Effect of concurrent grain growth on the stress-strain rate curve of superplastic materials

Abstract

where K is a constant, a the stress, m (= 1/n) the strain-rate sensitivity index, d the grain size, p the grain size exponent, Q the activation energy, R the gas constant and T the absolute temperature. The log alog ~ plots of superplastic materials are of sigmoidal shape in general. But in the Zn-A1 eutectoid alloy, an increase [1 4] and a decrease [5-9] in m at low strain rates were observed by different investigators. Rai and Grant [10] showed that the cause of sigmoidal shape of the a-~ plot in an A1 Cu alloy is the concurrent grain growth of fine grains at low strain rates. Consequently, the concurrent grain-gro~vth effect was used as an argument to interpret the low m observation in the ZnA1 eutectoid alloy [11]. In a study of the superplastic behaviour of the Sn Pb eutectoid alloy, we observed the opposite effect of an increase in m at low strain rates because of concurrent grain growth in a differential strain-rate test. The purpose of this communication is to present our observations in this regard and to interpret them in terms of the test procedure. The Sn-38wt%Pb eutectic alloy was prepared starting from 99.99% pure metals. The cast ingot of 75 mm diameter was extruded into 9.5mm diameter rods, from which tensile specimens of 6 mm diameter and 25 mm gauge length were obtained. Differential strain-rate tests were performed on an Instron machine making use of an electrically heated silicone oil bath. Three successive cycles of crosshead speed changes were performed on a single specimen in order to obtain the stress-strain-rate behaviour at a given test temperature. The crosshead speeds were varied in increasing order during the first two cycles of the test, whereas the decreasing sequence was followed in the third cycle. The stress-true strain-rate plots thus obtained are shown in Fig. 1. It is seen that the flow stress at low strain rates is lower in the first cycle than in the other two cycles. From a comparison of the slopes of these plots, the rate sensitivity index in the first cycle is higher than that of the other two cycles in the lowest strain-rate range. While the log a-log plots in the second and third cycles are linear over the whole strain-rate range, its slope in the first cycle becomes constant at strain rates higher than 10-Ssec -~. These results suggest that deformationinduced coarsening of the microstructure occurs mostly during the initial stages of the test. Metallographic examination of the specimens before and after these tests was carried out to assess the grain coarsening arising from a total elongation of ~ 50%. The mean intercept length in the starting condition is 5.5 #m + 1.0#m and after the tests at 355 and 423 K, the intercept lengths are 6.1 4- 0.9 and 6.9 + 0.8#m, respectively. The increase in m at low strain rates in this study differs from the trend observed by Rai and Grant [10]. Although the fine grain size of superplastic materials is generally stable because of the second-phase particles or duplex structures, some strain-enhanced grain growth does occur during superplastic deformation [12]. Recently, Sepulveda and Mishra [13] analysed the strain-enhanced grain-growth data of superplastic duplex materials with the grain-coarsening equation