ANALYSIS OF FORMING PROCESS OF AUTOMOTIVE ALUMINUM

ALLOYS CONSIDERING FORMABILITY AND SPRINGBACK

Wonoh Lee1,a, Daeyong Kim2,b, Junehyung Kim3,c, Kwansoo Chung4,d and Seung Hyun Hong2,e

1Department of mechanical engineering, Northwestern University,

2145 Sheridan Rd., Evanston, IL 60208-3111, U.S.A.

2Material Research Team, Corporate R&D Division for Hyundai Motor Company & Kia Motors

Corporation, 772-1 Jangduk-dong, Hwaseong-si, Gyeonggi-do 445-706, South Korea

3Mobile Communication Division, Samsung Electronics CO., LTD.,

416 Maetan-3dong, Yeongtong-gu, Suwon-si, Gyeonggi-do, 443-742, South Korea

4School of Materials Science and Engineering, ITRC, Seoul National University,

56-1, Shinlim-dong, Kwanak-gu, Seoul 151-742, South Korea

awonoh-lee@northwestern.edu,

bdaeyong.kim@hyundai-motor.com,

cjh0609.kim@samsung.com,

dkchung@snu.ac.kr (Corresponding author),

ehshmsd@hyundai-motor.com

Keywords: Formability, Springback, Automotive aluminum alloys, Combined isotropic-kinematic hardening law, Non-quadratic anisotropic yield functions, Hill’s bifurcation theory, M-K theory

Abstract. Formability and springback of the automotive aluminum alloy sheet, 6K21-T4, in the sheet

forming process were numerically investigated utilizing the combined isotropic-kinematic hardening

law based on the modified Chaboche model. To account for the anisotropic plastic behavior, the

non-quadratic anisotropic yield stress potential, Yld2004-18p was considered. In order to characterize

the mechanical properties, uni-axial tension tests were performed for the anisotropic yielding and

hardening behavior, while uni-axial tension/compression tests were performed for the Bauschinger

and transient behavior. The Erichsen test was carried out to partially obtain forming limit strains and

FLD was also calculated based on the M-K theory to complete the FLD. The failure location during

simulation was determined by comparing strains with FLD strains. For verification purposes, the

automotive hood outer panel was stamped in real. After forming, the amount of draw-in, thinning and

springback were measured and compared with numerical simulation results.

Introduction

Recently, many automakers are trying to utilize aluminum alloy sheets for their automotive parts to

reduce the weight of vehicles and improve the fuel efficiency. However, there are several technical

obstacles to overcome in aluminum applications besides higher material costs, which are associated

with their inferior formability and lager springback compared to conventional steels due to their

different material characteristics. Therefore, the proper understanding and description of their

mechanical properties are important for aluminum alloy sheet applications and also for computational

methods based on FEM in the design stage since the accurate and efficient numerical simulation

technique will save times and resources for the tool design and try-out.

Here, in order to examine the formability and springback of the aluminum automotive sheet in

stamping, the aluminum alloy 6K21-T4 sheet (supplied by Kobe Steel) was considered. To represent

material properties, the anisotropic yield function, Yld2004-18p [1] and the combined isotropic-

kinematic hardening law [2] were utilized for the constitutive law. The hardening behavior has been

measured using the uni-axial test, while, for the Bauschinger and transient behavior during reverse

loading, uni-axial tension/compression tests have been performed. Forming limit strains were

partially measured and also calculated based on the M-K theory [3] to complete the FLD curve.

Failure location was determined by comparing strains with FLD strains. The hood outer panel was

Key Engineering Materials Vols. 345-346 (2007) pp. 857-860online at http://www.scientific.net© (2007) Trans Tech Publications, Switzerland

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stamped in real and the amount of draw-in, thinning and springback were measured and compared

with numerical results.

Theory

For the anisotropic yield stress surface, Yld2004-18p, sixteen data to represent orthogonal anisotropy

are utilized, which are σ0, σ15, σ30, σ45, σ 60, σ75, σ90, R0, R15, R30, R45, R60, R75, R90, σb and Rb. These are simple tension yield stresses, R-values at every 15

o off the rolling direction, and yield stress and

in-plane principal strain ratio under the balanced biaxial tension condition, respectively. For

calculations under the plane stress condition, the reduced form for the plane stress condition of

Yld2004-18p was utilized.

The combined type isotropic-kinematic hardening constitutive law based on the modified

Chaboche model is given by

( ) 0Mf σ− − =σ α (1)

where αααα is the back stress and the effective stress, σ is the size of the yield surface. Based on crystal plasticity, the exponent M is recommended to be 8 for FCC materials. In the Chaboche model, the

back-stress increment is composed of two terms, dαααα=dαααα1-dαααα2 to differentiate transient hardening

behaviors during loading and reverse loading.

For the numerical formulation for large deformation, the incremental deformation theory [4] was

applied to the elasto-plastic formulation. Under this scheme, the strain increment in the flow

formulation becomes the discrete true strain increment while a material rotates by incremental

rotation obtained from the polar decomposition at each discrete step.

In order to calculate the theoretical FLD, the M-K theory was utilized based on the

rigid-plasticity with the isotropic hardening for simplicity.

Material Characterization

The aluminum alloy 6K21-T4 sheet with 1.0mm thickness was considered and the anisotropy was

characterized using uni-axial tension tests for 0, 45 and 90 degrees. From these results, Yld2004-18p

was calculated and yield characteristics were shown in Fig. 1. Note that Yld2000-2d was also utilized

in order to obtain yield stresses and R-values at 15, 30, 60 and 75 degrees off the rolling direction.

Also, the normalized balanced biaxial yield stress was assumed to be 1.0 and the condition, 12 21L L′ ′=

has been used for the Yld2000-2d calculation [5].

AA6K21-T4

Normalized stress in RD

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Normalized

stress in TD

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Yld2004-18pContour at every 0.05

(a)

R-value

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Exp.

Yld2004-18p

AA6K21-T4

Angle to loading direction (deg.)

0 15 30 45 60 75 90

Normalized

yield

stress

0.7

0.8

0.9

1.0

1.1

Exp.

Yld2004-18p

Normalized yield stress

R-value

(b)

Fig. 1. Characteristics of Yld2004-18p for AA6K21-T4: (a) yield surface contour and (b) anisotropy

of normalized stress and R-value.

The Mechanical Behavior of Materials X858

AA6K21-T4

True strain

-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08

True stress (MPa)

-300

-200

-100

0

100

200

300

Experiment

Simulation

AA6K21-T4

Minor true strain

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4

Major tru

e strain

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Exp. (raw)

Exp. (10% offset)

Cal.

Fig. 2. Calculated and measured hardening

behavior in tension-compression tests Fig. 3. Forming limit diagram for AA6K21-T4

In order to measure isotropic-kinematic hardening behavior, uni-axial tension/compression tests

were performed. Results are plotted in Fig. 2, which confirms that the modified Chaboche model well

represents Bauschinger and transient behaviors.

The Erichsen test was carried out to obtain forming limit strains. Note that the 10% offset method

was used for the safety factor commonly used in real part stamping. Since there is not enough data

successfully obtained, FLD was calculated using the M-K theory. For the calculation, the defect

parameter was determined so that the curve can fit well with measured offset limit strains.

Verification: Stamping of the Hood Outer Panel

The hood outer panel has been stamped. The die includes the draw-bead geometry and the

as-formed part shape was plotted in Fig. 4. Considering the part symmetry, only a half part was

numerically simulated, utilizing the commercial ABAQUS explicit and implicit codes with user

subroutines. The blank holding force was 150ton. The holding and punch speeds were 2m/s and 5m/s,

respectively, and the friction coefficient was assumed to be 0.12. In Fig. 4, boundary conditions for

the constraint of rigid-body movements during a springback analysis were described with the

symmetry boundary condition along the x-axis.

For verification purposes, the amount of draw-in, thinning and springback were measured and

compared with numerical simulation results. As shown in Fig. 4, draw-ins were measured at three

positions, DI-1, DI-2 and DI-3, and springback profiles were compared along two cross-sections

marked as SB-1 and SB-2. Thinning measurement was conducted at two regions, TR-1 and TR-2, in

which ten measurement locations (TN-1~TN-10) are drawn in Fig. 5.

DI-1 (x,y,z constrained)

DI-2

DI-3 (y,z constrained)

SB-1: Symmetric axis

x

y

SB-2

TR-1

TR-2

O

DI-1 (x,y,z constrained)

DI-2

DI-3 (y,z constrained)

SB-1: Symmetric axis

x

y

x

y

SB-2

TR-1

TR-2

O

TN-1TN-2

TN-3 TN-4

TN-5

TN-6

TN-7TR-1

TN-8

TN-9

TN-10

TR-2

x

z

TN-1TN-2

TN-3 TN-4

TN-5

TN-6

TN-7

TN-1TN-2

TN-3 TN-4

TN-5

TN-6

TN-7TR-1

TN-8

TN-9

TN-10

TN-8

TN-9

TN-10

TR-2

x

z

x

z

Fig. 4. Positions and regions for

draw-in, thinning and springback

Fig. 5. Locations of thinning measurement at regions, TR-1

and TR-2

Key Engineering Materials Vols. 345-346 859

Table 1. Experiemental and simulated amounts of draw-in and thinning

Draw-in (DI) [mm] Thinning (TN) [%]

No. 1 2* 3 1 2 3 4 5 6 7 8 9 10

Exp. 18 14/19 88 19 5 7 8 10 10 11 3 2 11

Sim. 21 16/17 81 22 6 6 10 12 11 9 1 1 14

*Each values corresponds to draw-in amounts at x and y directions, respectively.

FailureFailure

SB-1

X Coord.

-1000-50005001000

Z Coord.

-300

-200

-100

0

100

Before Springback

After Springback

SB-2

Y Coord.

0 200 400 600 800 1000

Z Coord.

-300

-200

-100

0

100

Before Springback

After Springback

Fig. 6. Simulated failure locations Fig. 7. Simulated springback profiles along SB-1 and SB-2

Numerical prediction shows good agreement with experimental results as listed in Table 1. The

simulated failure location was shown in Fig. 6 and the failure occurred near to TN-1 position where

the thinning is largest. Unlike numerical results, there was no failure in the real stamping. Since the

TN-1 region is most likely to fail, it is believed that the calculated FLD can give a pertinent forming

guide even though the prediction underestimated forming limits for this specific case. Springback

profiles along the SB-1 and SB-2 cross-sections were shown in Fig. 7. Springback was quite large

through the whole region. Therefore, modification in design might be needed to reduce springback.

Summary

The stamping process of the aluminum alloy 6K21-T4 sheet was examined considering formability

and springback. To represent mechanical properties, the anisotropic yield function Yld2004-18p and

the combined isotropic-kinematic hardening law were utilized, while the FLD was considered as a

failure criterion. To verify the numerical method, the hood outer panel was stamped and compared

with numerical predictions. The numerical results showed good agreement with experimental results.

Acknowledgement

This work was supported by Hyundai Motor R&D Center and also by the Korea Science and

Engineering Foundation (KOSEF) through the SRC/ERC Program of MOST/KOSEF

(R11-2005-065), which is greatly appreciated.

References

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[2] K. Chung, M.-G., Lee, D. Kim, C. Kim, M.L. Wenner and F. Barlat: Int. J. Plasticity Vol. 21

(2005), p. 861

[3] Z. Marciniak and K. Kuczynski: Int. J. Mech. Sci. Vol. 9 (1967), p. 609

[4] K. Chung and O. Richmond: Int. J. Plasticity Vol. 9 (1993), p. 907

[5] F. Barlat, J. C. Brem, J. W. Yoon, K. Chung, R. E. Dic, S-H. Choi. F. Pourbograt, E. Chu and D.

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