A topological study of superplastic deformation in an Al-Li alloy with a bimodal grain size distribution
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B~ m
[1]
where k is the strain rate, o- is the flow stress, m is the strain rate sensitivity, and B is a constant incorporating the effect of temperature and microstructure on the flow stress. Superplastic metallic alloys exhibit a sigmoidal relationship between the flow stress and the strain rate and this flow behavior may be divided into three regions: a superplastic region II with m -> 0.5 at intermediate strain rates, and the non-superplastic regions I and III with m --< 0.3 at low and high strain rates, respectively. This flow behavior is generally interpreted in terms of three different rate controlling mechanisms for the three regions of deformation. The rate-controlling mechanism for deformation in the superplastic region II has not yet been identified unambiguously; the various mechanisms proposed have been reviewed in detail by Kashyap and Mukherjee. I81 Ghosh a n d R a j Igl developed a model for superplastic deformation by recognizing that polycrystalline materials generally have a distribution of grain sizes. Their model postulated that fine grains will deform by a Newtonian viscous Coble diffusion creep mechanism and that coarse grains will deform by an intragranular dislocation powerlaw creep mechanism. It is to be noted that the Coble creep rates are inversely proportional to the cube of the grain size and that the power-law creep rates are independent of grain size. Assuming that the fine grains and the coarse grains deform at the same strain rate (iso-strain rate assumption), Ghosh and Raj t9'1~ were able to produce sigmoidal plots of the variation in stress with strain rate similar to those reported in superplastic alloys, and the model was shown to be in agreement with some of the available experimental resultsJ 9'1~ This is a simple and attractive model for superplasticity by which it is possible to obtain the three regions of flow based on a suitable combination of two creep mechanisms and an appropriate grain size distribution. However, Gifkins t~21raised an important objection to the validity of the iso-strain rate assumption. In addition, the Ghosh and Raj model does not take into ac-
ATUL H. CHOKSHI, Postdoctoral Research Engineer, and AMIYA K. MUKHERJEE, Professor, are with the Division of Materials Science and Engineering, Department of Mechanical Engineering, University of California, Davis, CA 95616. Manuscript submitted July 17, 1987.
METALLURGICAL TRANSACTIONS A
count explicitly the observed microstructural aspects of superplastic deformation such as grain boundary sliding, grain switching, and the emergence of new grains on the surface. The present study was undertaken with a view to examining the possibility that, in a superplastic alloy, fine grains and coarse grains may deform by different mechanisms. A superplastic A1-2.6 pct Cu-2.4 pct Li-0.2 pct Zr-0.07 pct Fe (constituents by wt pct) was obtained from Reynolds Aluminum Co. in the form of sheets of thickness --2.2 mm. The alloy had been processed to recrystallize statically prior to superplastic deformation. Annealing the
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