  We use three-dimensional discrete dislocation dynamics simulations (DDD) to
study the evolution of interfacial dislocation network (IDN) in
particle-strengthened alloy systems subjected to constant stress at high
temperatures. We have modified the dislocation mobility laws to incorporate the
recovery of the dislocation network by the climb. The microstructure consists
of uniformly distributed cuboidal inclusions embedded in the simulation box.
Based on the systematic simulations of IDN formation as a function of applied
stress for prescribed inter-particle spacing and glide-to-climb mobility ratio,
we derive a relation between effective stress and normalized dislocation
density. We use link-length analysis to show self-similarity of immobile
dislocation links irrespective of the level of applied stress. Moreover, we
derive the dependence of effective stress on the ratio between mobile to
immobile dislocation density based on the Taylor relation for strain hardening
materials. We justify the relation with the help of a theoretical model which
takes into account the balance of multiplication and annihilation rates of
dislocation density.
