[SY-A7] The fundamental instability of dislocation transport equations
We analyze the stability of transport equations which describe dislocation dynamics in terms of fluxes of dislocation densities defined on scales above the dislocation spacing. We demonstrate that such transport equations exhibit a generic instability which emerges as soon as a dislocation flux function, which in the simplest case is identical with the shear strain rate on a given slip system, has a negative derivative with respect to the flowing dislocation density. The criterion for instability is equivalent to the condition that the stress required to sustain plastic flow at a given rate is an increasing function of dislocation density. We conclude that dislocation patterning of some kind is an almost trivial, and practically unavoidable, consequence of dislocation transpoort in conjuction with work hardening. Implications for the theory and interpretation of different types of dislocation patterns, and for density-based simulations of plastic flow in general, are discussed.