Evolution of the shape of the fronts of a pair of semi‐infinite cracks during their coplanar coalescence

Abstract

AbstractThis paper studies the evolution of the shape of the fronts of a pair of tensile coplanar semi‐infinite cracks propagating in some homogeneous or inhomogeneous brittle material, during their final coalescence. It is based on a previous work which provides the distribution of the mode I stress intensity factor on the fronts of such cracks, after some small but otherwise arbitrary in‐plane perturbation of these fronts. It is first shown that the problem is ill‐posed for propagation in brittle fracture governed by Griffith's criterion, in the sense that the occurrence of multiple bifurcations makes it impossible to unambiguously define the shape of the crack fronts. At each instant, the bifurcation modes consist of symmetric sinusoidal perturbations of the two fronts with a certain “critical” wavelength, which is a characteristic multiple of the width of the ligament remaining between the cracks. There is also an effect of unstable growth of sinusoidal perturbations of wavelength greater than this critical value. For propagation in fatigue or subcritical crack growth governed by some Paris‐type law, these difficulties disappear and the evolution in time of the shape of the crack fronts can be calculated explicitly. The case of a medium with random spatial variations of Paris's constant is considered; statistical information on the shape of the fronts is derived. The results obtained exhibit significant differences with respect to those for the simpler case of a tensile slit‐crack previously considered in the literature.