In-plane perturbation of a system of two coplanar slit-cracks – I: Case of arbitrarily spaced crack fronts

In order to lay the grounds for a future study of the deformation of the fronts of coplanar cracks during their final coalescence, we consider the model problem of a system of two coplanar, parallel, identical slit-cracks loaded in mode I in some infinite body. The first, necessary task is to determine the distribution of the stress intensity factors along the crack fronts resulting from some small but otherwise arbitrary in-plane perturbation of these fronts. This is done here in the case where the distances between the various crack fronts are arbitrary and fixed.The first order expression of the local variation of the stress intensity factor is provided by a general formula of Rice (1989) in terms of some “fundamental kernel” tied to the mode I crack face weight function. In the specific case considered, this fundamental kernel reduces to six unknown functions; the problem is to determine them. This is done by using another formula of Rice (1989) which provides the variation of the fundamental kernel in a similar way. This second formula is applied to special perturbations of the crack fronts preserving the shape and relative dimensions of the cracks while modifying their absolute size and orientation. The output of this procedure consists of nonlinear integro-differential equations on the functions looked for, which are transformed into nonlinear ordinary differential equations through Fourier transform in the direction of the crack fronts, and then solved numerically.