Front shape and loading evolution during cracks coalescence using an incremental perturbation method

When two planar penny-shape cracks propagate and become sufficiently close to interact, the local stress intensity factor becomes no more constant along the fronts so that the cracks shape gradually deforms. The aim of this paper is to quantify these crack front deformations and their implication on the loading, up to their coalescence. The method used is based on numerical iterations of Bueckner-Rice weight functions perturbation approach which gives the variation of the stress intensity factor when the crack fronts are slightly perturbed in their plane. It is extended here to the case of several cracks. The advantage of this method in comparison to more standard finite element based methods is that the sole crack front lines have to be meshed and that the calculation of the mechanical fields is avoided. In fatigue, we show that for the most common materials, the deformations of the cracks are small and that the number of cycles leading to coalescence is smaller of a few percent than the one predicted for two isolated cracks. In brittle fracture, we notice, as soon as the size of the cracks becomes comparable to the distance between them, large deformations and considerable decrease of the threshold loading corresponding to the onset of crack propagation.