Forming limit diagrams (FLD) have been widely used as a powerful tool for predicting sheet metal forming failure in the industry. The common assumption for forming limits is that the deformation is limited to in-plane loading and through-thickness bending effects are negligible. In practical sheet metal applications, however, a sheet metal blank normally undergoes a combination of stretching, bending, and unbending, so the deformation is invariably three-dimensional. To understand the localized necking phenomenon under this condition, a new extended Marciniak–Kuczynski (M–K) model is proposed in this paper, which combines the FLD theoretical model with finite element analysis to predict the forming limits after a sheet metal undergoes under continuous-bending-under-tension (CBT) loading. In this hybrid approach, a finite element model is constructed to simulate the CBT process. The deformation variables after the sheet metal reaches steady state are then extracted from the simulation. They are carried over as the initial condition of the extended M–K analysis for forming limit predictions. The obtained results from proposed model are compared with experimental data from Yoshida et al. (2005, “Fracture Limits of Sheet Metals Under Stretch Bending,” Int. J. Mech. Sci., 47(12), pp. 1885–1986) under plane strain deformation mode and the Hutchinson and Neale's (1978(a), “Sheet Necking—II: Time-Independent Behavior,” Mech. Sheet Metal Forming, pp. 127–150) M–K model under in-plane deformation assumption. Several cases are studied, and the results under the CBT loading condition show that the forming limits of post-die-entry material largely depends on the strain, stress, and hardening distributions through the thickness direction. Reduced forming limits are observed for small die radius case. Furthermore, the proposed M–K analysis provides a new understanding of the FLD after this complex bending-unbending-stretching loading condition, which also can be used to evaluate the real process design of sheet metal stamping, especially when the ratio of die entry radii to the metal thickness becomes small.
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July 2013
Research-Article
Forming Limits of a Sheet Metal After Continuous-Bending-Under-Tension Loading
Ji He,
Ji He
Shanghai Key Laboratory of Digital Manufacture for Thin-Walled Structures,
Shanghai Jiao Tong University
,Shanghai 200240
, PRC
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Z. Cedric Xia,
Z. Cedric Xia
1
e-mail: zxia@ford.com
1Corresponding author.
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Danielle Zeng,
Danielle Zeng
Ford Motor Company
,Dearborn, MI 48121
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Shuhui Li
Shuhui Li
Shanghai Key Laboratory of Digital Manufacture for Thin-walled Structures,
State Key Laboratory of Mechanical System and Vibration,
Shanghai Jiao Tong University
,Shanghai 200240
, China
;State Key Laboratory of Mechanical System and Vibration,
Shanghai 200240
, PRC
Search for other works by this author on:
Ji He
Shanghai Key Laboratory of Digital Manufacture for Thin-Walled Structures,
Shanghai Jiao Tong University
,Shanghai 200240
, PRC
Z. Cedric Xia
e-mail: zxia@ford.com
Danielle Zeng
Ford Motor Company
,Dearborn, MI 48121
Shuhui Li
Shanghai Key Laboratory of Digital Manufacture for Thin-walled Structures,
State Key Laboratory of Mechanical System and Vibration,
Shanghai Jiao Tong University
,Shanghai 200240
, China
;State Key Laboratory of Mechanical System and Vibration,
Shanghai 200240
, PRC
1Corresponding author.
Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received November 2, 2012; final manuscript received January 7, 2013; published online May 8, 2013. Assoc. Editor: Tetsuya Ohashi.
J. Eng. Mater. Technol. Jul 2013, 135(3): 031009 (8 pages)
Published Online: May 8, 2013
Article history
Received:
November 2, 2012
Revision Received:
January 7, 2013
Citation
He, J., Cedric Xia, Z., Zeng, D., and Li, S. (May 8, 2013). "Forming Limits of a Sheet Metal After Continuous-Bending-Under-Tension Loading." ASME. J. Eng. Mater. Technol. July 2013; 135(3): 031009. https://doi.org/10.1115/1.4023676
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