The tensile tunnel-crack with a slightly wavy front

Several problems of three-dimensional fracture mechanics for a planar tunnel-crack loaded in pure mode I in an infinite elastic solid are investigated. The first is that of the bifurcation from the fundamental straight configuration of the crack front in brittle fracture, i.e. the possibility of the appearance of another, curved configuration still possessing the property that the stress intensity factor be constant along the front. The second is the stability of the same fundamental configuration versus small deviations from straightness within the crack plane in fatigue. The third is the (analytic at the start, but numerical in fine) determination of the fundamental “kernel” appearing in the integral expression of the variation of the stress intensity factor induced by a small perturbation of the crack front; this topic is considered after (and not before as would seem more natural) the first two in order to illustrate the fact that investigating the latter does not require a precise knowledge of that kernel as a necessary prerequisite. The last question envisaged is (again analytical first, but finally numerical) the calculation of the crack-face weight function in mode I for the crack configuration envisaged. Gao and Rice’s previous works (1985, ASME J. Appl. Mech. 52, 571-519; 1986, ASME J. Appl. Mech. 53, 774-778; 1987, Int. J. Fracture 33, 155-174; 1987, ASME J. Appl. Mech. 54, 627-634; 1988, Int. J. Solids Structures 24, 177-193) devoted to other crack shapes have been an important source of inspiration for this study with regard to both the topics investigated and some of the methods used