Diffraction coefficients of a semi-infinite planar crack embedded in a   transversely-isotropic space
  We have considered a semi-infinite crack embedded in a transversely isotropic medium and studied two special cases, one, in which the axis of symmetry is normal to the crack face and the wave incidence is arbitrary and another, in which the axis lies in the crack plane normal to the edge and the incident wave vector is also normal to the edge. The problem is of interest in Non-Destructive Evaluation, because austenitic steels that are found in claddings and other welds in the nuclear reactors are often modeled as transversely isotropic. In both of cases, we have expressed the scattered field in a closed form and computed the corresponding diffraction coefficients. 
A. Gautesen, V. Zernov, and L. Fradkin