Simulation of static and deformation-enhanced grain growth effects on superplastic ductility
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I.
INTRODUCTION
THE exceptional
ductility observed in superplastic alloys has been shown to be related to the strain-rate sensitivity exponent, m, and a rough correlation between elongation and m has been demonstrated experimentally [q and explained through solid mechanics considerations. [2,3,41 However, unique and absolute correlation between m and elongation has not been achieved, since other factors influence elongation. The factors affecting this correlation relate to microstructural dynamics occurring during deformation, such as grain growth and cavitation. Effects such as grain growth and grain-shape changes have been shown to cause the strain-rate sensitivity exponent, m, and therefore, the resistance to neck growth, to change with strain.[5'6'7] For example, the decrease o f m with strain has been shown to follow grain growth in Ti-6A1-4V alloys. [sl The magnitude of m can also increase with strain if the strain rate imposed is below the maximum m, mm~, and grain growth, in this case, causes a shift of mm~ toward lower strain rates. This was suggested by Ghosh and Ayres [91for data reported by Rai and Grant tS~ on an A1-33Cu alloy. Therefore, it is apparent that one of the more important microstructural changes during superplastic deformation is that of grain growth. Since the temperature range where superplasticity is observed is greater than 0.4 Tin, grain growth is to be expected. However, it is now well known that the grain growth observed in superplastic alloys may include "deformation-enhanced" grain growth, that is, grain growth accelerated by the superplastic deformation. The deformation-enhanced grain growth was initially reported by Clark and Alden [~~ for an Sn-lBi alloy, and similar results have subsequently been observed for many other alloys. [s,tt-~41 Since superplasticity is strongly related to a fine grain size, it has generally been considered that grain growth is damaging to superplasticity. Recently, however, Semiatin and Jonas [~51and Cficeres and Wilkinson ['1 have suggested that grain growth can result in hardening durC.H. HAMILTON, Professor, is with the Department of Materials Science and Engineering, Washington State University, Pullman, WA 99164-2920. Manuscript submitted April 1, 1988. METALLURGICAL TRANSACTIONS A
ing deformation, which may act like strain hardening, thereby enhancing ductility. In the study of a Cu-2.8A 11.8Si-0.4Co alloy, Cficeres and Wilkinson showed that grain growth observed at 823 K was predominantly due to strain enhancement and that the resulting grain size was linearly related to strain at a given initial strain rate. Through a consideration of a general constitutive law for superplastic deformation combined with grain size relationship to applied strain, they derived an expression for an instability parameter, I, (where I = (1 - y m)/m and 3' = (1/tr) (Oct/de) which was invoked in explaining exceptional ductility and necking resistance for the alloy deformed at strain rates corresponding to region I [161 of the log flow-stress vs log strain-rate gr
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