Some Unifying Relations for Moving Dislocations

Lothe's formula for the self‐force on a bent dislocation and Brown's formula for the stress in the plane of a planar loop are generalized to be valid for uniformly moving dislocations when the energy factor is replaced by the Lagrangian factor. Application to straight dislocations in isotropic media shows that the screw dislocation becomes unstable with regard to bends at high velocities. The Lagrangian factor is also used to extend Lothe's representation of the energy flow along a moving straight dislocation and to show the relationship between the mass, the back stress in acceleration, and the energy radiation from an oscillating straight dislocation.