Dislocation motion and instability

The Peach–Koehler expression for the stress generated by a single (non-planar) curvilinear dislocation is evaluated to calculate the dislocation self stress. This is combined with a law of motion to give the self-induced motion of a general dislocation curve. A stability analysis of a rectilinear, uniformly translating dislocation is then performed. The dislocation is found to be susceptible to a helical instability, with the maximum growth rate occurring when the dislocation is almost, but not exactly, pure screw. The non-linear evolution of the instability is determined numerically, and implications for slip band formation and non-Schmid behavior in yielding are discussed.