On 3D Cracks Intersecting a Free Surface in Laminated Composites

In two- and three-dimensional linear elasticity, the singularities together with matched asymptotic expansions allow to extend the brittle fracture mechanics. Although there exist some difference between 2D and 3D approaches, the usual crack tip singularity exponent \(\frac{1}{2}\) remains in both cases the hinge value between strong and weak singularities. In 3D, 0 was expected to be also a hinge, but it seems difficult to exhibit solutions with a negative exponent. One aim of this paper is to investigate numerically such specific cases and to derive some asymptotics of the classical stress intensity factors. The second part is dedicated to prove that, in case of a small linear ligament, negative exponents cannot exist.