Plasticity and avalanche behaviour in microfracturing phenomena

Inhomogeneous materials, such as plaster or concrete, subjected to an external elastic stress display sudden movements owing to the formation and propagation of microfractures. Studies of acoustic emission from these systems reveal power-law behaviour(1). Similar behaviour in damage propagation has also been seen in acoustic emission resulting from volcanic activity(2) and hydrogen precipitation in niobium(3). It has been suggested that the underlying fracture dynamics in these systems might display self-organized criticality(4), implying that long-ranged correlations between fracture events lead to a scale-free cascade of 'avalanches'. A hierarchy of avalanche events is also observed in a wide range of other systems, such as the dynamics of random magnets(5) and high-temperature superconductors(6) in magnetic fields, lung inflation(7) and seismic behaviour characterized by the Gutenberg-Richter law(8). The applicability of self-organized criticality to microfracturing has been questioned(9,10), however, as power laws alone are not unequivocal evidence for it. Here we present a scalar model of microfracturing which generates power-law behaviour in properties related to acoustic emission, and a scale-free hierarchy of avalanches characteristic of self-organized criticality. The geometric structure of the fracture surfaces agrees with that seen experimentally. We find that the critical steady state exhibits plastic macroscopic behaviour, which is commonly observed in real materials.