Instability and Disorder of the Front of a Tensile Tunnel-Crack Slightly Perturbed within its Plane

In this paper, we study the time evolution of the shape of the front of a tunnel-crack loaded in mode I in an infinite elastic body and propagating quasistatically according to some Paris-type law. The two parts of the front are assumed to remain symmetrical and differ only slightly from straight lines at each instant, and a first-order perturbation approach is used. It is notably found that the L² norm of the perturbation continuously increases with time, which means, in some sense, that the straight configuration of the front is inherently "unstable". 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.