Finite element analysis of a subsurface crack

The problem of a subsurface crack parallel to the surface of a half space was studied by the finite element method. Without using the interface or gap elements over the crack faces, the crack faces would penetrate into each other for the traction-free boundary condition under shear loading, which is physically impossible. Using the gap elements, this problem was avoided, and a contact zone was observed near one crack tip. The size of the contact zone decreases but the maximum contact pressure at the closed crack tip increases as the crack approaches the surface. For tensile and shear loadings, both K_I (mode I stress intensity factor) and K_II (mode II stress intensity factor) increase as the crack approaches the surface. For shear loading there is no K_I at the closed tip and the K_I and K_II at the open tip are comparable as the crack approaches the surface.