Analytical solution for mode I crack orthogonal to free surface

Abstract

In this paper, an analytical solution for the singular stress field near a flat crack which is orthogonal to the free surface is proposed. The singular stress field of a three-dimensional surface crack is obtained by the principle of superposition. The stresses of mode-I surface crack are derived by combining the solution of a three-dimensional crack and a second solution due to a singular traction on the free surface of a semi-infinite body. The closed form solution for the second solution is evaluated and the stress distribution at the free surface of the crack is compared with some existing results that appeared in the literature.