Cyclic stress-strain response of F.C.C. metals and alloys—II Dislocation structures and mechanisms

Abstract

In Part I, we have investigated the effects of four variables, namely, slip character, prior history, temperature and amplitude (giving lives of <10 4 cycles), on the hysteresis loop shape, the cyclic strain hardening and softening curves, and the cyclic stress-strain curves of copper and Cu-7.5% Al. In the present paper the dislocation structures associated with the cyclic stress-strain measurements in Part I have been studied by transmission electron microscopy. In copper, cell structures the size of which increases with both increase of temperature and decrease of amplitude were observed. On the other hand, the Cu-7.5% Al alloy showed dense bands of dislocations interspersed with dislocations distributed generally. The cell structures in copper were found to be independent of the initial condition of the material, whereas the structures in Cu-7.5% Al depended appreciably on initial material condition. The major conclusion drawn from these experiments and those of Part I is that for wavy slip mode materials like pure copper subjected to large cyclic plastic strains, a cyclic mechanical equation of state σ = f(Δε v, ϵ ̇ , T) is approximated (after passing through a transient) in which the saturation stress unique function of the plastic strain range, strain rate and temperature, independent of the prior strain history. Planar slip mode materials like Cu-7.5% Al on the other hand obey no such relationship and their saturation stress response depends strongly on prior history. The influence of the different variables on cyclic strain hardening and softening rates was determined in Part I. Combining these results with the observations in this paper and other evidence in the literature, we have developed a rationale for cyclic strain hardening and have elucidated the factors which either allow or control cyclic strain softening. The cyclic strain hardening rationale utilizes two ideas. The first of these requires that a distinction be made between “small” and “large” plastic strain amplitude hardening behavior. The second idea is that in f.c.c. metals distinct parallelisms exist (a) between stage I unidirectional and low amplitude cyclic strain hardening behavior and (b) between stage II unidirectional and high amplitude cyclic strain hardening behavior. From these ideas we are able to show that unidirectional and cyclic strain hardening mechanisms are largely similar and that cyclically straining a crystal only serves to accentuate those dislocation processes leading to unidirectional strain hardening. We have shown that a prerequisite to cyclic strain softening is reversed plastic strain. This in itself, however, is not sufficient for the complete reversion of an alien dislocation structure to one characteristic of the cyclic state. Incomplete reversion of the alien dislocation structure results when the reversed plastic strain is small and when cross slip is difficult. Further, the rate of cyclic strain softening is found to be controlled by frictional type impediments (jogs etc.) to the mobile dislocation. Finally our model of the high amplitude saturation flow stress employs the conceptually simple free mesh length theory as developed by Kuhlman-Wilsdorf (41) for stage II unidirectional strain hardening. Our adaptation of this model to cyclic behavior gives correct order of magnitude stress response and strain accommodation as well as explaining the instantaneous shape of the stored energy versus cumulative plastic strain curve.