The flow stress of body-centred cubic metals at low temperatures

Abstract

Recent measurements on iron single crystals of 99·999% purity, containing less than 0·05 p.p.m. of carbon, show that the strong increase of the flow stress with decreasing temperature in the range 10-300°K is largely independent of small concentrations of interstitial impurities; it appears to be due to the Peierls force. Theoretical considerations employing the double-kink mechanism of dislocation propagation do not account satisfactorily for the observations. A new, simple, model is developed in which dislocation movement is induced by thermally activated formation of curved segments of dislocations trapped in Peierls troughs, the curvature being determined essentially by the effective shear stress. The predominant role of the shear stress in the determination of the curvature of the dislocation segment in the saddle-point configuration is the principal feature differentiating the present model from earlier double-kink treatments. Measurements made on iron and other body-centred cubic metals are successfully explained on the basis of the model.

Dislocation mechanics-based constitutive equations

“…Hartley, [10] using a simple model for the dislocation intersection mechanism, showed that A was inversely proportional to glide-plane shear stress for small stresses. Similarly, in the case of the PeierlsNabarro stress due to the dislocation lattice interaction, Feltham [11] showed that A is proportional to Ϫ1/2 for small stresses and to Ϫ3/2 for large stresses, with an intermediate range in which A is inversely proportional to . Experimentally measured activation areas also showed a close correspondence to the inverse proportionality relation.…”

“…In summary, the relation for fcc metals is [9] and for bcc metals is [10] where [11] General Constitutive Equation…”

“…In mathematical terms, [18] The Eqs. [9] through [11] have successfully described the necking behavior of copper [8,13] and tantalum [18,28] as functions of temperature and strain rate, showing the contrasting behavior of fcc and bcc metals: the uniform strain before necking increases with strain rate for fcc metals and decreases with strain rate for bcc metals. The fcc instability condition was used [8] to discount dislocation drag being responsible for ds d Ͼ s observations of a significant upturn in flow stress of copper at strain rates greater than 10 3 s Ϫ1 .…”

Correlation between the temperature dependence of yield stress and the nature of solute distribution in Cu–Ni solid solutions

“…These barriers were regarded as "smeared out" over the segment length in a manner somewhat similar to the "kink-pair mode of escape" of screw dislocations from a Peierls barrier [34]. Pinning of screw dislocations with solute atoms was considered too weak by comparison to result in effective barriers to glide.…”

Comments on the paper `The flow stress of body-centred cubic metals at low temperatures'

“…In the paper by Feltham (1969) it is claimed that a new theory of the flow stress in bodycentred cubic metals is presented. The model is based on the simple bowing out of a dislocation bound in a 'Peierls' trough.…”