Establishment of a steady dislocation density by the Peierls stress in Harper-Dorn creep

Abstract

A model is proposed to understand the dynamic equilibration of dislocations in Harper-Dorn creep. It is assumed that a steady dislocation density is achieved when the stress due to the mutual interaction of dislocations is in balance not only with the applied stress τ but also with the Peierls stress τ_p which fluctuates and even changes sign in the crystal lattice. The model predicts that at steady state, under the condition of τ > τ_p, the dislocation density is dependent on the square of the applied stress. But under the condition of τ < τ_p, the dislocation density is determined by the Peierls stress and thus insensitive to the change of the applied stress. It is observed that these predictions are in excellent agreement with available experimental data. It is thus concluded that the operation of Harper-Dorn creep at stresses less than τ_p is a result of the dependence of the dislocation density on the Peierls stress.