Pradhan Srutarshi, Hansen Alex, Hemmer Per C
Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway.
Phys Rev Lett. 2005 Sep 16;95(12):125501. doi: 10.1103/PhysRevLett.95.125501. Epub 2005 Sep 12.
The statistics of damage avalanches during a failure process typically follows a power law. When these avalanches are recorded only near the point at which the system fails catastrophically, one finds that the power law has an exponent which is different from that one finds if the recording of events starts away from the vicinity of catastrophic failure. We demonstrate this analytically for bundles of many fibers, with statistically distributed breakdown thresholds for the individual fibers and where the load is uniformly distributed among the surviving fibers. In this case the distribution D(Delta) of the avalanches (Delta) follows the power law Delta-xi with xi=3/2 near catastrophic failure and xi=5/2 away from it. We also study numerically square networks of electrical fuses and find xi=2.0 near catastrophic failure and xi=3.0 away from it. We propose that this crossover in xi may be used as a signal of imminent failure.
失效过程中损伤雪崩的统计通常遵循幂律。当这些雪崩仅在系统发生灾难性失效的点附近被记录时，人们会发现幂律的指数与从远离灾难性失效附近开始记录事件时所发现的指数不同。我们对许多纤维束进行了分析论证，其中单个纤维的击穿阈值具有统计分布，并且负载在幸存纤维之间均匀分布。在这种情况下，雪崩（Δ）的分布D（Δ）遵循幂律Δ^-ξ，在接近灾难性失效时ξ = 3/2，远离时ξ = 5/2。我们还对电熔丝的方形网络进行了数值研究，发现在接近灾难性失效时ξ = 2.0，远离时ξ = 3.0。我们提出，ξ的这种转变可作为即将失效的信号。
