纤维束蠕变断裂模型中的破断记录
Record breaking bursts in a fiber bundle model of creep rupture
摘要：
本文研究了非均匀材料蠕变断裂的纤维束模型中裂纹时间序列中破记录事件的统计特性。在模型中，纤维断裂是由于两种机制：缓慢积累的损伤触发类似于实验中的声发射的立即断裂的爆发。破裂过程加速，使得破裂雪崩的大小增加，而连续事件之间的等待时间减少到失败。记录事件被定义为具有比时间序列中的所有先前事件更大的大小的突发。我们分析了记录的统计集中在限制的平等负载共享（ELS）的模型和比较的结果，独立同分布的随机变量序列的记录统计。计算机模拟表明，记录的数量增长与事件数的对数，除了附近的宏观故障的指数依赖性是有证据的。这两个制度可以归因于占主导地位的小突发大小的无序和应力增强引起有效的触发扩展突发，分别。记录的大小和连续记录事件之间的增量的特征在于由幂律分布与一个共同的指数1.33显着不同于通常的ELS突发大小指数的纤维束。然而，等待时间的分布遵循相同的行为，对于低负载和高负载具有两个不同的指数。研究记录的演变，我们确定了一个负载依赖的特征尺度的系统，分离慢下来和加速的记录打破失败的做法。
英文摘要：
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.
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