Disorder of the front of a tensile tunnelcrack propagating in some inhomogeneous medium

We study the time evolution of the shape of the front of a tunnelcrack loaded in mode I in an infinite heterogeneous medium and propagating quasistatically according to some Paristype law. The two parts of the front are assumed to remain symmetrical and differ only slightly from straight lines at each instant, and a firstorder perturbation approach is used. The geometrical disorder of the front is evaluated via the autocorrelation function of the perturbation. This disorder increases without bound, at a considerable rate, which means that the straight configuration of the front is inherently unstable in some sense. This growth rate is much larger than that found by Rice and coworkers for the problem of a semiinfinite crack propagating dynamically according to some Griffithtype law. This is due to the highly destabilizing effect of the finite crack geometry considered here. The "correlation distance" of the perturbation also increases, which mitigates the preceding conclusion since it means, in another sense, that the crack front tends to straighten back in time.