Effect of stress-strain-law transients on formability
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I.
INTRODUCTION
ABRUPTchanges in strain path, as, for example, between two different proportional paths, can produce unexpected stress-strain behavior immediately following the transition. This transitional region is often characterizable in one of two qualitative ways: Type 1: lowered flow stress accompanied by rapid workhardening. Type 2: increased flow stress accompanied by lowered or possibly negative work hardening. The exact form of the transient is difficult to determine experimentally because of its often small extent (in both stress and strain range affected) and because the rapidlychanging flow stress may lead to inhomogeneous deformation. For these same reasons, it is also difficult to assess experimentally the impact of these transients on subsequent deformation behavior. The importance of the transient may, however, be separated from other complications by predictive modeling of an arbitrarily-chosen transient, subsequent deformation behavior, and formability. A sheet tensile test provides a simple and computationally-efficient example of a forming operation for this purpose. Changing strain paths have long been known to correlate with the appearance of inhomogeneous deformation and unusual stress-strain curves. Polakowski and Mostovoy ~'2 observed both strain-softening (gross macroscopic) and "wavy deformation" in copper and iron alloys. Pascoe 3 measured stress-strain transients of the second type in HSLA steels after changes of axes in uniaxial tensile tests. Detailed measurements of deformation behavior following small-strain path changes have shown a range 47 of transient effects. Ghosh and Backofen 8 used two-stage strain path tests to investigate work-hardening rates in proportional, but nontensile, strain states. They identified two kinds of material behavior, the first of which they labeled the "ferritic" type (aluminum-killed steel), corresponding to an increased tenK. CHUNG, Postdoctoral Research Fellow, and R.H. WAGONER, Associate Professor, are with the Department of Metallurgical Engineering, The Ohio State University, Columbus, OH 43201. Manuscript submitted June 20, 1985.
METALLURGICAL TRANSACTIONS A
sile yield stress following biaxial straining. The second kind of behavior, labeled "nonferritic" (70/30 brass), showed premature yielding during the tensile part of the test. In each case, the magnitude of the effect increased with increasing prestrain. Commercially pure aluminum showed only small changes with changing strain path. Although not discussed by Ghosh and Backofen, the subsequent work-hardening rate was reduced for steel, increased for brass, and little changed in aluminum. Therefore, in each case, the subsequent stress-strain curve tended to converge with the one extrapolated from the first proportional path. Ghosh and Backofen concluded that formability was different in balanced biaxial tension than in uniaxial tension because of the underlying difference in work-hardening rate between the two strain states. Ranta-Eskola 9 criticized this conclusion because of uncertainti
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