Singularity and distribution of stresses around tip of a shallow crack

This report concerns a mode I edge crack of a cusp-type morphology, analytically deriving the increased stress intensity due to the presence of the traction-free surface. The surface effect upon the stress intensity K-I is shown to be given by a factor beta = 3.2(-3/2) in K-I = beta sigma [pi c](1/2), where sigma and c are the mode I stress applied at infinity and the surface crack depth, respectively. The derived stress intensity is 6 percent greater, which means an effective crack length is 12.5 percent greater, than that of an internal crack with a half crack length equal to the surface crack depth, and compares inferiorly with 1.1215 sigma [pi c](1/2) for an edge crack with rectangular corners and with depth c.