Constitutive Relation for Rate-Dependent Plastic Flow in Polycrystalline Metals

Abstract

The rate‐dependent constitutive relation developed by Taylor, which considers dislocation motion only in glide directions and on glide planes for which the shear stress is maximum, is extended to include dislocation motion in all glide directions on all glide planes. The theory requires that grain orientation be random, that expanding dislocation loops be rectangular, and that the velocity of edge dislocations be much greater than the velocity of screw dislocations. The velocity of screw dislocations is assumed to be given by v_s=v_m exp (‐B/τ), where τ is the applied shear stress, B is a constant, and v_m is the elastic shear wave velocity. On the basis of this theory, elastic wave attenuation in Armco iron is calculated and compared with the experimental data of Taylor and Rice. It is found that the mobile dislocation density necessary for the theoretical calculation to agree with experimental data is five times greater than that obtained by Taylor on the basis of the simpler theory. Likewise, for a given shear stress, it is found that the dislocation velocity is greater than that determined previously. This indicates that the results obtained on the basis of the simpler theory may significantly underestimate the velocity of individual dislocations as well as the mobile dislocation density.