plane-strain work hardening and transient behavior of interstitial-free steel
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I.
INTRODUCTION
A B R U P T changes in strain path or strain rate can occur during multistage forming operations. In order to understand the effect of such changes on the subsequent formability, the material behavior in each strain state should be known, as well as any transient behavior resulting from the change. Such information is required for the accurate mathematical modeling of multistage forming operations. The evaluation of flow behavior in non-tensile proportional path strain states can be carried out using two methods. First, monotonic tests can be performed in the desired strain state during which loads and strains are monitored and the flow curve calculated. Second, two-stage tests can be performed in which prestraining in the strain state under investigation is followed by straining in uniaxial tension to deduce the flow curve of the first strain path. ~Ranta-Eskola 2 has criticized the two-stage procedure, recognizing that twostage tests do not necessarily reproduce proportional path work-hardening curves. It has long been known that such a change in strain path may be accompanied by inhomogeneous deformation and unusual stress-strain curves. 3.4.5This behavior is not limited to activation by changes in strain path; abrupt changes in strain rate can also produce similar transient behavior. 6-1~ Two-stage strain path tests have also been used to model abrupt changes in strain path (rather than work hardening in the first path), such as those that occur between successive forming operations. Experimental work has been conducted in the balanced biaxial/uniaxial tension mode by Ghosh and Backofen 1 and the tensile/tensile mode by several authors.12-16 Wagoner,17'18 and Wagoner and Laukonis 19'2~ performed two-stage strain path experiments in the plane strain/uniaxial tension mode using an inplane plane-strain tension test. 21'22 Generally the results follow two patterns: A. B. DOUCET, formerly A. E. Browning, Graduate Research Associate, Department of Metallurgical Engineering, The Ohio State University, is Assistant Professor, Department of Mechanical Engineering, Louisiana State University. R.H. WAGONER is Professor, Department of Metallurgical Engineering, The Ohio State University, 116 West 19th Avenue, Columbus, OH 43210. Manuscript submitted December 18, 1986, METALLURGICAL TRANSACTIONS A
Positive Transient: High subsequent yield stress followed by reduced work-hardening rate and premature load instability (ferritic-type s t e e l s l~ , or Negative Transient: Lowered subsequent ,,ield stress followed by increased work-hardening and ennanceo or unaffected load instability strain (brass type~2'la). Aluminum alloys 12'13 and a dual phase steel 2~ generally showed little transient behavior. Ranta-Eskola 2 claimed the different localization behaviors of steels and brass were determined by the sign of the stress change following the abrupt change in strain path. In contrast, Wagoner and Laukonis j9 proposed that the change in work-hardening rate was the important feature in the transient. Reduced work
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