Half-plane crack under normal load: Complete solution

A half-plane flat crack in a transversely isotropic elastic space subjected to arbitrary normal load is considered. An exact closed-form solution is obtained in terms of elementary functions to the complete field of stresses and displacements in the whole space due to a point force loading. Both transversely isotropic and purely isotropic cases are considered. The solution is based on the results previously reported by the first writer. The transversely isotropic solution does not seem to have been reported in the literature. The isotropic case was considered by Ufliand who used the integral transform approach. A comparison with his results shows exact correspondence. Explicit formulas are also given for the stress intensity factor, as well as for the stresses and displacements in the plane of the crack.