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Avalanches and extreme value statistics in interfacial crackling dynamics

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Details

Original languageEnglish
Article number20170394
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume377
Issue number2136
Early online date26 Nov 2018
DOIs
Publication statusPublished - 14 Jan 2019
Publication typeA1 Journal article-refereed

Abstract

We study the avalanche and extreme statistics of the global velocity of a crack front, propagating slowly along a weak heterogeneous interface of a transparent polymethyl methacrylate block. The different loading conditions used (imposed constant velocity or creep relaxation) lead to a broad range of average crack front velocities. Our high-resolution and large dataset allows one to characterize in detail the observed intermittent crackling dynamics. We specifically measure the size S, the duration D, as well as the maximum amplitude Vmax of the global avalanches, defined as bursts in the interfacial crack global velocity time series. Those quantities characterizing the crackling dynamics follow robust power-law distributions, with scaling exponents in agreement with the values predicted and obtained in numerical simulations of the critical depinning of a long-range elastic string, slowly driven in a random medium. Nevertheless, our experimental results also set the limit of such model which cannot reproduce the power-law distribution of the maximum amplitudes of avalanches of a given duration reminiscent of the underlying fat-tail statistics of the local crack front velocities.

Keywords

  • Avalanches, Depinning transition, Extreme value statistics

Publication forum classification

Field of science, Statistics Finland