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 me chanics. Although there exist some differences between 2D and 3D approaches , the usual crack tip singularity exponent 1/2 remains in both cases the hi nge value between strong and weak singularities. In 3D, 0 was expected to b e also a hinge, but it seems difficult to exhibit solutions with a negative exponent. One aim of this paper is to investigate numerically such specifi c cases and to derive some asymptotics of the classical stress intensity fa ctors. The second part is dedicated to prove that, in case of a small linea r ligament, negative exponents cannot exist.