Statistical theories of crack propagation

The mechanism of crack growth in rocks has been the subject of much recent interest, not only on account of its engineering importance, but also as a background to the study of precursory phenomena for earthquakes. One feature which appears to play a significant role in the fracture mechanism is the formation of microfractures prior to a major failure. Microfractures also play a key role in statistical theories as developed by Weibull and later writers. Some recent work in these two fields is reviewed and the suggestion is put forward that it may be possible to extend the statistical models so as to describe the dynamics of crack formation. As a preliminary step in this direction, it is shown that a branching model for the coalescence of microfractures lead to a simple derivation of the frequency-magnitude law of fracture energies. Other methods of introducing statistical ideas into the dynamics of crack propagation are also briefly reviewed, and compared to deterministic models of crack growth.

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