Pradhan Srutarshi, Hansen Alex, Hemmer Per C
Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jul;74(1 Pt 2):016122. doi: 10.1103/PhysRevE.74.016122. Epub 2006 Jul 27.
Composite materials, with statistically distributed thresholds for breakdown of individual elements, are considered. During the failure process of such materials under external stress (load or voltage), avalanches consisting of simultaneous rupture of several elements occur, with a distribution D(Delta) of the magnitude Delta of such avalanches. The distribution is typically a power law D(Delta) proportional to Delta (-xi). For the systems we study here, a crossover behavior is seen between two power laws, with a small exponent xi in the vicinity of complete breakdown and a larger exponent xi for failures away from the breakdown point. We demonstrate this analytically for bundles of many fibers where the load is uniformly distributed among the surviving fibers. In this case xi=3/2 near the breakdown point and xi=5/2 away from it. The latter is known to be the generic behavior. This crossover is a signal of imminent catastrophic failure of the material. Near the breakdown point, avalanche statistics show nontrivial finite size scaling. We observe similar crossover behavior in a network of electric fuses, and find xi=2 near the catastrophic failure and xi=3 away from it. For this fuse model power dissipation avalanches show a similar crossover near breakdown.
考虑具有单个元素击穿阈值呈统计分布的复合材料。在这种材料在外加应力（载荷或电压）作用下的失效过程中，会发生由几个元素同时破裂组成的雪崩现象，这种雪崩的大小Δ具有分布D(Δ)。该分布通常是幂律D(Δ)∝Δ^(-ξ)。对于我们在此研究的系统，在两个幂律之间观察到一种交叉行为，在完全击穿附近指数ξ较小，而在远离击穿点的失效情况下指数ξ较大。我们针对许多纤维束进行了分析证明，其中载荷在幸存纤维之间均匀分布。在这种情况下，在击穿点附近ξ = 3/2，远离击穿点时ξ = 5/2。后者是已知的一般行为。这种交叉是材料即将发生灾难性失效的信号。在击穿点附近，雪崩统计显示出非平凡的有限尺寸标度。我们在电熔丝网络中观察到类似的交叉行为，发现在灾难性失效附近ξ = 2，远离时ξ = 3。对于这种熔丝模型，功率耗散雪崩在击穿附近也显示出类似的交叉。
