Avalanche scaling law for heterogeneous interfacial fracture

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.