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Research Papers

M–K Analysis of Forming Limit Diagram Under Stretch-Bending

[+] Author and Article Information
Ji He, Shuhui Li

State Key Laboratory of Mechanical System and Vibration,
Shanghai 200240, China;
Shanghai Key Laboratory of Digital Manufacture for Thin-walled Structures,
Shanghai Jiao Tong University,
Shanghai 200240, China

Z. Cedric Xia

Ford Motor Company,
Dearborn, MI 48121
e-mail: zxia@ford.com

Danielle Zeng

Ford Motor Company,
Dearborn, MI 48121

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the Journal of Manufacturing Science and Engineering. Manuscript received September 18, 2012; final manuscript received April 15, 2013; published online July 17, 2013. Assoc. Editor: Jyhwen Wang.

J. Manuf. Sci. Eng 135(4), 041017 (Jul 17, 2013) (10 pages) Paper No: MANU-12-1282; doi: 10.1115/1.4024536 History: Received September 18, 2012; Revised April 15, 2013; Accepted April 17, 2013

Since the forming limit diagram (FLD) was introduced by Keeler, etc., five decades ago, it has been intensively studied by researchers and engineers. Most work has focused on the in-plane deformation which is considered as the dominant mode of the majority forming processes. However the effect of out-of-plane deformation becomes important in the accurate prediction of formability when thick sheet metals and/or smaller forming radii are encountered. Recent research on the stretch-bending induced FLD (BFLD) has been inconclusive. Some studies indicated that the bending effect will enhance a sheet metal's formability while others suggested otherwise. In this paper, we present an in-depth study of the through-thickness bending effect on the forming limits. The Marciniak–Kuczynski (M–K) analysis is extended to include bending, and models based on both flow theory and deformation theory of plasticity are proposed. The study is limited to the right-hand-side of FLD where the bending is along the major stretch direction. The radial return method is adopted as the framework to integrate constitutive equations. The results show that the bending process decreases the sheet metal formability with the flow-theory based model, while the opposite is true if the deformation theory based analysis is adopted. A detailed examination of the deformation histories from those two models reveals that the loading–unloading-reverse loading process during stretch-bending holds the key to the understanding of the conflicting results. The insight gained from the proposed FLD prediction model in this paper provides a new understanding of how the bending process affects the FLD, which can be used to predict and explain the localized necking phenomenon under the stretch-bending condition.

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References

Figures

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Fig. 2

A cross section of sheet metal with bending radius RDie

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Fig. 1

A thin sheet metal with M–K analysis

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Fig. 7

Bending Effect on right-hand side of FLD in flow theory

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Fig. 8

Bending Effect on right-hand side of FLD in deformation theory

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Fig. 4

Validate flow theory based model with Hutchinson M–K analysis results

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Fig. 5

Effect of Defect Size on limit strain FLD0 in deformation theory

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Fig. 6

Effect of Defect Size on limit strain FLD0 in flow theory

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Fig. 3

Validate deformation theory based model with Hutchinson M–K analysis results

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Fig. 9

Illustration of the stress condition with loading and unloading processes in flow theory

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Fig. 10

Illustration of the stress condition in deformation theory

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Fig. 11

Top surface strain at the onset of localized necking in flow theory

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Fig. 12

Effect of Anisotropy r-values on right-hand side of deformation theory based BFLD

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Fig. 13

Effect of Anisotropy r-values on right-hand side of flow theory based BFLD

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