Quantitative assessment of the implications of strain-induced microstructural changes in superplasticity
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I.
INTRODUCTION
SUPERPLASTIC (SP) metals are generally two-phase, eutectic or eutectoid alloys. [1.2] As superplasticity is a diffusion-controlled process, grain growth is likely to occur under its operative conditions (i.e., high temperature, low strain rate), but this is reduced, to a certain extent, by the presence of two phases, such as in Pb62 pct Sn,[3.4] Zn-22 pct Al,[5.6] and AI-33 pct CU,[7] as in CI' + f3-type alloys Ti-6 pct AI-4 pct V[1,8-12] (hereinafter labeled TA6V) and 60-40 brass,[13] or by the presence of a fme dispersion of second phase which acts either as a grain boundary stabilizer, such as y' in the y-y' , 95,[14.15] INCONEL ** 713 nickel-base superalloys RENE* LC,[16,17] or ASTROLOY* NK17CDAT,D,18,19] or as a *RENE and ASTROLOY are trademarks of General Electric Company, Fairfield, CT. **INCONEL is a trademark of Inco Alloys International, Inc" Huntington, WV.
grain refiner, such as ZrAl3 in aluminum alloys[20.21] or a Co-rich phase in the Cu-2.8 pct AI-I.8 pct Si-O.4 pct Co alloy. [22,23] Since the introduction of the term superplasticity into metallurgy in 1945, [24] the first criterion that has been used is the comparison of ductilities for large ranges of temperatures and strain rates. Then, by relating the ductility of several materials to the strain rate sensitivity exponent,[25] it has therefore been set as a first-order relationship: the higher this sensitivity, the larger the ductility in tension. This exponent can be determined calculating the slope of a In O'-ln i plot, where fT and i refer to the stress and the strain rate, respectively. Figure 1 schematizes such a plot. Three regions labeled I through III can be distinguished. In region II, superplasticity is likely to occur, and it corresponds to a maximum of the strain rate sensitivity exponent.
Looking at Figure 1 in the case of a constant grain size J5 plot, the point at which the transition between regions II and III occurs is of particular importance for the purpose of SP forming. The operative conditions, in terms of strain rate, should take place just below this point in region 11.[26] Consequently, it seems attractive to determine such a transition using either experiment or modeling. Moreover, it is well known that during a loading in the SP range, all of the precited materials are likely to exhibit some microstructural evolution, the implications of which being either favorable or detrimental to the SP behavior. In particular, the transition point position can be affected by these structural changes. Therefore, the purpose of this paper is, first, to classify all of the dynamic changes in the SP range, then, to propose some possible theoretical account of these changes, and finally, to apply the results of the modeling to some particular cases.
II. MICROSTRUCTURAL EVOLUTIONS AND THE STRAIN RATE SENSITIVITY EXPONENT A. Two Types of Strain Rate Sensitivity Exponents
There is not a unique way to calculate the strain rate sensitivity exponent and to represent the stress-strain rate relation. The first representation
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