Kinetics of solution hardening
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The flow stress of solution hardened single crystals and polycrystals is analyzed with respect to its dependence on temperature and strain rate. An evaluation of literature data, especially at low temperatures and low concentrations in fcc alloys, reveals that the interaction between dislocations and discrete, atomic-sized obstacles (or fixed clusters of them) cannot be responsible for solution hardening. A 'trough' model is favored in which the effect of the solutes is postulated to be equivalent to a continuous locking of the dislocations along their entire length, during every waiting period. The macroscopic features of this model are similar to Suzuki's chemical-hardening model. It can also explain the strong interaction of solution hardening and strain hardening at elevated temperatures, as well as basic features of dynamic strain-aging, in particular its strain dependence.
I.
INTRODUCTION
THEeffects of solutes on mechanical properties are manifold and virtually ever-present. They were one of the first to be considered in terms of dislocation theory 1.2 and are one of the last to be understood. There is an extensive and still active literature in the field, which may give the impression of a quantitative understanding including many details. 3 On the other hand, some basic issues are still seriously debated. There are various kinds of interaction between solute atoms and dislocations. A useful classification of these interactions was discovered by Fleischer: 4'5 one large group is 'weak', another is 'strong'; the ratio of the interaction strengths is more than a factor of 10, with few if any materials in between. Strong interactions, giving rise to 'rapid hardening' (with concentration) are always due to solutes with tetragonal distortions, such as the defect pairs typically observed in ionic solids and presumably interstitials in bcc metals 4 (though see Leslie and Sober6). When such tetragonal distortions are not present, such as in substitutional solutions in metals, or interstitials in fcc metals, the various remaining solute/dislocation interactions are weak by comparison. We shall here be concerned only with the latter. We will concentrate on the regime of behavior that has been perhaps the most widely studied: that near the so-called plateau stress at intermediate temperatures. Some of the materials to be considered exhibit abrupt yielding and/or jerky flow over some part of the regime, and others yield and flow smoothly throughout; they all show plateau-like behavior in an 'intermediate' temperature range. Our aim is to analyze a wide range of phenomena, relating to this central regime and contiguous regimes of behavior, and illustrate them by typical examples. This must unfortunately be at the expense of a general coverage of the literature, and of much important detail. Solution hardening has classically been treated as a contribution to the 'friction stress', which shifts the whole stress/strain curve to higher stresses. The real situation is much more complicated; this will be reviewed in Sectio
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