Abstract
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.
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References
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Barnett, D.M., Zimmerman, J.A. (2002). Nonradiating Dislocations in Uniform Supersonic Motion in Anisotropic Linear Elastic Solids. In: Constanda, C., Schiavone, P., Mioduchowski, A. (eds) Integral Methods in Science and Engineering. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0111-3_7
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DOI: https://doi.org/10.1007/978-1-4612-0111-3_7
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6617-4
Online ISBN: 978-1-4612-0111-3
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