Gauge field theoretic solution of a uniformly moving screw dislocation and admissibility of supersonic speeds

Analysis for a screw dislocation accelerating through the shear-wave speed barrier

“…Holian and Lomdahl, 1998;Meyers et al, 2003;Bringa et al, 2005), but despite a surge of recent activity (Gumbsch and Gao, 1999;Li and Shi, 2002;Olmsted et al, 2005;Sharma and Zhang, 2006;Mordehai et al, 2006;Marian and Caro, 2006), dislocation motion near or at supersonic (transonic for edge) speeds (exceeding the shear-wave speed) is still not well understood. The motion of a dislocation in a crystal is controlled by two physical phenomena of dissipation of energy: first, damping by scattering of elementary excitations in the lattice, which is modeled by a viscous law; and second, radiation of waves excited by the dislocation as it moves through the lattice.…”

“…In the review article of Weertman and Weertman (1980), the existence of a ''Lorentz'' force on the dislocation is addressed, with the conclusion that the analog of the Lorentz force of electromagnetism does not exist for a moving dislocation, because the electromagnetic analogy is imperfect (Weertman and Weertman, 1980). From the theoretical physics point of view, the gauge field approach to the problem (Kadic and Edelen, 1983;Edelen and Lagoudas, 1988;O'Raifeartaigh, 1997) removes the singularity at the core of the moving dislocation at supersonic speed as well as at subsonic (Sharma and Zhang, 2006), the approach in essence being reminiscent of non-local elasticity.…”

The gauge theory of dislocations: a uniformly moving screw dislocation

“…All the elastic fields are nonsingular in the gauge theoretical framework. On the other hand, the solution (4.20) and (4.21) has the same form as the expression given by Sharma & Zhang (2006) if c T = a T and γ = 0.…”

“…Let us mention that the solution of Sharma & Zhang (2006) does not possess the correct behavior in the supersonic region. The solution given by Sharma & Zhang (2006) does not show Mach cones, which are predicted in computer simulations (Gumbsch & Gao, 1999;Koizumi et al, 2002;Li & Shi, 2002;Tsuzuki et al, 2008) and found experimentally (Nosenko et al, 2007). in this field-theoretical framework.…”

“…Neither no Mach cones appear in the supersonic regime. At best, the solution given by Sharma & Zhang (2006) is only valid in the subsonic regime if the characteristic gauge velocity is equal to the shear speed of sound.…”