A note on the diffraction coefficients for elastodynamic diffraction by sharp edges

The three dimensional elastodynamic problem of diffraction of waves by a semi-infinite crack is reexamined. The application of Fourier transforms leads to a Wiener–Hopf matrix equation for its solution. An improved product factorization of this matrix due to Abrahams [1] is used to obtain relatively simple expressions for the various diffraction coefficients for incidence of plane and Rayleigh waves. This product factorization does not suffer from the technical difficulty of their inverses having a pole in the wrong half of the complex plane of the transform variable – a difficulty which has been encountered in previous works. For plane or Rayleigh wave incidence it is shown that the diffraction coefficients for body waves can be written in terms of the dynamic stress-intensity factors.