### Abstract

We investigate the statistics of record breaking (RB) 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 toward 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 to 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 RB as failure is approached.

Original language | English |
---|---|

Article number | A008 |

Pages (from-to) | 1-8 |

Number of pages | 8 |

Journal | Frontiers of Physics |

Volume | 2 |

DOIs | |

Publication status | Published - 2014 |

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### Keywords

- Avalanche
- Crackling noise
- Fiber bundle model
- Fracture
- Record breaking statistics

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Frontiers of Physics*,

*2*, 1-8. [A008]. https://doi.org/10.3389/fphy.2014.00008

**Record breaking bursts in a fiber bundle model of creep rupture.** / Danku, Zsuzsa; Kun, F.

Research output: Contribution to journal › Article

*Frontiers of Physics*, vol. 2, A008, pp. 1-8. https://doi.org/10.3389/fphy.2014.00008

}

TY - JOUR

T1 - Record breaking bursts in a fiber bundle model of creep rupture

AU - Danku, Zsuzsa

AU - Kun, F.

PY - 2014

Y1 - 2014

N2 - We investigate the statistics of record breaking (RB) 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 toward 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 to 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 RB as failure is approached.

AB - We investigate the statistics of record breaking (RB) 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 toward 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 to 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 RB as failure is approached.

KW - Avalanche

KW - Crackling noise

KW - Fiber bundle model

KW - Fracture

KW - Record breaking statistics

UR - http://www.scopus.com/inward/record.url?scp=84948752621&partnerID=8YFLogxK

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U2 - 10.3389/fphy.2014.00008

DO - 10.3389/fphy.2014.00008

M3 - Article

AN - SCOPUS:84948752621

VL - 2

SP - 1

EP - 8

JO - Frontiers of Physics

JF - Frontiers of Physics

SN - 2095-0462

M1 - A008

ER -