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 behaviour1. Similar behaviour in damage propagation has also been seen in acoustic emission resulting from volcanic activity2 and hydrogen precipitation in niobium3. It has been suggested that the underlying fracture dynamics in these systems might display self-organized criticality4, 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 magnets5 and high-temperature superconductors6 in magnetic fields, lung inflation7 and seismic behaviour characterized by the Gutenberg–Richter law8. The applicability of self-organized criticality to microfracturing has been questioned9,10, 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.