Sheet Hydroforming Simulation of a License-Plate-Pocket Panel Nader Abedrabbo*, Farhang Pourboghrat* and John Carsley† *Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226 † General Motors Research & Development Center, Warren, MI 48090 Abstract. The objective of this research was to numerically study the application of the sheet hydroforming process to a real-world complex automotive part. In sheet hydroforming, one or both surfaces of the sheet metal are supported with a pressurized viscous fluid to assist with the forming of the part where a female die is not required. The pressurized fluid supports the blank during the forming process, delays the onset of material failure and acts as an active blank-holding force. The commercial finite element analysis code LS-Dyna was used to simulate the process using Barlat’s anisotropic yield function [2] to represent material behavior during deformation. Pressure and blank holding force profiles were developed for forming this complex part without defects. In addition, it is numerically shown that through the application of an appropriate fluid pressure profile, wrinkles could be eliminated.

INTRODUCTION The sheet metal hydroforming process to form body panels is gaining interest in the automotive and aerospace industries. The method has shown promise to form shapes that are too complex for conventional stamping methods because strains can be more uniformly distributed to avoid localization and failure. In the sheet hydroforming process, the sheet is supported on one side with a bed of viscous fluid that provides a through-thickness compressive stress that delays the onset of tensile instabilities and reduces the formation of wrinkles due to tensile frictional forces. Advantages of the sheet hydroforming process include improved formability of the blank due to the applied fluid pressure, low wear rate of dies and punch, improved distribution of plastic deformation compared to conventional stamping, potential savings with simpler tooling, and the potential for reducing the amount of finishing work required. Previous efforts [1], which focused on suppressing the wrinkling behavior of AA6111-T4 during the hydroforming of hemispherical punch samples, were expanded in this study to the hydroforming process of a license-plate-pocket shape, which is considered too complex for conventional stamping with aluminum sheet. Numerical simulations of the license plate panel

were performed with the explicit finite element code, LS-Dyna, using the BARLAT-YLD-96 [2] model to account for the anisotropic behavior of AA6111-T4. Figure 1 shows the license-plate-pocket used in the simulation with the dimensions of the full model. Only half symmetry exists in the model.

FIGURE 1. License plate pocket panel. Dimensions of the full panel were 750 mm (29.5 in) width, 286 mm (11.3 in) length and 55 mm (2.16 in) depth. (Half model shown).

Numerical Simulation Procedure To simulate the hydroforming process for this part, a male punch was created from the product data of the license plate pocket shape. The punch had the following dimensions: 750 mm (2.16 mm) width, 286 mm (11.3 in) length and 55 mm (2.16 in) depth. Associated tooling for the punch was created as a fixed flat lower draw ring and a flat, upper blank holder. The rigid dies were created with an 8 mm (0.32 in) fillet radius, and a 2 mm (0.079 in) clearance between the dies and the punch to allow material draw-in. To simulate hydroforming of this panel, product detail was included on the punch, which pressed the aluminum blank against pressurized fluid. The correct fluid pressure path enabled the blank to form to the desired punch shape without any defects. A controllable blank holding force (BHF) was also used in the simulation. Several different simulation conditions, conducted to understand the forming process for this license plate pocket panel, are outlined below: 1. No fluid pressure: a. Pure stretch conditions (high BHF). b. Partial draw-in conditions (low BHF). c. Draw-in conditions (zero BHF). A 5 mm (0.2 in) gap was maintained between the blankholder and the draw ring to allow unrestricted drawing of the blank. 2. Variable fluid back pressure: a. Draw-in conditions with a 5 mm gap between the two dies. Fluid pressure supplied the blank holding force. b. A combination of fluid pressure and blank holding force. 3. Tailored blank shapes: a. Rectangular blank. b. Round-cornered blank. c. Blank shape determined from the IdealForm program [3]. 4. Segmented blankholder: a. Five segments each had a different blank holding force.

Numerical Analysis Numerical analysis of sheet metal forming processes is an important tool in achieving a better understanding of deformation behavior during the forming process. Once confidence in the model is established through comparisons with experimental results, the model’s capabilities can be used to test

ideas that would be otherwise difficult or expensive to validate. The accuracy of the numerical model to simulate the hydroforming process with regards to multiple factors such as isotropic vs. anisotropic model effects, geometric effects and integration schemes were established in a previous study [1]. In that research, the accuracy of the numerical model was verified against experiments, the model was then used to simulate the hydroforming process with the explicit finite element code, LS-Dyna. Finite Element Model In the current model of the license plate pocket, only half symmetry exists along the centerline of the pocket, and only the half model was used in this simulation. The initial model (punch and dies) was created using Unigraphics and imported as IGES files. Hypermesh was used to create the finite element mesh, assign the boundary conditions and to build the LS-Dyna input deck for the analysis. Manual editing of the input deck was needed since Hypermesh does not fully support all LS-Dyna input cards. The half finite element model used approximately between 50,000 and 140,000 four- & three-node shell elements (depending on the initial blank shape and element size). The punch, die, and blank-holder were created using rigid materials (Material 20 in LS-Dyna). Constitutive Model Effects One of the most important issues in numerical analysis is having a constitutive model that accurately describes the behavior of the material under investigation. Since AA6111-T4 aluminum clearly possesses anisotropic properties, it is very important to choose an appropriate material model that will capture this behavior during the deformation process. Therefore, Barlat’s anisotropic model implemented in LS-Dyna (*MAT_BARLAT_YLD96) was used. Barlat et al. (1997) [2] presented this material model as an improvement to their YLD91 model. The model is based on a phenomological description of the material. To represent the behavior of these materials mathematically, a yield function was proposed, and then generalized to include the most general stress tensor with six components as shown in the following equations:

Φ = α1 | S 2 − S3 |a +α 2 | S3 − S1 |a + α 3 | S1 − S 2 |a = 2σ a .

(1)

Where

S = Lσ ,   

(2)

c3 + c2 c3 c2   s1 = 3 σ x − 3 σ y − 3 σ z  c3 c3 + c1 c  σ y − 1 σ z (3)  s2 = − σ x + 3 3 3  c2 c1 c1 + c2   s3 = − 3 σ x − 3 σ y + 3 σ z 

α k = α x p12k + α y p22k + α z p3k2 .

(4)

Where c1, c2, c3, α1, α2, α3 are material coefficients that describe anisotropy. P is the transformation matrix from the principal axes of anisotropy (x, y and z) to the principal axes of s (Pij is the i-th component of the j-th unit principal vector Pj). With this it is possible to increase the pure shear yield stress without increasing the other plane strain yield stresses. The material coefficients c1, c2, c3, α1, α2, α3 for AA6111-T4 used in the current paper are shown in Table1. TABLE 1. AA6111-T4 Material Properties. E ν t K σy MPa GPa mm MPa 180.0 71 0.33 1.0 400.5 c1 0.939

c2 0.851

c3 1.063

α1 2.45

α2 2.35

Failure Points

FIGURE 2. Cross section of the pure stretch condition. Failure depth is 28 mm (1.1 in).

For unrestricted draw-in conditions (zero BHF using a 5 mm gap between the two dies), Fig. 3 shows the final shape of the part, which exhibited severe primary and secondary wrinkling.

n 0.202 α3 0.68

Results and Discussion No Fluid Pressure In pure stretch conditions using the rectangular blank, the sheet ruptured at a depth of 28 mm (1.1 in), as shown in Fig. 2. With controlled draw-in conditions (using low BHF), the blank did not fail through the full stroke of the punch. In both previous cases, however, the blank only formed to the bottom surface of the punch and did not fill in the complex shape on the sides of the punch, as shown in Fig. 2. This occurred because there was no fluid pressure or female die to work against the punch.

FIGURE 3. Final shape of blank after unrestricted draw in using 5 mm gap and without fluid pressure.

As expected, pure stretch conditions limit the forming depth and complexity of potential products; while unrestricted drawing conditions without fluid pressure cannot prevent the development of wrinkles in the final product. From these results, it is shown that a counter acting fluid pressure is required to work against the sheet so as to make the sheet take the final required shape. Variable Fluid Pressure The fluid pressure shown in Fig. 4, which increased with punch stroke roughly linearly, was used to form the rectangular blank.

Tailored Blank Shapes

5.0 4.5

To reduce wrinkling in the corner regions of the pocket, the initial blank shape was modified with rounded corners as shown in Fig. 6.

Pressure (MPa)

4.0 3.5 3.0 2.5 2.0

Rounded Corners

1.5 1.0 0.5 0.0 0

5

10

15

20

25

30

35

Time (ms)

FIGURE 4. Initial fluid forming pressure profile.

The simulation result of hydroforming with this pressure profile is shown in Fig. 5.

Wrinkles

FIGURE 5. Controlled draw-in results for the rectangular blank using the pressure profile shown in Fig. 4.

While primary wrinkling around the flange (under the blank holder) was eliminated, wrinkles did develop in the sharp corner regions of the license plate pocket depression. The sharp corners of the original blank contributed to the formation of these wrinkles because there was too much material trying to flow into the depression that resulted in very high compressive stresses and ultimately caused the wrinkles. Another defect revealed by this simulation was the reverse bulging of material in the unsupported regions between the punch and the blankholder, along with excess material drawn in the beginning of the process. Fluid pressure could be reduced to correct these issues, but at the risk of forming additional wrinkles where there is less support from the fluid. To compliment this solution, the blankholder force could also be increased along the straight sections of the panel to reduce the excess draw of material.

FIGURE 6. Tailored blank with rounded corners (corner radius = 100 mm).

After failing to find a suitable fluid pressure that could form the current part without wrinkles, a controlled blankholder force, in combination with the fluid pressure, was found to be necessary for this model to allow sufficient material flow from the flange region in order to form deep products with enough tensile traction to cause the blank to stretch and work harden. The blankholder force must also be sufficient to resist compressive stresses in the flange and prevent wrinkling. For this tailored blank, the BHF was varied along with the fluid pressure as shown in Fig. 7 for the simulation results shown in Figs. 8 and 9. These modifications greatly improved the formability of this panel, which closely matched the shape of the punch except for small wrinkles remaining in corner regions of the pocket. Also, as seen in Fig. 9, the blank did not fill-in the sharp bottom radius of the punch in the vicinity of these corner wrinkles. A cross section of the center portion of the die/panel geometry indicates the blank matched the shape of the punch very closely. Failure criteria in the analysis were based on the forming limit diagrams (FLD). The forming limit diagram for the AA6111-T4 material was calculated using the M-K model [4]. Figure 10 shows the result of projecting the strain distribution of the blank on the FLD.

1400

Pressure Profile BHF

10

1200 1000

8 800 6 600 4

BH Force (kN)

12

Pressure ( MPa)

blank shape according to the design of the punch. This optimal shape is shown in Fig. 11.

1600

14

Failure Line

400

2

200

0

0 0

5

10

15

20

25

30

35

T ime (ms)

FIGURE 7. Blank holding force and fluid pressure profile used in simulation of the blank tailored with rounded corners. FIGURE 10. FLD graph of the simulation in Figs. 8 and 9.

FIGURE 8. Top view of the round corner blank using the pressure profile in Fig. 7. FIGURE 11. Optimized blank shape from the IdealForming program.

Simulation results using this shape are shown in Fig. 12, which suggests that corner wrinkles remain probable. As can be seen from the graph, the wrinkles could not be eliminated using this special shape either. Additional optimization of the BHF and the fluid pressure profile is needed to completely eliminate the formation of corner wrinkles from this license plate pocket panel. Also special techniques, e.g. segmented blank holder, could be used to help form a defect free part.

FIGURE 9. Bottom view of the round corner blank using the pressure profile in Fig. 7.

To further address the corner wrinkling issue, the tailored shape of the blank was modified according to the Ideal-Form [3] program that can predict an optimal

Segmented Blankholder The previous results indicate that wrinkling in this complex shape occurred at the sharp corners due to extra material that was drawn-in from the longer sides rather than the shorter side.

Conclusions

FIGURE 12. Simulation using the optimized blank shape from the Ideal-Forming program.

This caused the material to fold when the fluid pressure was applied. To be able to control the draw-in in these regions, a segmented blank holder will be simulated as shown in Fig.13.

4 5

3 2

A methodology was developed to enable aluminum sheet hydroforming of complex shapes through the optimization of blank geometry, fluid pressure and blank holder force. Using a rectangular blank with sharp corners to form a rectangular-shaped depression in a panel led to wrinkling failures in the corner regions because there was too much material in the flange corners that obstructed the drawing behavior to form the panel. These corner wrinkles were greatly reduced by using a tailored blank with rounded corners. Both fluid forming pressure and blankholder force must be controlled as a function of punch stroke to successfully form complex shapes like this license plate pocket panel. Further optimization of these two parameters with a program such as HEEDS is necessary to completely eliminate the formation of wrinkles in the sheet hydroforming of complex panels. In order to eliminate wrinkle formation at the corner regions, a female die impression will be used. The forming mechanics at the sharp corners using a female die is that of stretching rather than compressive forces. This can help in eliminating the folding behavior that occurs at the corners of the male die.

ACKNOWLEDGMENTS

1

Many years of support for manufacturing research from the industrial members of the Michigan State University Manufacturing Research Consortium (MRC) is greatly appreciated.

FIGURE 13. Segmented Blankholder. Contains 5 segments.

Using this, each section could be controlled separately with its own BHF so as to control material draw-in. Simulations are currently under way for this process.

Process Optimization To make the process robust, a more general method is needed to determine the optimum fluid pressure and blankholder force profiles. The optimization program HEEDS [5] will be used in future analyses. In this method, the minor and major strains in the blank could be set as constraints in which the program tries to optimize the fluid pressure and the blank holding force such that the strains remain below and above set limits in the FLD region.

REFERENCES 1. Abedrabbo N., Zampaloni M. and Pourboghrat F., “Numerical Study of Wrinkling Behavior of AL6111-T4 in Stamp Hydroforming” in NUMISHEET2002, edited by Dong-Yal Yang et al., Korea, pp. 331-336 (2002). 2. Barlat F., Maeda Y., Chung K., Yanagawa M., Brem J.C., Hayashida Y., Lege D, Matsui K., Murtha S., Hattori S., Becker R. and Makosey S., Jour. Mech. Phys. Solids., Vol. 45. No. 11/12, pp. 1727-1763 (1997). 3. Chung K and Richmond O., J. of Appl. Mech. ASME, Vol. 61, p.176 (1994). 4. Marciniak Z. and Kuczynski K., Int. J. Mech. Sci. Vol. 9, No. 9, pp. 609-612 (1967). 5. HEEDS (Hierarchical Evolutionary Engineering Design System). Getting started Manual by Red Cedar Tech., www.redcedartech.com, MI, 48823, USA.

Sheet Hydroforming Simulation of a License-Plate ...

yield function [2] to represent material behavior during deformation. Pressure and blank ... compared to conventional stamping, potential savings with simpler tooling ... account for the anisotropic behavior of AA6111-T4. Figure 1 shows the ...

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