The scattering of a surface wave by a pinned edge dislocation in a semi-infinite, homogeneous, isotropic, 3-dimensional elastic solid was investigated analytically and numerically. An incident wave excited the dislocation that responded by oscillating as a string endowed with mass, line tension and damping. The oscillations of the string-like dislocation generated the secondary (scattered) elastic waves that were of interest here. The back-reaction of the re-emitted waves on the dislocation dynamics was neglected, but the wavelength of the radiation was allowed to be large, comparable or small, as compared to the length of the dislocation. Particular attention was focussed on the field behaviour at the free surface near to the dislocation; and not just on the far-field. The vertical component of displacement at the free surface was studied in detail. An efficient numerical procedure for the computation of the appropriate components of the Green’s function, using a Filon quadrature for the integration of rapidly oscillating functions, was developed. This was validated using known analytical expressions. The secondary radiation generated by the response of the dislocation to the incident wave was also calculated numerically, and the results were also checked by comparing them with analytical expressions for the case where when the radiation wavelength was very long compared to the dislocation length. The interference pattern between the incident wave and secondary wave that was generated at the free surface was studied in detail and found to depend strongly upon the wavelength and dislocation geometry (length and orientation) and also upon the dislocation depth. The response of the dislocation was a particularly sensitive function of the depth. The results were compared with experimental visualizations of the surface-wave–dislocation interaction, made using stroboscopic X-ray imaging. Satisfactory agreement was found. Dislocation velocities of a few percent of the speed of sound, and viscosity coefficients of about 10−5Pas, were deduced.

Interaction of a Surface Wave with a Dislocation. A.Maurel, V.Pagneux, F.Barra, F.Lund: Physical Review B, 2007, 75[22], 224112 (15pp)