A simple 1-dimensional model of dislocation activity, including a stress-activated source and mutually interacting dislocations, was examined. It was demonstrated, using numerical and analytical methods, that the dislocations emitted from a 1-dimensional stress-activated source evolved towards a distribution which was self-similar in time. The power-law forms and distribution function were derived. It was shown that the asymptotic distribution was a step function, and that the dislocation front moved linearly with time. The spacing between dislocations in the asymptotic distribution was uniform, and increased logarithmically in time. The number of dislocations increased as t/ln[t], and the strain increased as t2/ln[t].

Dynamic Scaling in a Simple One-Dimensional Model of Dislocation Activity. J.Deslippe, R.Tedstrom, M.S.Daw, D.Chrzan, T.Neeraj, M.Mills: Philosophical Magazine, 2004, 84[23], 2445-54