On the formation and stability of dislocation patterns—III: Three-dimensional considerations

Abstract By distinguishing among mobile and immobile dislocations and operating within the framework of continuum mechanics it is possible to derive a set of partial differential equations of the diffusion-reaction type for the evolution of dislocation species. On examining the competition between gradient dependent terms modelling the motion of dislocations and nonlinear terms modelling their interactions, it is shown that stable solutions are possible. The wavelength turns out to be a material property in agreement with observations. The discussion is limited to one dimension, that is to glide of straight dislocations in the slip direction, and the model corresponds physically to the ladder-like structure of persistent slip bands.

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