describes fragment-size distributions across different dimensions.
    • The interplay of crack branching and Poisson processes governs fragmentation patterns.
    • Real-world material properties (e.g., grain size) introduce deviations from ideal models.