A new approach is proposed to study the statistical law of avalanches due to the fracture of a heterogeneous interface. Firstly, a discrete interface is considered as a bundle of fibers clamped with two elastic circular plates, fiber strength being either a random variable or a stochastic field. Based on the theory of solid mechanics, equations governing the dynamic fracture process of fibers under tension are exactly derived and solved. The statistical law of fracture avalanches is accurately obtained. By tuning parameters, the model covers the whole scheme of stress-transfer mechanism due to fiber breaking from local load sharing to equal load sharing. Results show that the distribution of avalanche size of interfacial fracture follows a power-law relation, with the power exponent in the range [1.5,2.5], depending on both disorders of interface and stiffness of plates. Particularly, the exponent monotonically increases with plate stiffness to the value 2.5, a universal constant obtained by Hemmer and Hansen (1992). Then, the fracture of a laminated interface is analyzed. By discretizing the interface to a set of prismatic elements, the problem reduces to that of a discrete interface. Similar statistical behaviors are also observed. Furthermore, the temporal variation of avalanche scaling law is investigated. It is shown that in the vicinity of collapse point, the exponent of each time window is smaller than the exponent evaluated with the whole time series of event, probably a precursor for imminent catastrophic failure of interface.

中文翻译：

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异质界面断裂的雪崩缩放定律

提出了一种新方法来研究异质界面断裂引起的雪崩的统计规律。首先，离散界面被认为是用两个弹性圆板夹紧的一束纤维，纤维强度是随机变量或随机场。基于固体力学理论，精确推导并求解了纤维在拉伸作用下的动态断裂过程方程。准确地得到了断裂雪崩的统计规律。通过调整参数，该模型涵盖了纤维断裂引起的应力传递机制的整个方案，从局部载荷分配到均等载荷分配。结果表明，界面断裂雪崩尺寸的分布遵循幂律关系，幂指数范围为[1.5，2.5]，取决于界面的紊乱和板的刚度。特别是，指数随着板刚度单调增加到值 2.5，这是 Hemmer 和 Hansen (1992) 获得的通用常数。然后，对层压界面的断裂进行分析。通过将界面离散化为一组棱柱形元素，问题就简化为离散界面的问题。还观察到类似的统计行为。此外，还研究了雪崩标度定律的时间变化。结果表明，在塌陷点附近，每个时间窗口的指数小于整个事件时间序列评估的指数，这可能是界面即将发生灾难性破坏的前兆。