Record breaking bursts in a fiber bundle model of creep rupture

TL;DR

This paper studies the statistics of record-breaking crackling bursts in a fiber bundle model of creep rupture, revealing how burst sizes and waiting times evolve and differ from independent random sequences, especially near failure.

Contribution

It introduces a detailed analysis of record statistics in a fiber bundle creep rupture model, highlighting load-dependent regimes and power law distributions of burst sizes and waiting times.

Findings

Number of records grows logarithmically with events, exponential near failure.

Record sizes and increments follow power law distributions with exponent 1.33.

Waiting times exhibit different power law behaviors at low and high loads.

Abstract

We investigate the statistics of record breaking events in the time series of crackling bursts in a fiber bundle model of the creep rupture of heterogeneous materials. In the model fibers break due to two mechanisms: slowly accumulating damage triggers bursts of immediate breakings analogous to acoustic emissions in experiments. The rupture process accelerates such that the size of breaking avalanches increases while the waiting time between consecutive events decreases towards failure. Record events are defined as bursts which have a larger size than all previous events in the time series. We analyze the statistics of records focusing on the limit of equal load sharing (ELS) of the model and compare the results to the record statistics of sequences of independent identically distributed random variables. Computer simulations revealed that the number of records grows with the logarithm of the event number except for the close vicinity of macroscopic failure where an exponential dependence is evidenced. The two regimes can be attributed to the dominance of disorder with small burst sizes and to stress enhancements giving rise efficient triggering of extended bursts, respectively. Both the size of records and the increments between consecutive record events are characterized by power law distributions with a common exponent 1.33 significantly different from the usual ELS burst size exponents of fiber bundles. The distribution of waiting times follows the same behavior, however, with two distinct exponents for low and high loads. Studying the evolution of records we identify a load dependent characteristic scale of the system which separates slow down and acceleration of record breaking as failure is approached.