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.
Several examples show the field and limits of application.
The expressions unite the subsurface behaviour well-known from Finite Element calculations with the boundary layer effect at the free surface. An application to the problem of a quarter circular crack under a linearly varying load shows good agreement with known solutions in the literature. In the present article this behavior is matched asymptotically with the surface solution derived by Benthem yielding a C 1 continuous function along the complete crack front. The resulting boundary layer at the free surface is made up of a power-law segment linked to a logarithmic function. It is shown that its size decreases as the point force approaches the location of the boundary layer and increases for increasing values of Poisson's coefficient.