The upper yield stress of polycrystalline iron

Abstract

At the upper yield stress σ uy , a limited number of grains are deforming plastically. Through the influence of their total volume on the effective strain rate in them and consequently on the friction experienced by a moving dislocation, it is calculated that σ uy = σ o u + Δσ 0 log 10 ( 1 Nl 3 ) + kl − 1 2 Here, σ 0 u is the value the friction stress would have if all the grains were deforming, Δσ 0 is the change in friction produced by a tenfold change in strain rate, N is the number of grains per unit volume actually deforming at σ uy , l is the grain diameter and kl − 1 2 is the resistance to the spread of a slip band associated with the presence of the grain boundaries. This relationship agrees well with experimental measurements in which lack of uniformity of the applied stress is minimised. From this, the yield drop in polycrystals emerges as a strain rate effect, although the existence of inhomogeneous yielding depends on dislocation locking.