Nonradiating Dislocations in Uniform Supersonic Motion in Anisotropic Linear Elastic Solids

Over 50 years ago, the late J.D. Eshelby [1] pointed out that an edge dislocation moving at the uniform supersonic speed $$ \sqrt {2{c_s}} $$ , where Csis the shear wave speed, in an infinite isotropic linear elastic solid would not radiate energy in its far-field, provided that the dislocation Burgers vector was along the direction of uniform motion, that is, the dislocation, though moving at a supersonic speed, has an associated field displaying totally subsonic character. Recently Rosakis, Samudrala, and Coker [2] experimentally observed shear cracks in near steady-state propagation at speeds close to this “magic speed” in a brittle polyester resin. Gao et al. [3] showed that in linear elastic media of general anisotropy nonradiating uniformly moving crack solutions and nonradiating uniformly moving dislocation solutions coexist at common supersonic speeds. Using Fourier transform methods, Payton [4] had earlier found nonradiating supersonic dislocation solutions in media of hexagonal symmetry. In this chapter, we adopt a method which is closer in spirit to that given in [3] and deduce the general criteria for the existence of supersonic nonradiating dislocation solutions in media of arbitrary anisotropy along with a simple geometrical method for determining the Burgers vectors of the nonradiating dislocations.