Theory of Steady-State Creep Based on Dislocation Climb

Abstract

A theory of steady‐state creep is developed using Mott's mechanism of dislocation climb. It is assumed in the analysis that the rate‐controlling process is the diffusion of vacancies between dislocations which are creating vacancies and those which are destroying them. The concentration of vacancies along a dislocation line is determined by setting the change in the free energy caused by a decrease or increase in the number of vacancies equal to the change in the elastic energy occuring during dislocation climb. The creep equation that results from the analysis is $$\mathrm{creep\; rate}=\mathrm{const}{\mathrm{\hspace{0.17em}(\sigma }}^{\alpha }\mathrm{/kT)}\exp \mathrm{(-Q/kT)}$$ where α is a constant $\text{(α∼3\hspace{0.17em}}\mathrm{to}\text{\hspace{0.17em}4)}$ , Q is the activation energy of self‐diffusion, kT has its usual meaning, and σ is the stress. This equation is valid in the stress range from the critical shear stress to a stress about equal to 10⁸ to 10⁹ dynes/cm². At larger stresses the creep rate increases much more rapidly with stress.