On Dislocation Link Length Statistics for Plastic Deformation of Crystals

Abstract

The statistical distribution function for dislocation link lengths in a unit volume of plastically deformed crystalline materials as proposed by Wang et al. is used to derive the relationship between the average dislocation link length, 〈γ〉, and the dislocation density, Q. It is shown that 〈γ〉 = βϱ−½: β = (2/πc)½ where c is the dislocation network geometrical factor. Also, the mobile dislocation density, Qm, is shown to be directly proportional to the total dislocation density, Q, and the proportionality constant is determined by such factors as mobile dislocation fraction factor, fp, the geometrical factor, c, the Taylor factor, M, and a constant, α. The applicability of the distribution function, φ(λ), is also demonstrated with respect to the statistical constraints for the normalized distribution function, Φ (u), where u = λ/〈λ〉 is the normalized dislocation link length. The analysis is then applied to the strain-hardening and recovery processes during plastic deformation. It is shown that the strain-hardening coefficient, H, is related to the geometry of the three-dimensional dislocation network and is of the order of Young's modulus, E, which is in good agreement with other strain-hardening models and experimental measurements made by the stress change test. A creep rate equation is also obtained for high temperature recovery creep deformation.