Stress distribution due to a griffith crack at the interface of an elastic half plane and a rigid foundation

The stress field in a semi-infinite elastic media bonded to a rigid foundation and containing a crack at its interface is determined. Two specific problems are discussed-first when the elastic half space is under shear such that σ_xv ~ P as √(x² + y²) → ∞ and next when the crack is opened by equal and opposite pressure on each of its sides. The solution is obtained via Fourier transforms which lead to a simultaneous set of dual integral equations containing a trigonometric kernel. It is observed that in a small region near the ends of the crack, violent oscillations occur in both the stress and displacement components.