Uniformly Moving Transonic and Supersonic Dislocations

Abstract

General solutions have been obtained for screw, gliding edge, climbing edge, and mixed dislocations traveling with a uniform motion at velocities in the transonic and supersonic velocity range. The motion is considered to occur on planes that give up finite amounts of energy per unit distance of dislocation movement. The only previous work on this problem is Eshelby's general solution of the supersonic screw dislocation and Stroh's and Ang and Williams' work on discrete dislocations that move on planes that give up an infinite amount of energy per unit distance of dislocation movement. The most interesting new result is that the limiting dislocation velocity of an ordinary dislocation pushed by an applied stress lies in the transonic velocity region, not at the shear‐wave velocity as is usually assumed in the literature. Only the screw dislocation is limited by this latter velocity. We have reached the following conclusions: Any dislocation that runs on a plane that gives up energy must move at a supersonic velocity if the force law across the plane never changes sign. A supersonic dislocation, like a subsonic dislocation, can move at an arbitrary velocity. A dislocation that moves on a plane that gives up energy will move in the transonic velocity region if the force law does have a sign reversal. A dislocation that moves in the transonic velocity region cannot move at an arbitrary velocity; it moves at a unique velocity whose value depends on the exact force law.