Effect of changing strain paths on
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I.
INTRODUCTION
F O R M I N G limit diagrams (FLDs) have been a valuable tool for analyzing sheet metal forming ever since they were first introduced by Keeler.l~l They describe the strain combinations (e~ - e2) that lead to failure by localized necking. The experimental methods for determining FLDs are well established. IL2j Most of the FLDs in the literature and in industrial data bases have been obtained by stretching over a hemispherical dome. Differences between results obtained by in-plane loading and punch stretching have been found, 13] but recent work 14] indicates that these differences are smaller than previously reported. Such differences are caused, at least partially, by the small gradual curvature of the strain paths tsj during punch stretching. The strain path changes in real stampings are often much greater. These may be gradual as metal flows through the die or abrupt when metal is transferred from one press to another. The influence of these strain path changes on formability has been known by FLD users, who have noted that occasionally some parts will have regions strained well above the accepted limits without evidence of localized necking or that necking failures sometimes occur in regions where the strains are well below the FLD. Such observations have triggered a number of research efforts to explore the effects of changing strain paths, t6-~~ It is generally accepted that the strain limits can be either raised or lowered depending on the nature of the strain path change. However, the ways the strain limits change vary with materials, I~II making generalization difficult. Even for alloys of the same base material, the response to these changes can be quite different. 1~21 Most of the previous studies have been on steel. Mtischenborn and S6nne ~61 have made a rather complete study on drawing quality steel. The work of Sang and Lloyd jl21 is one of very few on A1 alloys. There is a growing use of aluminum in automobile
A L E J A N D R O GRAF, is with Automated Analysis Corp., Ann Arbor, MI 48104-6767, and W I L L I A M HOSFORD, Professor, is with the Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI 48109-2136. Manuscript submitted December 10, 1992. METALLURGICAL TRANSACTIONS A
bodies to replace steel parts, thereby reducing weight and improving fuel efficiency. It is important to document the FLDs of aluminum alloys, particularly because their formability is generally poorer than steel. This article presents the results obtained on A1 2008 T4, which is one of the potential alloys for automobile bodies.
II.
MATERIAL
The chemical composition of the alloy was 0.93 pct Cu, 0.67 pct Si, 0.34 pct Mg, 0.19 pct Fe, and 0.05 pct Mn, with the balance of aluminum. The microstructure consisted of pancake-shaped grains. The average intercept length of random lines on the cross section was 27 /zm. Average intercepts in the principal directions were about 20 txm normal to the plane of the sheet and about 45 /xm parallel to both the rolling direction (RD) and tran
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