ON THE PHYSICAL ORIGINS OF CHARLES’ FRACTURE GROWTH LAW IN ROCK

Static fatigue and double torsion load relaxation experiments, carried out since the late 1970’s, have shown that the macroscopic, i.e., observable rate of subcritical crack growth, v, in a wide variety of rocks (and other brittle/quasi-brittle materials like ceramics or concrete) and conditions, correlates well with the macroscopic stress intensity factor, K, exponentiated to some power, n: v=CK^n, where n is the subcritical cracking index. Focusing on the high stress zone (HSZ) immediately ahead of a growing, experimentally constrained crack, we propose a simple physical model in which each member of a pre-existing distribution of elliptic microcracks explosively evolves, over a small time interval, ∆t, into a small, fresh, macroscale fracture surface, ∆A(t). The proposed model differs significantly from that proposed by Le, et al., (2009; J. Phys. D.) who picture macroscopic crack formation – equivalent to formation of ∆A(t) over ∆t – as a tree growth process, in which a growing macroscale crack has numerous, growing mesoscale branches, each of which, in turn, has numerous growing micro/atomic-scale branches The present model assumes that each active member of the initial microcrack distribution: a) remains mechanically isolated, and b) grows sequentially via a series of local critical growth/fracture energy release events. The resulting mechanical and probabilistic model suggests that: a) observed, random ∆A(t) is the remnant of m (micro- to meso- to macroscale) critical cracking/energy release and stress build-up cycles, undergone by each (active) member of the initial microcrack distribution, and b) the probability density of ∆A(t) is proportional to the initial microscale crack area pdf, p (A_{micro}). The model appears to provide a physically consistent explanation for the origin of Charles’ law, and possibly the origin of acoustic emissions observed during subcritical cracking experiments.