Dynamic scaling in a simple one-dimensional model of dislocation activity

Abstract

We examine a simple one-dimensional (1D) model of dislocation activity, including a stress-activated source and mutually interacting dislocations. We demonstrate, through numerical and analytical steps, that the dislocations emitted from a 1D stress-activated source evolve towards a distribution which is self-similar in time, and we derive the power-law forms and distribution function. We show that the asymptotic distribution is a step function, and the dislocation front moves out linearly in time. The spacing between dislocations in the asymptotic distribution is uniform and increases logarithmically in time. The number of dislocations increases as t/ln(t), and the strain increases as t ²/ln(t).

Acknowledgements

D.C.C. acknowledges the support of the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract DE-AC03-76SF00098. M.J.M. and N.T. acknowledge support from the Air Force Office of Scientific Research under grant F496200-02-1-0013. The Clemson group acknowledges support from the Department of Energy (Office of Basic Energy Sciences) under grant DE-FG02-03ER46031.

Notes

Present address: Advanced Structural Materials Section, Corporate Strategic Research, Exxon Mobil Research and Engineering Co., Annandale, New Jersey 08801, USA

Of course, for such a single source, the opposing dislocations have opposite line directions and the same Burgers vector magnitudes. The same forces are created by considering that all dislocations in this model have the same line directions and opposite Burgers vector magnitudes.