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Research Papers

Developments of Multistep Inverse Finite Element Method and Its Application in Formability Prediction of Multistage Sheet Metal Forming

[+] Author and Article Information
Bingtao Tang1

Institute of Engineering Mechanics, Shandong Jianzhu University, Jinan 250101, China; State Key Laboratory of Materials Processing and Die and Mould Technology, Huazhong University of Science and Technology, Wuhan 410082, Chinatbtsh@hotmail.com

Yunjiang Li, Xiaoyang Lu

Institute of Engineering Mechanics, Shandong Jianzhu University, Jinan, China

1

Corresponding author.

J. Manuf. Sci. Eng 132(4), 041013 (Jul 23, 2010) (9 pages) doi:10.1115/1.4001868 History: Received May 26, 2009; Revised May 14, 2010; Published July 23, 2010; Online July 23, 2010

In the paper, the multistep inverse finite element method (FEM) has been introduced to improve the accuracy of simulation in sheet metal stamping. Furthermore, the multistep inverse FEM can be used to obtain the strain/thickness distribution and shape of blank in the intermediate configurations. But there are three key problems, which are essential to implement multistep inverse FEM: the fist one is how to obtain the intermediate configurations of intermediate steps, the second one is how to find the corresponding Z coordinates in the sliding constraint surface, and the last one is how to update strain/stress distribution in the intermediate configurations in a fast and reliable way. Based on the known configurations of punch and die of the current step, the strategy of area minimization coupled with feasible sequential quadratic programming code is used to obtain initial intermediate configurations. An efficient walk-through point location algorithm with its complexity O(n1/d) per point (d means the space dimension) is used to deal with contact searching problem and restrain the movement of corresponding nodes of intermediate configurations. In order to preserve the computational efficiency of inverse FEM, a pseudodeformation theory of plasticity based constitutive equation is proposed, which can well reflect the actual forming condition such as elastic/plastic deformation or loading/unloading condition. The above-mentioned improvements are implemented in our in-house inverse analysis software INVERSTAMP/MULTISTEP module. The presented algorithms are applied to a two-step cylinder cup deep-drawing product and three-step S-rail forming case. The numerical results compared with explicit dynamic solver LS-DYNA3D confirm its validity in formability prediction of intermediate shapes and final workpiece.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

The kinematics relations of a thin shell model with intermediate configuration

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Figure 2

Generation of intermediate sheet configuration with known die and punch profiles

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Figure 3

Two mesh system of final and intermediate configuration: (a) 40 mm punch travel, (b) 30 mm punch travel, and (c) 20 mm punch travel

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Figure 4

Walk-through algorithm to constrain the node movement

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Figure 5

Barycentric coordinates and their signs: (a) point in a triangular and (b) signs of barycentric coordinates

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Figure 6

Walk-through algorithm based on barycentric coordinates

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Figure 7

Uniaxial tress-strain curve for multistep forming process

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Figure 8

Flowchart of multistep inverse FEM

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Figure 9

Two-step forming workpiece: (a) CAD modeling of final workpiece and (b) dimensions of half of the final workpiece

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Figure 10

Comparisons of thickness distribution between proposed algorithm and incremental based FEM code: (a) from flat blank to intermediate sheet and (b) from flat blank to intermediate sheet and then final workpiece

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Figure 11

Tools location with 10 mm drawing depth

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Figure 12

Tools location with 20 mm drawing depth

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Figure 13

Initial solution of intermediate configuration with 10 mm drawing depth

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Figure 14

Initial solution of intermediate configuration with 20 mm drawing depth

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Figure 15

Final workpiece with 40 mm drawing depth

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Figure 16

Contour of final workpiece with cutting sections AB and CD

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Figure 17

Comparison of thickness distribution (along AB section line)

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Figure 18

Comparison of thickness distribution (along CD section line)

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