Radiation From Expanding Circular Dislocation Loops and Elastic Precursor Decay

The solution is given for a circular dislocation loop that instantaneously begins to expand by gliding in its plane at constant velocity. The material is assumed to be elastic and isotropic. The solution, expressed as an integral over the loop and over previous times, is evaluated explicitly near the wavefront. This wavefront solution is used to derive an expression for the decay in amplitude of an elastic plane wave propagating in the direction perpendicular to the plane of the loop due to the radiation of elastic waves from the expanding loops. By superimposing the effects of many loops set in motion as the plane wavefront passes, a relation is derived for the decay of the front of the plane wave. This precursor decay relation is found to be the same as obtained previously for infinitely long, straight dislocations based on consideration of either elastic waves radiated from discrete dislocations or energy dissipated in an elastic/viscoplastic continuum model of the material. Thus, dislocation line curvature can apparently be regarded as unimportant in the attenuation of the amplitude of the wavefront. Because detectors have finite rise times, measured precursor amplitudes are indicative of wave amplitudes at small but finite times Δt after the wavefront arrives. Evaluation of the effects of dislocation line curvature on wave amplitudes behind the wavefront requires the consideration of higher order terms in Δt which are neglected in the present analysis.