Phenomenological explanation for necking resistance in superplastic deformation
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Table I. Details of Experiments on Expruded Pb-Sn Eutectic Alloy
Condition
Average Grain Size
Annealed 1 h at 100° C Annealed 1 day at 150° C Annealed 20 days at 150° C
Strain Rate Sensitivity, m Measured at e = 5.0 X 1 O -3 nnn 1
0.41 2p 5i0.33 l0µ 0.20
1. T. Erturk, W. L. Otto, and H. A. Kuhn: Met. Trans., 1974, vol. 5, p. 1883. 2. G. S. Sangdahl, E. L. Aul and G. Sachs: Proc. Soc. Exp. Stress Anal., 1948 vol. 6, pp. 1 -18.
Phenomenological Explanation for Necking Resistance in Superplastic Deformation
Fig. 1—Tensile specimen with an initial inhomogeneity (mm). 6A 0 = 5.66 mm 2 .
TOSHIYUKI HIRANO, MIKISHIGE IHARAGI, MASAHARU YAMAGUCHI, AND TOSHIMI YAMANE In superplastic materials there are good correlations between the amount of elongation and strain rate sensitivity, m. 1-4 It has been explained phenomenologically by W. A. Backofen et al. that these correlations are due to large necking resistance observed when m is high.' E. W. Hart also have explained phenomenologically large necking resistance with explicit formulae. 5 We consider that in high m materials neck formation is not only suppressed but also the growth of necks is resisted even if necking occurs during deformation. In this paper, we present a direct test of superplasticity i.e. necking resistance is related to the material's ability to deform in a stable manner in the presence of cross section inhomogeneities. Pb-Sn eutectic alloy (32 pct Pb-68 pet Sn) made from 99.99 pct Pb and 99.99 pct Sn, was cast and extruded to 5.5 mm diam rod. Tensile specimens were prepared from this rod, with a gage section of 50 mm length and 5.5 mm diam. The average grain sizes from 2.r to 10 lt were developed by annealing these specimens for various times at 100°C and 150°C. an was measured at room temperature in the pulling speed range from 0.05 to 10 mm/min by the successive speed change method due to W. A. Backofen et al.' The average grain sizes and an measured at the strain rate of 1 x 10 -3 min' are listed in Table I. An initial inhomogeneity of tensile specimen, SA o (MA 0 = 5.66 mm 2) was made by mechanical working as shown in Fig. 1.
TOSHIYUKI HIRANO, formerly a Graduate Student, Department of Metallurgy, Osaka University, Suita 565, Japan, is now with the National Research Institute for Metals, Tokyo 153, Japan. MIKISHIGE IHARAGI, MASAHARU YAMAGUCHI and TOSHIMI YAMANE are Graduate Student, Associate Professor and Professor, respectively, Department of Metallurgy, Osaka University, Suita 565, Japan. Manuscript submitted December 27, 1974. METALLURGICAL TRANSACTIONS A
20
,8 m=0.33 /d
• m=0.20
É
15
E
i
/ /
%
f
100
m=0.41
.%
200
300 400 TIME (min)
500
600
Fig. 2—The growth of the inhomogeneities for the three specimens with different strain rate sensitivities. The growth of the inhomogeneities, SA is evaluated by the Equation [1] SA
= 4 (DB — DN)
[1]
where D B and D A, are diameters of neck shoulder and neck, respectively as shown in Fig. 1. We measured continuously D B and D N from the projected profile on the screen during tensile t
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