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TECHNICAL PAPERS

# Semi-Analytic Hybrid Method to Predict Springback in the 2D Draw Bend Test

[+] Author and Article Information
Myoung-Gyu Lee1

Department of Materials Science and Engineering, 2041 College Road, Ohio State University, Columbus, OH 43210

Daeyong Kim

Research and Development Division for Hyundai Motor Company and Kia Motors Corporation, 772-1, Jangduk-Dong, Whasung-Si, Gyunggi-Do, 445-706, Korea

R. H. Wagoner

Department of Materials Science and Engineering, 2041 College Road, Ohio State University, Columbus, OH 43210

Kwansoo Chung2

School of Material Science and Engineering,  Seoul National University, 56-1, Shinlim-Dong, Kwanak-Ku, Seoul 151-742, Koreakchung@snu.ac.kr

This is the solution of the ordinary differential equation, $dα¯=C1−C2α¯$, which is the relationship at the reference state (or the uniaxial tension test condition).

In the conventional U channel draw bend test, friction by the blank holder or the draw bead should be considered, which makes the analysis a little more complicated.

1

Current address: Eco-Materials Research Center, Korea Institute of Machinery and Materials 66, Sangnam, Changwon, Kyungnam 641-101, Korea.

2

Corresponding author.

J. Appl. Mech 74(6), 1264-1275 (Apr 10, 2007) (12 pages) doi:10.1115/1.2745390 History: Received September 22, 2006; Revised April 10, 2007

## Abstract

A simplified numerical procedure to predict springback in a 2D draw bend test was developed based on the hybrid method which superposes bending effects onto membrane solutions. In particular, the procedure was applied for springback analysis of a specially designed draw bend test with directly controllable restraining forces. As a semi-analytical method, the new approach was especially useful to analyze the effects of various process and material parameters on springback. The model can accommodate general anisotropic yield functions along with nonlinear isotropic-kinematic hardening under the plane strain condition. For sensitivity analysis, process effects such as the amount of bending curvature, normalized back force and friction, as well as material property effects such as hardening behavior including the Bauschinger effect and yield surface shapes were studied. Also, for validation purposes, the new procedure was applied for the springback analysis of the dual-phase high strength steel and results were compared with experiments.

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## Figures

Figure 1

(a) Geometry of the draw bend test with (b) deformed shape before and after springback

Figure 2

(a) Stress state of a thin sheet in the plane-stress stress field under the plane strain deformation in elasto-plasticity and (b) rapid development of the proportional stress state during the initial plastic deformation

Figure 3

Definition of N layers through the thickness

Figure 4

(a) An element in region I under the tension and in region II under tension and bending moment, (b) tensile force increase at the entrance of region II

Figure 5

Stress-strain curve with the Voce fit for sensitivity tests

Figure 6

Final shapes for the variation of radius of tool-to-thickness

Figure 7

Variation of the springback angle (Δθ) with the radius of tool-to-sheet thickness (r∕t)

Figure 8

Effect of the radius of tool-to-thickness (r∕t) on moment-curvature curves

Figure 9

Final shapes for the variation of normalized back force (Fb)

Figure 10

Variation of the springback angle with the normalized back force (Fb)

Figure 11

Effect of normalized back force (Fb) on moment-curvature curves

Figure 12

Normalized back force versus normalized front force

Figure 13

Final shapes for the variation of friction coefficient

Figure 14

Variation of the springback angle with friction coefficient

Figure 15

Effect of friction on moment-curvature curves

Figure 16

Final shapes for the variation of hardening laws: (a) low back force, (b) high back force

Figure 17

Variation of the springback angle with hardening laws: (a) low back force, (b) high back force

Figure 18

Effect of hardening laws on moment-curvature curves: (a) low back force, (b) high back force

Figure 19

Schematic shape of the Yld2000-2d surface with three different exponents

Figure 20

Final shapes for the variation of the yield surface exponent

Figure 21

Variation of the springback angle with the yield surface exponent

Figure 22

Effect of yield surface exponent on moment-curvature curves

Figure 23

Measured stress-strain curve and the Voce fit of DP-Steel

Figure 24

Comparison between predicted and measured deformed shapes after springback with various normalized back forces for r∕t=11.28

Figure 25

Comparison between predicted and measured deformed shapes after springback with variant of normalized back force for r∕t=4.8

Figure 26

Magnitude of the springback angle with normalized back force (r∕t=11.28)

Figure 27

Magnitude of the springback angle with normalized back force (r∕t=4.8)

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