On radiation-free transonic motion of cracks and dislocations

Eshelby has shown that a glide dislocation can move without radiation of en ergy at root 2 of the shear wave speed. It is also known that the same velo city plays a special role in shear crack propagation. This result has not r eceived wide attention in the past due to lack of experiments and numerical simulations of transonic defects. Recent experiments on transonic shear fr acture and molecular dynamics simulations of dislocation motion have stimul ated renewed interest in the behavior of cracks and dislocations beyond the subsonic regime. We attempt to provide a unified treatment of transonic cr acks and dislocations by elaborating on the fundamental result of Eshelby. We develop a unified treatment of radiation-free transonic motion of both c racks and dislocations. We use Stroh's method to generalize the Eshelby the orem to orthotropic and anisotropic elastic solids. In the case of orthotro pic solids, we provide a proof of existence of the radiation-free speed. In the case of general anisotropic solids, there are three wave speeds c(3) < c(2) < c(1) in any given crystal orientation at which a moving defect is c onsidered. In the first transonic regime c(3) < v < c(2), we show that ther e always exists a radiation-free state for any given velocity v of a moving defect. In the second transonic regime c(2) < v < c(1), the existence of r adiation-free states appears to depend on both the symmetry properties of t he material and the defect orientation. Examples of existence in the second transonic regime include a crack propagating in anisotropic solid and a cr ack propagating along a plane of symmetry in an orthotropic solid. (C) 1999 Elsevier Science Ltd. All rights reserved.