On radiation-free transonic motion of cracks and dislocations

Eshelby has shown that a glide dislocation can move without radiation of energy at  2 p of the shear wave speed. It is also known that the same velocity plays a special role in shear crack propagation. This result has not received wide attention in the past due to lack of experiments and numerical simulations of transonic defects. Recent experiments on transonic shear fracture and molecular dynamics simulations of dislocation motion have stimulated renewed interest in the behavior of cracks and dislocations beyond the subsonic regime. We attempt to provide a uni®ed treatment of transonic cracks and dislocations by elaborating on the fundamental result of Eshelby. We develop a uni®ed treatment of radiation-free transonic motion of both cracks and dislocations. We use Stroh's method to generalize the Eshelby theorem to orthotropic and anisotropic elastic solids. In the case of orthotropic solids, we provide a proof of existence of the radiation-free speed. In the case of general anisotropic solids, there are three wave speeds c3 < c2 < c1 in any given crystal orientation at which a moving defect is considered. In the ®rst transonic regime c3< v< c2, we show that there always exists a radiation-free state for any given velocity v of a moving defect. In the second transonic regime c2 < v < c1, the existence of radiation-free states appears to depend on both the symmetry properties of the material and the defect orientation. Examples of existence in the second transonic regime include a crack 0022-5096/99/$ see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S0022 -5096 (98)00126 -4 Journal of the Mechanics and Physics of Solids 47 (1999) 1941±1961 * Corresponding author. Fax: +1 415 723 1778. E-mail address: [email protected] (H. Gao) propagating in an isotropic solid and a crack propagating along a plane of symmetry in an orthotropic solid. # 1999 Elsevier Science Ltd. All rights reserved.