A NEW DYNAMIC MODEL FOR STUDY OF DISLOCATION PATTERN FORMATION

Based on the principle given in nonlinear diffusion-reaction dynam-ics, a new dynamic model for dislocation patterning is proposed by introducing arelaxation time to the relation between dislocation density and dislocation flux. Theso-called chemical potential like quantities, which appear in the model can be derivedfrom variation principle for free energy functional of dislocated media, where the freeenergy density function is expressed in terms of not only the dislocation density itselfbut also their spatial gradients. The linear stability analysis on the governing equa-tions of a simple dislocation density shows that there exists an intrinsic wave numberleading to bifurcation of space structure of dislocation density. At the same time, thenumerical results also demonstrate the coexistence and transition between differentdislocation patterns.