The diffraction of elastic waves by an imperfect fusion bond

We consider diffraction by a semi-infinite crack located along a fusion interface between two differing elastic media. Two types of crack, namely open and partially closed cracks, are investigated. An open crack is modelled by a stress-free contact boundary condition and a partially closed crack is modelled by a spring contact boundary condition. For the latter, the jump in the stress across the crack is assumed to be proportional to the jump in the displacement across the crack. This situation arises in, for example, a K-weld where the fine grain of the parent material (for example, ferritic or forged austenitic steel) is in stark contrast with the coarse-grained weld metal (for example, austenitic weld metal). In the metal weld the direction of the grain axis varies through the metal. However, diffraction is a local phenomenon and so the austenitic steel is assumed to have a zonal axis so that it may be modelled by a transversely isotropic composite. The ferritic or forged austenitic steel will be modelled as an isotropic material.