On constant membrane stress test for superplastic metals
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On Constant Membrane Stress Test for Superplastic Metals A. K. G H O S H A N D C. H. H A M I L T O N For describing flow properties suitable for thinning calculations in superplastic sheet metal forming, flow stress is assumed to be a unique function of strain-rate and any strain dependence is neglected. While an improvement in such a description is desirable, m a n y calculations ~-3 have reportedly used such simplified descriptions to a fairly successful degree. On the other hand, the stress/strain rate relations in superplastic metals are obtained from uniaxial tensile tests (by progressively stepping the applied strain rate and noting the level of stress when load saturates) and are applied to stress states that are biaxial and in some cases triaxial, by using the effective stress and effective strain-rate concepts of plasticity theory. There is concern a m o n g those involved in the manufacturing of hardware as to the validity of such concepts, and interest exists therefore in conducting biaxial tests to verify these concepts. A balanced biaxial test 4.5 has been successfully used for strain hardening materials at ambient temperatures. This test consists of hydraulic bulging of a circular diaphragm and the measurements of the radius of curvature and surface strain around the pole of the bulge. This test has been automated to the extent of using a biaxial extensometer for closed loop control of the hydraulic pressure so that a constant strain-rate may be maintained near the pole. 6 Since superplastic forming of most metals require very high temperatures and often inert atmosphere, contact extensometers such as these are very difficult to use. It is not surprising, therefore, that simplified assumptions regarding thinning and curvature are being made in order to bypass potentially difficult experimental measurements. 7. In gas pressure bulging o f a circular membrane, assumptions are made that the dome is always a part of a sphere and that thinning is uniform throughout the dome. The pressure, p = ( 2 h / p ) o m a y be expressed in terms of pole displacement, 6 as p = 4 R 2ho6 (R 2 + (~2) - 2 O'.
[
1]
where R = radius of circular die opening, p = radius of curvature of the sheet and h 0 and h are initial and current sheet thickness, repectively. Typical p vs 6 curves based on a preselected o are shown in Fig. 1. If a constant m e m b r a n e stress test is desired, an on-line computer m a y be used to follow such a curve by measuring 3 with a pole displacement gage, during a test and adjusting the pressure according to Eq. [1]. The strain-rate m a y be determined from A. K. G H O S H is Manager, Metals Processing, and C. H. H A M I L T O N is Principal Scientist, Materials Synthesis and Processing, Rockwell International Science Center, Thousand Oaks, CA 91360. Manuscript submitted October 22, 1979.
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If o is a function only of ~, p r e p r o g r a m m i n g of pressure may be made directly in terms of time, the on-line comparison with measured 3 and p being unnecessary.
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