PLASTICITY AND AVALANCHE BEHAVIOR IN MICROFRACTURING PHENOMENA

Inhomogeneous materials, such as plaster or concrete, subjected to an external elastic stress display sudden movements owing to the formatio n and propagation of microfractures. Studies of acoustic emission from these systems reveal power-law behaviour(1). Similar behaviour in dam age 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-range d correlations between fracture events lead to a scale-free cascade of 'avalanches'. A hierarchy of avalanche events is also observed in a w ide range of other systems, such as the dynamics of random magnets(5) and high-temperature superconductors(6) in magnetic fields, lung infla tion(7) and seismic behaviour characterized by the Gutenberg-Richter l aw(8). The applicability of self-organized criticality to microfractur ing has been questioned(9,10), however, as power laws alone are not un equivocal evidence for it. Here we present a scalar model of microfrac turing which generates power-law behaviour in properties related to ac oustic emission, and a scale-free hierarchy of avalanches characterist ic of self-organized criticality. The geometric structure of the fract ure surfaces agrees with that seen experimentally. We find that the cr itical steady state exhibits plastic macroscopic behaviour, which is c ommonly observed in real materials.