Transient elastic P and SV wave edge diffraction by a semi-infinite perfect-slip fracture in an isotropic dispersive solid: A canonical problem

The canonical problem of edge diffraction of transient P or SV waves by a perfect-slip (fluid-filled) fracture is investigated. Closed-form analytic expressions for the time domain particle velocities of the reflected, transmitted, and converted waves on either side of the fracture, for the cylindrical edge-diffracted waves, and for the excited Rayleigh surface waves along the plane of the fracture are obtained. The hosting solid is taken to be homogeneous, isotropic, and dispersive. As to the seismic loss mechanism, two cases are considered: the frictional force/bulk viscosity mechanism and the standard linear solid or Zener mechanism. Numerical illustrations of the different wave constituents are presented, including those applying to postcritical incidence of SV waves. They deal with the case of a well-developed, stationary fracture; the significance of the results to the theory of fracture mechanics with a view to the problem of a transient load at a crack face is briefly indicated.