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Research Papers

Forming Limits Under Stretch-Bending Through Distortionless and Distortional Anisotropic Hardening

[+] Author and Article Information
Ji He

State Key Laboratory of Mechanical System
and Vibration,
Shanghai Key Laboratory of Digital Manufacture
for Thin-walled Structures,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: benbenhj@sjtu.edu.cn

Bin Gu, Yongfeng Li

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

Shuhui Li

State Key Laboratory of Mechanical System
and Vibration,
Shanghai Key Laboratory of Digital Manufacture
for Thin-Walled Structures,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: lishuhui@sjtu.edu.cn

1Corresponding authors.

Manuscript received May 4, 2018; final manuscript received August 18, 2018; published online October 5, 2018. Assoc. Editor: Gracious Ngaile.

J. Manuf. Sci. Eng 140(12), 121013 (Oct 05, 2018) (14 pages) Paper No: MANU-18-1299; doi: 10.1115/1.4041329 History: Received May 04, 2018; Revised August 18, 2018

The necking behavior of sheet metals under stretch-bending process is a challenge for the forming limit prediction. State-of-the-art forming limit curves (FLCs) allow the prediction under the in-plane stretching but fall short in the case under out-of-plane loading condition. To account for the bending and straightening deformation when sheet metal enters a die cavity or slide along a radius, anisotropic hardening model is essential to reflect the nonproportional loading effect on stress evolution. This paper aims to revisit the M-K analysis under the stretch-bending condition and extend it to accommodate both distortionless and distortional anisotropic hardening behavior. Furthermore, hardening models are calibrated based on the same material response. Then the detailed comparison is proposed for providing better insight into the numerical prediction and necking behavior. Finally, the evolution of the yield surface and stress transition states is examined. It is found that the forming limit prediction under stretch-bending condition through the M-K analysis strongly depends on the employed anisotropic hardening model.

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Figures

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Fig. 1

Uniaxial tensile tests along three different directions of selected steel sheets

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Fig. 2

Experimental setup and specimen of the tension-compression test

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Fig. 3

Comparison between prediction and experimental results of cyclic loading ((a) CBC model, (b) YU model, and (c) HAH model)

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Fig. 4

Uniaxial tensile test comparison between different models and experimental result

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Fig. 5

The illustration of the numerical models of the angular stretch bend test

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Fig. 6

The strain evolution of FE simulation under different conditions: (a) illustration of the position of the material layers, (b) two-step loading condition, (c) punch radius equals to 5, and (d) punch radius equals to 1)

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Fig. 7

The stress comparison of the bottom layer under different conditions ((a) punch radius equals to 1 and (b) punch radius equals to 5)

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Fig. 8

A common situation of plastic deformation for sheet metal material near the clamp

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Fig. 9

States between two continuous stretch-bending steps

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Fig. 10

A cross section of sheet metal with bending radius Rdie and a schematic depiction of strain evolution during stretch-bending process through-thickness direction

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Fig. 11

Bending strain comparison between two different methods

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Fig. 12

Forming limit curves under linear loading condition

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Fig. 13

A schematic depiction of yield loci evolution with different continuum constitutive hardening theories under proportional loading

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Fig. 14

Predicted FLC under stretch-bending process with different Rdie/t ratios ((a) Rdie/t = 10 and (b) Rdie/t = 5)

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Fig. 15

Stress evolutions under biaxial tension after the bending process from different hardening models ((a) bending ratio equals to 5 and (b) bending ratio equals to 10)

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Fig. 16

Stress increments evolution along the major direction from different models

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Fig. 17

Average tension strain evolution and the thickness evolution ((a) average strain evolution of different models, (b) enlarged average strain evolution, and (c) thickness defect evolution)

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Fig. 18

Yield surface evolution in the HAH model for concave side material, during a specific level compression by bending (bending ratio equals to 5) followed by equibiaxial tension deformation (Dot line represents the stress evolution during the forming limit analysis in normal area, solid lines are evolved yield surfaces with hollow circles as the stress state accordingly)

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Fig. 19

Defect evolution for different anisotropic hardening models under different bending ratios followed by equibiaxial tension mode ((a) bending ratio equals to 1 and (b) bending ratio equals to 10)

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