A bifurcation analysis of forming limits for an orthotropic sheet metal is presented in this paper. The approach extends Stören and Rice's (S–R) bifurcation analysis for isotropic materials, with materials following a vertex theory of plasticity at the onset of localized necking. The sheet orthotropy is represented by the Hill’48 yield criterion with three r-values in the rolling (r0), the transverse (r90) and the diagonal direction (r45). The emphasis of the study is on the examination of r-value effect on the sheet metal forming limit, expressed as a combination of the average r-value raverage and the planar anisotropy (Δr). Forming limits under both zero extension assumption and minimum extension assumption as well as necking band orientation evolution are investigated in detail. The comparison between the experimental result and predicted forming limit diagram (FLD) is presented to validate the extended bifurcation analysis. The r-value effect is observed under uniaxial and equal-biaxial loadings. However, no difference is found under plane strain condition in strain-based FLD which is consistent with Hill's theory. The force maximum criterion is also used to analyze FLD for verification.
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October 2014
Research-Article
Bifurcation Analysis of Forming Limits for an Orthotropic Sheet Metal
Shuhui Li,
Shuhui Li
1
State Key Laboratory of Mechanical
System and Vibration
,Shanghai 200240
, China
Shanghai Key Laboratory of Digital
Manufacture for Thin-Walled Structures,
e-mail: lishuhui@sjtu.edu.cn
Manufacture for Thin-Walled Structures,
Shanghai Jiao Tong University
,Shanghai 200240
, China
e-mail: lishuhui@sjtu.edu.cn
1Corresponding author.
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Ji He,
Ji He
State Key Laboratory of Mechanical
System and Vibration
,Shanghai 200240
, China
Shanghai Key Laboratory of Digital
Manufacture for Thin-Walled Structures,
Manufacture for Thin-Walled Structures,
Shanghai Jiao Tong University
,Shanghai 200240
, China
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Z. Cedric Xia,
Z. Cedric Xia
Research and Innovation Center,
Ford Motor Company
,Dearborn, MI 48121
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Danielle Zeng,
Danielle Zeng
Research and Innovation Center,
Ford Motor Company
,Dearborn, MI 48121
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Bo Hou
Bo Hou
Department of Engineering Technology
Non-Linear Solid Mechanics,
Non-Linear Solid Mechanics,
University of Twente
,Enschede 7500 AE
, The Netherlands
Search for other works by this author on:
Shuhui Li
State Key Laboratory of Mechanical
System and Vibration
,Shanghai 200240
, China
Shanghai Key Laboratory of Digital
Manufacture for Thin-Walled Structures,
e-mail: lishuhui@sjtu.edu.cn
Manufacture for Thin-Walled Structures,
Shanghai Jiao Tong University
,Shanghai 200240
, China
e-mail: lishuhui@sjtu.edu.cn
Ji He
State Key Laboratory of Mechanical
System and Vibration
,Shanghai 200240
, China
Shanghai Key Laboratory of Digital
Manufacture for Thin-Walled Structures,
Manufacture for Thin-Walled Structures,
Shanghai Jiao Tong University
,Shanghai 200240
, China
Z. Cedric Xia
Research and Innovation Center,
Ford Motor Company
,Dearborn, MI 48121
Danielle Zeng
Research and Innovation Center,
Ford Motor Company
,Dearborn, MI 48121
Bo Hou
Department of Engineering Technology
Non-Linear Solid Mechanics,
Non-Linear Solid Mechanics,
University of Twente
,Enschede 7500 AE
, The Netherlands
1Corresponding author.
Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received July 17, 2013; final manuscript received May 27, 2014; published online August 6, 2014. Assoc. Editor: Brad L. Kinsey.
J. Manuf. Sci. Eng. Oct 2014, 136(5): 051005 (10 pages)
Published Online: August 6, 2014
Article history
Received:
July 17, 2013
Revision Received:
May 27, 2014
Citation
Li, S., He, J., Cedric Xia, Z., Zeng, D., and Hou, B. (August 6, 2014). "Bifurcation Analysis of Forming Limits for an Orthotropic Sheet Metal." ASME. J. Manuf. Sci. Eng. October 2014; 136(5): 051005. https://doi.org/10.1115/1.4027757
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