Crossover behavior in failure avalanches

2005/12/31 by Srutarshi Pradhan, Alex Hansen, P. C. Hemmer +1 · 46 citations
Earth and Planetary Sciences · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Computer science #Crossover #Dissipation #Earthquake Detection and Analysis #Exponent #Geometry #Mathematics #Mechanics #Physics #Power law #Scaling #Statistical physics #Statistics #Theoretical and Computational Physics #Thermodynamics #cond-mat.mtrl-sci #cond-mat.soft

paper · pdf · doi:10.1103/physreve.74.016122

published in Physical Review E 74(1), 016122 (American Physical Society) · 9 pages, 12 figures

arxiv created 2006/03/23 · openalex publication_date 2006/07/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Composite materials, with statistically distributed thresholds for breakdown of individual elements, are considered. During the failure process of such materials under external stress (load or voltage), avalanches consisting of simultaneous rupture of several elements occur, with a distribution D(Delta) of the magnitude Delta of such avalanches. The distribution is typically a power law D(Delta) proportional to Delta (-xi). For the systems we study here, a crossover behavior is seen between two power laws, with a small exponent xi in the vicinity of complete breakdown and a larger exponent xi for failures away from the breakdown point. We demonstrate this analytically for bundles of many fibers where the load is uniformly distributed among the surviving fibers. In this case xi=3/2 near the breakdown point and xi=5/2 away from it. The latter is known to be the generic behavior. This crossover is a signal of imminent catastrophic failure of the material. Near the breakdown point, avalanche statistics show nontrivial finite size scaling. We observe similar crossover behavior in a network of electric fuses, and find xi=2 near the catastrophic failure and xi=3 away from it. For this fuse model power dissipation avalanches show a similar crossover near breakdown.

Citations

• The statistical theory of the strength of bundles of threads. I

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