This paper revisits the sliding interface crack problem between elastic and rigid
half-planes studied by Bui and Oueslati and provides an alternative method of
derivation of the solution, which will then be extended to three-dimensional (3D)
crack problems. Based upon the displacement continuation technique of complex
potentials, an appropriate Green function for the isolated edge dislocation dipole at
the interface is given. Then by considering the sliding condition along the interface
crack, the field equations can be obtained for the two-dimensional (2D) problem.
Furthermore, it is shown that the edge dislocation dipole in 2D appears to be a
particular form of the fundamental Kupradze–Basheleishvili tensor in 3D, which
provides a method for deriving the coupled nonlinear integral equations for the
same frictional interface plane crack of an arbitrary shape. The present work
describes how the 3D sliding interface crack is related to the same problem in
2D.
Keywords
interface crack, edge dislocation dipole,
Kupradze–Basheleishvili tensor, singular integral equation
