The stress intensity factor distribution along a half circular crack in a half infinite space due to a point force acting normal to the crack faces, is derived by means of the alternating method.
Special attention is given to the solution near the free surface.
Asymptotic expressions are derived for the zero and first iteration of the stresses, displacements and the stress intensity factor. It is proven that after one iteration the stress intensity factor distribution tends to zero very near to the free surface, leaving an extremely small pressure zone at the free surface. The results are compared with other recent theoretical research and experimental evidence. Using a perturbation theory first introduced by Rice, the theory is extended to somewhat half circular cracks. This technique allows for the cycle by cycle calculation of arbitrarily shaped surface cracks subject to an arbitrary mode I stress distribution.