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International Journal of Mechanical Sciences 45 (2003) 1815 – 1848

Experimental and numerical study of stamp hydroforming of sheet metals M. Zampaloni, N. Abedrabbo, F. Pourboghrat∗ Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226, USA Received 17 December 2001; received in revised form 10 November 2003; accepted 18 December 2003

Abstract The objectives of this research was to experimentally and numerically study the stamp hydroforming process as a means for shaping aluminum alloy sheets. In stamp hydroforming, one or both surfaces of the sheet metal are supported with a pressurized viscous 4uid to assist with the stamping of the part thereby eliminating the need for a female die. The pressurized 4uid serves several purposes: (1) supports the sheet metal from the start to the end of the forming process, thus yielding a better formed part, (2) delays the onset of material failure and (3) reduces wrinkle formation. This paper focuses on the experimental and numerical results of the stamp hydroforming process utilizing a 4uid pressure applied to one surface of the sheet metal. The e7ects of applying a constant, varying and localized pressure to the surface of 3003-H14-aluminum sheet alloy were evaluated. Experiments demonstrated draw depths improvements up to 31% before the material failed. A failure prediction analysis by Hsu was also carried out to predict an optimal 4uid pressure path for the varying 4uid pressure case. The commercial ;nite element analysis code Ls-Dyna3D was used to numerically simulate the stamp hydroforming process. Both isotropic and anisotropic material models were used and their predictions compared against the experimental results. The numerical simulations utilizing Barlat’s anisotropic yield function accurately predicted the location of the material failure and the wrinkling characteristics of the aluminum sheet. ? 2003 Elsevier Ltd. All rights reserved. Keywords: Sheet hydroforming; Stamping; Fluid forming; Fluid pressure; Failure; Tearing; Wrinkling; Material anisotropy

1. Introduction There are a multitude of parts, both in size and complexity that can be made from sheet metals, usually produced in large quantities on mechanical presses. There are signi;cant expenses associated ∗

Corresponding author. Tel.: +1-517-353-0819; fax: +1-517-353-1750. E-mail address: [email protected] (F. Pourboghrat).

0020-7403/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmecsci.2003.11.006

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Table 1 Advantages and disadvantages of the stamp hydroforming process

Optimized processing Complex shapes

Advantages Applied pressure delays fracture onset Eliminates contact between forming tools Pressure aids in the uniform distribution of strains Eliminates the need for a female die and heating/curing oven Consolidates multiple stamping operations, eliminates some ;nishing operations and reduces scrap/waste Better ;nish and all inclusive heating/forming/curing Forms complex parts with convex contours

Cycle time Temperature challenges Fluid pressure–punch stroke

Disadvantages Longer than traditional stamping DiIcult to maintain isothermal conditions throughout processing Optimal path may be part-speci;c

Improved drawability Low wear rate of tooling Reduced thinning in ;nal part Signi;cant economic savings Environmentally friendly

with the necessary tooling and the processes require a fair amount of ingenuity and skill to bring the economic costs down to a suitable level. Numerous studies have been conducted on traditional sheet stamping methods such as mechanical stretch forming and deep drawing, both methods that require a male and female die for the proper forming of a ;nished part. McClintock [1] and Rice and Tracey [2] conducted studies on sheet metals demonstrating a rapid decrease in fracture ductility as a hydrostatic pressure, applied across the material, was increased. Clift et al. [3] and Hartley et al. [4] demonstrated that for sheet metals, the use of a hydrostatic pressure prevented the initiation and spreading of microcracks within the metallic material. Based on the success found using a hydrostatic pressure to delay the onset of fracture, the idea of stamp hydroforming was investigated both experimentally and numerically as a possible method for shaping aluminum and ferrous sheet metals. The process of stamp hydroforming, unlike conventional stamping, involves supporting the bottom of the sheet with a bed of viscous 4uid during the stamping process. This external support provides a through-thickness compressive stress that delays the onset of tensile instabilities as well as reduces the formation of wrinkles due to tensile frictional forces. The advantages of the stamp hydroforming process are numerous and the process is receiving signi;cant attention from both the automotive and aerospace industries. Advantages, illustrated in Table 1, include improved formability of the blank due to the applied pressure by the 4uid, low wear rate of dies and punch, a better distribution of plastic deformation when compared to conventional stamping, signi;cant economic savings associated with the decreased tooling, and the potential for reducing the amount of ;nishing work required [5]. A schematic of the hydroforming process, as shown in Fig. 1, represents a part that is being formed by a hemispherical punch. At the start of the process the sheet is placed across the clamping mechanism, as shown in Fig. 1(1). Fig. 1(2) shows the upper 4uid chamber lowered and the sheet clamped securely between the two die halves, creating a seal for the upper 4uid chamber. The 4uid is injected into the chamber and then pressurized. At this point in the process the punch begins to travel into the sheet forcing it to take the hemispherical shape, ;nally deforming into a fully formed

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Fig. 1. A schematic of the stamp hydroforming process with a hemispherical punch. (1) Material is placed on the draw bead with the 4uid chamber in the raised position. (2) Fluid chamber is lowered and ;lled. Material held in place by clamping mechanism. (3) Punch begins to move upward. Fluid pressure in chamber is controlled to force the material to conform to the shape of the punch. (4) Fluid is drained. The 4uid chamber is raised and the punch is lowered to remove the part.

part after the punch penetrates deeper into the blank, Fig. 1(3). As the punch begins to deform the material the volume in the upper 4uid chamber decreases thereby causing the pressure to increase due to its incompressible nature. This 4uid pressure serves two main purposes. First, it delays the onset of material fracture as described earlier [1–4] and secondly, it forces the material to conform much more closely to the shape of the punch than the parts formed without the resisting 4uid. The latter causes a larger volume of the sheet to deform uniformly at a lower punch stroke, thus delaying excessive thinning and postponing the onset of material fracture. Once the punch has reached the prescribed draw depth, the 4uid is drained and the upper chamber removed, Fig. 1(4).

2. Hydroforming challenges The challenges that are present during the stamp hydroforming process can be classi;ed into two broad categories: material and 4uid pressure. The material challenge refers to the choice and behavior of the sheet metal. One of the major obstacles concerns the delicate balance between the 4uid pressure and the ductility of the material chosen for the hydroforming process. The 4uid pressure needs to be high enough to stretch and bend the work piece through its radius of curvature to conform to the shape of the punch, yet the material needs to be ductile enough to form without rupturing.

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Fig. 2. A generic curve illustrating the optimum 4uid pressure–punch stroke path for the stamp hydroforming process.

The second challenge is the relationship between the 4uid pressure and the punch stroke during the process. As shown by Yossifon and Tirosh [6–10] 4uid pressures within the upper 4uid chamber that are too high will cause the material to bend to the radius of curvature of the punch much faster than the ductility of the material may allow. This will lead to premature rupturing of the sheet metal. On the other hand, if the 4uid pressure is too low the sheet may not stretch enough during the process and wrinkle. Therefore, there is the need to establish an upper and lower limit on the 4uid pressure, as it relates to the punch stroke, to determine an optimum 4uid pressure–punch stroke path to ensure limited rupturing and wrinkling failures of the ;nished part. A generic curve is shown in Fig. 2 to help illustrate this idea. In the stamp hydroforming of sheet metals the diIculty lies in ;nding this appropriate 4uid pressure–punch stroke path while avoiding rupture and wrinkling instabilities. Lo et al. [11] and Hsu and Hsieh [12] performed a series of experiments and analyses that established this 4uid pressure– punch stroke path for the stamp hydroforming of metallic hemispherical cups. In this paper, the stamp hydroforming experiments that were conducted with 3003-H14-aluminum sheet alloy and a common ferrous sheet metal purchased o7 the shelf from a local supplier will be described. The signi;cance of this work is in its thoroughness in studying stamp hydroforming both experimentally and numerically, as described below: (A) Experimental studies: (1) Types of deformation: (a) Pure stretch. (b) Draw-in. (c) Combination of draw-in and pure stretch. (2) Types of pressure loading: (a) Fluid pressure applied to one surface of the sheet metal: (i) Constant 4uid pressure. (ii) Varying 4uid pressure. (b) Pressure applied at the punch–sheet interface, using a vinyl sheet.

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(B) Numerical studies: (1) Simulating sheet hydroforming process, with the explicit dynamic ;nite element analysis (FEA) code Ls-Dyna 3D, using the above experimental conditions. (2) Comparing predictions of the von Mises isotropic yield function against Barlat’s 1989 anisotropic yield function that was developed for aluminum sheets. In the following sections the experimental work will be described, followed by the numerical analysis. In addition, some conclusions will be made and research directions for future papers will be discussed. 3. Experimental work 3.1. Experimental apparatus The experimental apparatus was built around an Interlaken 75 double action servo press, shown in Fig. 3a, where the double action refers to the clamping mechanism moving independently of the punch mechanism. The ability to independently control both the clamp and the punch a7ords the opportunity for various modi;cations of the experimental procedure. The experimental process started with a few modi;cations that were made to a limiting dome height (LDH) test setup, including drilling ports for pressure measurement, removing the air during the ;lling process and for ;lling and draining the 4uid chamber. Fig. 3b shows a picture of the in-house designed die that was used to study the stamp hydroforming process. Attached to the 4uid line is a regulator/controller that is used to accurately control the 4uid pressure within the 4uid chamber as the sheet is deformed by the punch, as shown in Fig. 4. If the pressure is too high, based on a user-de;ned pro;le, then the pressure in the system is reduced to the appropriate level. If the pressure is too low then the regulator pulls additional pressurized 4uid from a pressure vessel that is in-line with the rest of the system. A pressure intensi;er is used to supply the necessary volume and pressure to the reservoir prior to the start of the hydroforming process. The experimental procedure used vegetable oil as a resisting 4uid. Due to its incompressible nature, as the punch began to deform the sheet metal, the volume in the 4uid chamber decreased causing the pressure to increase. In the case of the 4uid pressure being applied to the topside of the sheet, the 4uid pressure served two main purposes. Firstly, it delayed the onset of material fracture as described earlier [1–4]. Secondly, the 4uid pressure forced the material to conform much more closely to the shape of the punch than the parts formed without the resisting 4uid. The latter also caused a larger volume of the sheet to deform plastically at a lower punch stroke, thus delaying shear localization and postponing the onset of fracture. 3.2. Hydroforming with hemispherical punch The experimental setup was used to form 101:6 mm (4 in) diameter hemispherical cups using 3003-H14-aluminum alloy sheet and a common ferrous sheet material purchased o7 the shelf from a local material supplier. The experiments that were conducted could be broken down into two major categories: 4uid pressure applied from one side of the material, and a localized punch–sheet contact region pressure applied using a stretchable vinyl sheet. It should be mentioned that in all

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Fig. 3. (a) The modi;ed Interlaken servo press 75 used for the stamp hydroforming process. (b) the in-house designed die set for the stamp hydroforming process with 4uid applied form one side of the draw blank [13].

the experiments the punch contacted the bottom of the sheet and the 4uid pressure was applied to the top surface of the sheet (see Fig. 4). Three di7erent types of experiments were performed using the 4uid pressure applied from one side of the sheet metals: (1) Evaluation of pure stretching. (2) Allowing the material to draw-in. (3) Combination of stretch and draw-in. Each of the above three di7erent categories were further evaluated using the following pressure loading: (a) Constant 4uid pressure, Fig. 5a.

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Constant Fluid Pressure

3

Pressure (MPa)

2.5 2 1.5 1 0.5 0

(a)

0

5

10

15

20

25

30

Punch Displacement (mm)

35

40

Fluid Pressure (MPa )(Kn/mm^2)

Fig. 4. The regulator and controller system used for sheet hydroforming from one side.

(b)

Variable Fluid Pressure

16 14 12 10 8 6 4 2 0 0.000

5.000 10.000 15.000 20.000 Punch Displacement (mm)

25.000

Fig. 5. Experimental 4uid pressure curves. (a) Constant, (b) varying 4uid pressure pro;les.

(b) Varying 4uid pressure, Fig. 5b. (c) Localized hydrostatic pressure using a stretchable vinyl sheet. Therefore, a total of nine di7erent combinations of experiments were conducted to evaluate the sheet hydroforming process. Below, the results and signi;cant ;ndings of each test will be discussed.

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Fig. 6. Example of material sag in unsupported regions when a constant 4uid pressure is applied on one side of the draw blank material (gap exaggerated to illustrate e7ect).

3.3. Constant 3uid pressure applied to one-side of the sheet 3.3.1. Pure stretch experiments For the experiments conducted under pure stretch conditions a 1 mm (0:04 in) thick, square blank (178 mm × 178 mm (7 in × 7 in)) was placed over a draw bead and clamped with a blank holding force (BHF) of approximately 267 kN (60; 000 lbf ). To ensure no material draw-in, several tests were conducted where the edge of the sheet on either side of the draw bead were marked with a thin pencil before forming. After the forming, the location of these lines with respect to the draw bead was checked for any possible movement. In all the tests it was veri;ed that the marked lines did not move at all, con;rming the pure stretch condition of the sheet metal. After clamping the sheet, the 4uid chamber was ;lled and then given an initial pressure up to 2758 kPa (400 psi). As the pressure within the chamber increased, the sheet bulged towards the punch (away from the 4uid chamber) prior to the punch beginning its movement into the sheet metal. This bulging, schematically illustrated in Fig. 6, created a strain concentration around the rigid die corner, which had a radius of curvature of 6:1 mm (0:24 in). With the constant 4uid pressures above 3448 kPa (500 psi), the material sheared o7 at the sheet/die corner interface prior to the punch moving into the 4uid chamber. Maintaining the 4uid pressures below the critical 3448 kPa (500 psi) level led to increased draw depths for the 3003-H14-aluminum alloy as illustrated in Fig. 7. Experiments were conducted at

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Punch Force versus Displacement for 3003-H14 Aluminum Sheets under a constant fluid pressure applied from one side of the material 40000 35000

Punch Force (N)

30000 25000 20000

2758 kPa 2069 kPa

15000

1370 kPa 10000 690 kPa 5000

0 kPa

0 0

5

10

15

20

25

30

35

Displacement (mm)

Fig. 7. Punch force versus displacement for 3003-H14-aluminum alloy sheet metal using a constant 4uid pressure applied form one side of the draw blank, pure stretch experiments.

several pressure levels in order to quantify the upper bound of the 4uid pressure/punch stroke diagram for the constant 4uid pressure, pure stretch experiments. Maintaining a constant 4uid pressure allowed for an impressive increase in the forming depth of 12–31% over parts that were formed without the resisting 4uid (i.e., conventional stamping). This improved formability could be attributed to several factors, but is mostly caused by changes in the boundary conditions. One explanation could be that when the sheet bulges in one direction (e.g., toward the punch) followed by a deformation in the opposite direction, the in-plane and bending strains in the sheet will reverse, causing the sheet to work harden. Depending on the amount of the work hardening, the resistance of the sheet to failure will increase. Also, this reverse bending and stretching causes the entire sheet metal in the die cavity to deform plastically and therefore strain localization over the punch surface will be delayed. Another reason for the improved formability could be that when the initial bulging occurs it creates more material in the die cavity to be deformed by the punch (see Fig. 6), in comparison with conventional stamping where the length of the sheet in the die cavity is shorter (see Fig. 1(1)). As is discussed in Section 5, this improved draw-depth was also observed in the numerical modeling. 3.3.2. Draw-in experiments By reducing the blank holding force (BHF), the sheet was allowed to draw into the die cavity. For these experiments a 4uid pressure of 483 kPa (70 psi) was applied to the sheet. The goal was to study the wrinkling and tearing characteristics of the sheet formed with (hydroforming) and without the 4uid pressure (conventional stamping) applied on one side of the material. As the sheet draws into the die cavity, the compressive stresses developing in the sheet under the blank holder and

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Fig. 8. Wrinkling in the aluminum sheet after draw-in. (a) No 4uid pressure, (b) 70 psi 4uid pressure applied to the topside of the sheet.

in the unsupported region (between the punch–sheet interface and the die corner region) increases, resulting in the eventual wrinkling of the sheet metal in these regions. Figs. 8a and b show the wrinkles that form in a sheet formed without (conventional stamping) and with a 4uid pressure of 483 kPa (70 psi). The wrinkles initiate in the 4ange area (under the blank holder) and gradually extend toward the center of the cup, as the draw depth increases. It was noted that although the loading was symmetrical, the wrinkles occurred along one side of the sheet metal. It was later found that this was caused by the anisotropic properties of the 3003-H14-aluminum alloy sheet, as shown in Table 4. This table shows that the values of the parameter (R=t =w ) are di7erent along the rolling (R0 ), transverse (R90 ) and 45◦ direction (R45 ). The R values for an isotropic sheet metal would be 1.0 everywhere. Overall, the application of the 4uid pressure from one side of the sheet did not help with the wrinkling problem. In fact, to some extent the application of the 4uid pressure exacerbated it by creating larger compressive stresses, as the unsupported sheet was pushed over the surface of the punch. The wrinkling problem became proportionally worse with the increase in the 4uid pressure applied to one-side of the sheet. 3.3.3. Combination experiments In the combination experiments, the sheet was ;rst drawn into the die cavity with a low 4uid pressure of 483 kPa (70 psi), followed by locking the boundary and stretching the sheet until it ruptured. During both the draw-in and combination experiments the presence of this initial pressurization caused the shear localization to occur earlier and led to the shearing of the sheet metal as the punch moved into the 4uid chamber. Therefore, for these experiments rupture occurred at shallower draw depths than those parts formed without the presence of a resisting hydrostatic 4uid. The reason for the early rupture is that suIcient initial bulging of the sheet metal did not occur (as in Section 3.3.1) to create additional material in the die cavity to help with the punch deformation. Also, because of the extra tension that is created in the sheet by the 4uid pressure, excessive thinning occurs in the punch–sheet contact region, resulting in an earlier failure in comparison with the case of no 4uid pressure (conventional stamping) [14].

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P unch Force versus D isplacem ent for V arying Fluid P ressure, P ure S tretch E xperim ents 120000 110000 100000

Punch Force (N)

90000 80000

Fe w/pressure

70000

A l w/pressure

60000

Fe no pressure A l no pressure

50000 40000 30000 20000 10000 0 0

5

10

15

20

25

30

35

40

D isplacem ent (m m )

Fig. 9. Punch force versus displacement for both the Al and Fe sheet materials using a varying 4uid pressure applied from one side of the sheet blank, pure stretch experiments.

3.4. Varying 3uid pressure applied to one-side of the sheet 3.4.1. Pure stretch experiments The goal of the varying 4uid pressure experiments was to try to delay the occurrence of the strain localization by gradually increasing the pressure in the 4uid chamber (see Fig. 5b) as the punch deformed the sheet, while maintaining an upper pressure bound of 2758 kPa (400 psi). The main obstacle with these experiments was the control of the 4uid pressure. At times, the 4uid pressure was found to spike at levels that were over twice the set boundary level of 2758 kPa (400 psi). Though these spikes lasted for only milliseconds they were long enough to impart signi;cant stress concentrations to the material. Several experiments were successfully run with both aluminum and ferrous sheet metals, with overall results for the pure stretch case illustrated in Fig. 9. Parts that were being formed using an applied varying hydrostatic 4uid pressure were rupturing at shallower punch depths than those parts formed without any resisting 4uid pressure. These premature ruptures were primarily due to excessive thinning of the sheet metal, caused by the extra tension created by the applied pressure. The higher the 4uid pressure was, the earlier the sheet failed in these experiments. 3.4.2. Draw-in experiments When the part was not rigidly clamped the material was allowed to draw into the 4uid chamber as the part was formed. An interesting trend was found during this procedure. As the material was drawn to a depth of approximately 12:7 mm (0:5 in) some wrinkling started to occur on the cup surface. To try to eliminate this instability it was attempted to utilize the 4uid pressure to iron out the wrinkles. A series of experiments were run and the results showed that the wrinkles were

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not ironed out; in fact as the 4uid pressure was increased the wrinkling became more pronounced. This was attributed to the increased compressive stresses in the hoop direction caused by the 4uid pressure pushing the sheet over the punch surface, exacerbating the already wrinkled part. 3.4.3. Combination experiments The third case evaluated with varying 4uid pressure was the investigation into the e7ects of a combination of pure stretch and draw-in during the stamp hydroforming process. The material was allowed to draw-in to a depth of 12:7 mm (0:5 in). As explained before, at this depth the material that was drawn into the chamber began to exhibit wrinkling characteristics. During the next step of the process the material was tightly clamped and 4uid introduced and pressurized. The goal was to use the 4uid pressure to ;rst counteract the movement of the material into the chamber to delay the onset of fracture while also ironing out the wrinkles that formed during the draw-in process. So far the preliminary results have shown some promise but further minor modi;cations will need to be made to the procedure to ensure a consistent wrinkling pattern during the draw-in phase. Again, due to the 4uid pressure spikes and the unsupported regions the results were not as anticipated, parts were either rupturing at shallower draw depths or the wrinkling that was occurring during the draw-in phase were not removed but became more pronounced. 3.5. Localized hydrostatic pressure In an attempt to explore di7erent design ideas, the process was conducted using a thin vinyl sheet in place of the counteracting 4uid. The vinyl material was a stretchable material that was used to simulate the e7ect of a localized hydrostatic pressure. As the punch moved into the sheet metal the vinyl counteracted the motion and added a pressure at the location of the sheet metal that was in contact with the punch. The goal of these experiments was to investigate the overall e7ect the pressure has on the unsupported regions of the material during processing. Since the vinyl only provided a counteracting force over the area of the material being shaped by the punch there was no reverse bulging of the material within the unsupported regions of the sheet metal. Fig. 10 illustrates the results achieved through the use of the localized pressure for the 3003-H14aluminum alloy sheets, while Fig. 11 represents the results for the ferrous sheets. In both cases the use of the localized pressure increased the draw depth by 3–10%. This may indicate the advantages of applying the 4uid pressure where only the punch and the sheet come into contact and will be discussed further in Section 3.6. By coating the punch with a thin layer of grease prior to forming, the surface area that contacts the vinyl could be quanti;ed. Using this value an approximate equivalent pressure could be calculated using the relationship between the forces applied by the punch and the surface area (P = F=A). For the single vinyl sheet this was calculated as 148 kPa (21:5 psi), while the use of two vinyl sheets was calculated as being equivalent to applying a 4uid pressure of 159 kPa (23 psi). Since the vinyl sheet had no e7ect on the sheet metal that was not in contact with the punch then it was concluded that this vinyl sheet was applying an equivalent 4uid pressure locally instead of globally. Therefore, based on the increased draw depths achieved using a relatively low localized pressure, it could be assumed that increases in the 4uid pressure, applied locally, should result in better formability of the sheet metals.

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Punch Force versus Displacement for 3003-H14 Aluminum using Localized Hydrostatic Pressure, Pure Stretch Experiments 20000

19000

Punch Force (N)

No Vinyl 1 Vinyl Sheet

18000

2 Vinyl Sheets 17000

16000

15000 19

20

21

22

23

24

25

26

27

Displacem ent (m m )

Fig. 10. Force versus displacement for 3003-H14-aluminum sheets with a hydrostatic force applied by vinyl sheets, pure stretch experiments.

Force versus Displacement for Ferrous Sheet Metal, Localized Hydrostaic Pressure Experiments 49000 48000

Punch Force (N)

47000 46000 45000 44000 No Vinyl Sheet

43000

1 Vinyl Sheet

42000

2 Vinyl Sheets 41000 40000 32

33

34

35

36

37

38

39

Displacement (mm)

Fig. 11. Force versus displacement for ferrous sheet metal with a hydrostatic pressure applied by vinyl sheets.

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M. Zampaloni et al. / International Journal of Mechanical Sciences 45 (2003) 1815 – 1848 Localized Hydrostatic Pressure Experiments using 3003-H14 Aluminum Alloy Metal Blanks, Combination Experiments 20500 19500 18500 17500

Punch Force (N)

16500 15500 14500 13500 12500

Al No Vinyl Al 1 Vinyl Al 2 Vinyl

11500 10500 9500 8500 7500 12

14

16

18

20

22

24

26

Displacement (mm)

Fig. 12. Results for the combination experiments performed on the 3003-H14-aluminum alloy sheet, using vinyl sheet to apply a localized pressure at the punch–sheet interface.

For the draw-in experiments the vinyl sheets showed no discernible trend. The vinyl requires a tight clamp at the edges of the sheet so that as the part is being formed the vinyl counteracted this movement. Since the part was allowed to draw-in, the vinyl material moved along with the part and therefore applied no counteractive pressure as the part was formed. The use of the localized pressure was also investigated during the combination experiments. Results for the aluminum alloy could be found in Fig. 12, while the results for the ferrous sheet are shown in Fig. 13. For both materials increased draw depths of approximately 1.5 –3% were achieved through the use of the small-localized pressures. 3.6. Fluid pressure applied from both sides of the sheet material A new experimental die, illustrated in Fig. 14, was designed that o7ers several advantages over the existing die design. The new die ;lls the sealed bottom chamber with 4uid that is equalized with the 4uid in the upper chamber. As the pressure in the upper 4uid chamber increases due to the volume change, the displaced 4uid will be forced into the bottom chamber thereby equalizing the pressure between the chambers. This equal pressurization on both sides of the sheet metal allows for the support of the material that is not in contact with the punch and prevents the sheet from an uncontrolled bulging in these regions. On the other hand, the new die design would still be able to o7er the increased formability caused by reverse loading the sheet (see Fig. 7), through creating a di7erential pressure between the top and bottom chambers. In the case of equal pressurization, the material that is in contact with the punch will experience a pressure that is representative of the localized hydrostatic pressure applied

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Localized Hydrostatic Pressure Experiments using Fe Sheet Metal Blanks, Combination Experiments 55000 50000

Punch Force (N)

45000 40000 35000 30000 Fe No Vinyl Fe 1 Vinyl Fe 2 Vinyl

25000 20000 15000 10000 12

14

16

18

20

22

24

26

28

30

32

34

36

38

Displacement (mm)

Fig. 13. Results for the combination experiments performed on the ferrous sheet, using a vinyl sheet to apply a localized pressure at the punch–sheet interface.

Fig. 14. The dual 4uid pressure die design that allows the pressurized 4uid to be applied on both sides of the sheet metal [13].

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Fig. 15. Hydroforming process with a blank holding support [12].

Fig. 16. Hemispherical forming process [12].

by the vinyl sheet, resulting in deeper draw depth prior to material failure. This new die design should also be able to use 4uid pressures above the limiting 3848 kPa pressure with the current onesided die design. Results from the experiments conducted with this new die, 4uid from both sides of the sheet metal, will be presented in future papers. The 4uid pressure-spiking problem discussed before will be alleviated through the implementation of a constant 4uid pressure reservoir in-line with the current regulator/controller. This constant source will allow for better tuning of the controllers and will help eliminate any spikes that could occur outside the error of the physical devices. 4. Theoretical analysis The limit theorem of plasticity has been used by Hsu and Hsieh [12] to study the hemispherical punch hydroforming process. Following their analysis, the limit (failure) pressure for the hemispherical punch has been determined for the experiments described in Section 3.4. A geometrical interpretation of the hydroforming process is shown in Figs. 15 and 16. The workpiece under consideration is divided into three zones according to the deformed shape: The region where the workpiece stays contact-free from the die (zone I), the unsupported area (zone II), and where the workpiece has been compressed onto the surface of the punch (zone III). In their

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analysis, Hsu and Hsieh [12] used the Tresca yield criterion and considered the normal anisotropy of the material. Below, the set of equations derived by Hsu and Hsieh [12] for hemispherical sheet hydroforming will be given. For the axisymmetric problem, the polar equilibrium equation in the rim area is d t (t r ) + ( r −  ) + f(P1 ) = 0; dx r

(1)

where r and  are radial and hoop stresses, respectively, r is the polar coordinate, t is the thickness, P1 is the blank holding pressure, f(P1 ) = 2P1 is friction stress, and  is the coeIcient of friction. From the incremental theory of plasticity due to Hill [15], equivalent strain-rate is 1=2  1+R 2R 2 2 ˙e = √ (˙r ) + ; ˙r ˙ + (˙ ) 1+R 1 + 2R

(2)

where ˙r ; ˙ correspond to strain rate components and ˙e is the e7ective strain rate, and R is the normal anisotropy parameter. Solving the equilibrium equation for zone I: rI (r)

rI

 =

b

a

f(P1 ) dr + t

 a

b

0 (rI )n Rn=2 e dr; r

 G(r; h; ) ; = ln r

(3)



(4)

where 1=2   2  r  2 2     − 1+ cos      a a            2        + 2(1 − sin ) 1 −   a G(r; h; ) = a ;             1 + −  cos  + 2     a a 2   



    h   h      +2 − − 1 HV − −1  a a a a

 = sin

Re =

−1



a+−h a+

2(1 + R) ; 1 + 2R



   h      − − 160 a a ; when   h     − − 1¿0 a a

(5)

(6)

(7)

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M. Zampaloni et al. / International Journal of Mechanical Sciences 45 (2003) 1815 – 1848

0 is a material constant (strength coeIcient), geometrical parameters ; a; b and h are de;ned in Fig. 16, and the Heaviside unit step function is    h   

  1 when − − 1 ¿ 0  h  a a : (8) − −1 = Hv   a a h     0 when − − 1 6 0  a a For zone II, with the continuity condition:  (a+) cos  0 (rII )n Rn=2 e dr; (9) rII (r) = rI [r = (a + ) cos ] + r a   F(r; h; ) ; (10) rII = ln r where    1=2        1 + −  −  cos  1 − sin  +     a a 2         √  (sin  − cos ) + F(r; h; ) = 2a (11)  

a     h  h        + − − 1 HV − −1 a a a a and   −1 (a + ) cos  − r : (12)  = sin  When combining the instability criterion of anisotropic material under biaxial plane strain condition and the power–law hardening relationship, the critical 4uid pressure causing rupture in the workpiece can be determined by equating the critical stress to Eq. (9), which can be expressed as    2P1 [b − (a + ) cos ]        0 t        

n+1  G n n=2 b   ln R 1+R e r n dr + √ n = (13) r   1 + 2R (a+) cos         (a+) cos  n=2   n     Re ln Fr   +  dr  r a cos  and   n+1 1=2 n √1+R 2n   1+2R  = 1 + (14)  − 1; Q a P where PQ is the normalized blank holding pressure. To solve Eq. (13) for the experiments described in Section 3.3, a general numerical method was used to calculate for the limit (failure) pressure as follows: The Newton–Raphson method was used to solve for the value of the 4uid pressure as f(PQ n ) PQ n+1 = PQ n −  (15) f (PQ n )

M. Zampaloni et al. / International Journal of Mechanical Sciences 45 (2003) 1815 – 1848

1833

the derivative of the function was taken using f(x + ) − f(x) ; f (x) ≈ 

(16)

where  is a small number (∼ 10−6 ). The Secant method was also used to ;nd the new value of the pressure to avoid the calculation of the derivative and the results were similar. The value of the integrals of F and G in Eq. (13) was calculated using the Gauss–Legendre quadrature with (n = 4) weight points as follows:  1 n  f(x) d x ≈ wj f(xj ); (17) −1

where

 a

b

j=1

f(t) dt =

b−a 2



1

−1

f

a + b + (b − a)x 2

d x:

(18)

The following values for the constants were used in the calculations (taken from the experimental setup) (Table 2): Fig. 17 shows the predicted limit (failure) 4uid pressure from the numerical analysis and the variable 4uid pressure applied in the actual experiment. Rupture in the sheet occurred when the Table 2 Data input to numerical analysis n

R



0

y

BHF

t

A

b

0.0476

0.89

0.13

95:0 MPa

202:4 MPa

482:2 MPa

1 mm

50:8 mm

88:9 mm

(BHF = blank holding force). Fluid Pressure Path 20.0 18.0

Fluid Pressure (Mpa)

16.0 14.0 12.0 10.0 8.0 6.0 4.0

Exprimental Numerical Analysis

2.0 0.0 0.0

5.0

10.0

15.0

20.0

25.0

30.0

Punch Stroke (mm)

Fig. 17. Experimental 4uid pressure compared against numerical analysis from Ref. [12].

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M. Zampaloni et al. / International Journal of Mechanical Sciences 45 (2003) 1815 – 1848

pressure crossed the limiting “failure” pressure curve. This compares well with the results shown in Fig. 32, for varying 4uid pressure case. Although the analytical model developed in Ref. [12] can be used as a guide for choosing the limit (failure) 4uid pressure, its application is limited to hydroforming of hemispherical cups formed by varying 4uid pressure. Furthermore, its results cannot be applied to experiments conducted in Section 3.3, where constant 4uid pressure is applied throughout the forming process, which resulted in maximum deformation prior to rupture (e.g., compare Figs. 7 and 32). Therefore, to predict the limiting (failure) 4uid pressure for hydroforming of complex parts, the FEA method must be used. In this paper, FEA of hydroforming of a 3003-H14-aluminum alloy sheet was carried out using Barlat Yield 89 anisotropic yield function. This numerical analysis will be presented next. 5. Finite element analysis An important goal of this research is to determine an optimum method of production for a new product. To achieve a better understanding of the deformation of the sheet metal during the forming process, numerical analysis was employed. The goal was to aid in the prediction of the ;nal part geometry, compare results against experimental data and to reduce the amount of trial and error associated with the experimental aspect of the work. For the stamp hydroforming process the numerical study was performed using the explicit ;nite element code, Ls-Dyna3D [17]. Two types of ;nite element models were used for this study: quarter- and full-model. Two types of element were used for the blank, shell elements with 7 integration points through the thickness and solid elements consisting of ;ve layers with 1 integration point through the thickness. The initial models were created using UnigraphicsJ and imported as IGES ;les. HypermeshJ was then used to create the ;nite element mesh, assigning the boundary conditions, and build the Ls-Dyna input deck for the analysis. The full-size ;nite element shell model used approximately 10,500 four-noded shell elements, while the quarter-model, illustrated in Fig. 18, used 4600 shell elements. The punch, die, and the blank holder were created using rigid material. The sheet blank was initially modeled using the isotropic material number 18 in Ls-Dyna (*MAT POWER LAW PLASTICITY). This is the von Mises yield function de;ned as follows: ! = 12 Sij Sij − 13 Q 2 ;

(19)

where Sij is the deviatoric stress, and Q is the hardening law. This material uses the Hollomon power–law hardening rule de;ned as Q = k Q n ;

(20)

where “k” is the strength coeIcient, and “n” is the work hardening exponent. To determine the hardening coeIcients for the AA3003-H14 material, a uniaxial tensile test was carried out. The results are reported in Table 3. Fig. 19 shows the experimental true stress–strain curve for the material and the curve ;t with the power–law hardening model using the calculated values of “k” and “n”. The fully integrated shell element (ELEFORM #16) with 7 integration points through the thickness was used in the modeling of the blank. To prevent draw-in, the blank holder was given a constant

M. Zampaloni et al. / International Journal of Mechanical Sciences 45 (2003) 1815 – 1848

1835

Fig. 18. A quarter-model of the hydroforming process using a hemispherical punch.

Table 3 Aluminum alloy, 3003-H14, properties 3003-H14

y (yield stress)

E

& (Poisson ratio)

150:6 MPa

69 GPa

0.33

k

n

Thickness (t)

202:2 MPa

0.0476

1 mm

force applied to its center of gravity (250 kN (56 kip)). Since the part has symmetric features, a quarter-model was used for the same process, as shown in Fig. 18. In the quarter-model the edge of the material on both forming axes (x; y) were constrained to enforce symmetry, while in the full 3D model no constraints were applied to the sheet. Forming limit diagrams (FLD) displaying contour plots of the minor and major strains were used to determine the locations, and the punch height, at which the sheet metal would fail due to tearing. The Ls-Dyna code’s new post-processor has the ability to calculate the FLD plot and to project them on the desired shell elements. This allows the location of the failure points to be easily determined. To reduce the calculation time while maintaining accuracy, an adaptive meshing scheme was used. In this scheme only those areas coming into contact are re;ned. The re;nement scheme uses an angle change re;nement method with a maximum re;nement level of three. In addition, a one-pass adaptivity with an approach criterion is used.

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M. Zampaloni et al. / International Journal of Mechanical Sciences 45 (2003) 1815 – 1848 True Stress Vs. True Strain

y = 202.2ε 0.0476

200 180

True Stress (MPa)

160 140 120 100 80 60 40 20 0 0.00

0.01

0.02

0.03

0.04

0.05

0.06

True Strain (mm/mm)

Fig. 19. Punch force versus punch displacement, using k and n values from Table 3.

Punch Velocity 2.5

Velocity (mm/ms)

2

1.5

1

0.5

0 0

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 30

Time (ms)

Fig. 20. Punch velocity used for the ;nite element simulation.

The main goal of the numerical analysis was to verify the predictions of the hydroforming model for the aluminum alloy. Once the accuracy of the numerical model is established, it could be used as a design tool for other materials. Various examples were run including pure stretch (stamping), draw-in, constant and varying 4uid pressure applied to one side of the sheet. Each of these cases will be discussed next. 5.1. No 3uid pressure (pure stretch) For the traditional stamping case the punch was given a trapezoidal velocity pro;le to ;t the curve shown in Fig. 20 with a maximum punch speed of 2 mm=ms. The results of both the FLD-numerical

M. Zampaloni et al. / International Journal of Mechanical Sciences 45 (2003) 1815 – 1848

1837

Fig. 21. Sheet metal forming without pressure (conventional stamping).

and experimental analysis for sheet stamping without pressure are shown in Fig. 21. The experimental result shows that the material failure occurs at a stamping depth of 24:6 mm (0:969 in). For the numerical result the FLD contour plot was used to determine the failure point. From the plot it was determined that the initial failure would occur around the center of the sheet at a punch depth of 23:6 mm (0:93 in). This represents a 4% discrepancy between the experimental and the numerical results, which for all practical purposes is acceptable. Fig. 22 shows the punch force–displacement for the experimental and numerical analysis up to the initial failure. It was noted that the experimental punch force was slightly higher than the numerical predictions. The load cell used in the experimental investigations has a capacity of 311 kN (70; 000 lbf ) with an error of 1%. If an error of less than 0.5% is assumed (1500 N (337 lbf )), and this error is subtracted from the experimental data, then we get the results shown in Fig. 22 (Adjusted force), which matches the numerical predictions very well. 5.2. Constant 3uid pressure applied to one-side of the sheet (pure stretch) In the experimental procedure, the punch was ;rst raised until it touched the bottom of the sheet and then stopped. Then, the 4uid pressure was increased to a desired value and kept constant at that level before the punch was allowed to move up to deform the sheet. To simulate this in the numerical model, the punch was controlled by the displacement pro;le shown in Fig. 23. The constant pressure used in the simulation was ramped up over a time period of 7 ms. Similar to the experiments, at the constant pressure level of 3448 kPa (500 psi), the numerical model predicted that the sheet would fail, before the punch moves, along its corner radii due to strain localization (see Fig. 24). In the experiments with a constant 4uid pressure of 2758 kPa (400 psi) it was found that the sheet sometimes fails along the corner radii, as shown in Fig. 25, soon after the punch starts deforming the sheet. With further investigation, it was found that due to an initial controller–regulator problem in the experimental setup the 4uid pressure was not being kept at the desired constant level of

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M. Zampaloni et al. / International Journal of Mechanical Sciences 45 (2003) 1815 – 1848 Experimental K=202, n=0.0475 Adjusted Force

Numerical Vs. Experimental Without Pressure 20000 18000 16000

Punch Force (N)

14000 12000 10000 8000 6000 4000 2000

.0 0

.5 0

.2 7

.7 4

24

22

21

.7 7

.4 9

.0 2

20

19

17

.9 9

.7 3

.4 9

.2 6

.2 5

16

15

13

12

11

01

10

43

20

70

9.

7.

6.

5.

69

41

95 3.

2.

1.

0.

15

0

Punch Displacement (mm)

Fig. 22. Predicted and measured punch force versus punch displacement curve.

Punch Displacement 50.0 45.0

Z-Displacement (mm)

40.0 35.0 30.0 25.0 20.0 15.0 10.0 5.0 0.0 0.00

5.00

10.00

15.00

20.00

25.00

30.00

Time (ms)

Fig. 23. Punch displacement pro;le for one-sided hydroforming simulation.

35.00

M. Zampaloni et al. / International Journal of Mechanical Sciences 45 (2003) 1815 – 1848

1839

Fig. 24. FLD results. Failure is predicted at the edges for a 3448 kPa (500 psi) pressure.

Fig. 25. Pressure pro;le shown in Fig. 26 was applied to the topside of the sheet. Failure occurred at a draw depth of 0:32 in.

2758 kPa (400 psi), but instead was ramping up from 2758 kPa (400 psi) to 7000 kPa (1015 psi). Fig. 26 shows the actual 4uid pressure curve, which was applied to the sheet, resulting in the premature sheet failure, as shown in Fig. 25. To verify the robustness of our numerical modeling, it

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M. Zampaloni et al. / International Journal of Mechanical Sciences 45 (2003) 1815 – 1848 Constant-variable Pressure Profile 8000.0

7000 kPa (1000psi) 7000.0

Pressure (kPa)

6000.0

5000.0

4000.0

2758 kPa (400 psi) 3000.0

2000.0

1000.0

0.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

Time (ms)

Fig. 26. The actual pressure pro;le applied to the topside of a 3003-H14-aluminum sheet alloy.

was decided to apply the same pressure pro;le (Fig. 26) to the blank, modeled with solid elements, and to calculate the punch height and location where the sheet fails, using plastic strain data. Fig. 27 shows the corresponding plastic strain contours developed on the upper surface (where the pressure was applied) and the bottom surface of the hydroformed sheet metal. The model predicts that the aluminum sheet would fail at its corner radii on the top (Fig. 27a). This compares very well with the actual failure location observed in the experiments (Fig. 25). The numerically predicted punch height at the failure point was 6:6 mm (0:26 in), which faired well against the experimental punch height of 8:1 mm (0:32 in). In pure stretch experiments, with constant 4uid pressure maintained throughout the whole process, a signi;cant increase in the punch depth, before failure, was noticed (see Fig. 7). The numerical model also predicts higher punch depths, before failure, when constant pressure is applied to the topside of the sheet. Fig. 28 shows the numerical punch force–displacement plots, up to the failure point, for several constant 4uid pressures. It is obvious that compared to conventional stamping (no 4uid pressure), the hydroformed aluminum sheet reaches signi;cantly deeper punch depths, before it fails. This increase in the punch depth improves with increasing the 4uid pressure, up to a maximum value of 2758 kPa (400 psi). Fig. 29 shows the failure punch depth–pressure plot for both the experiments and the numerical simulations. Fig. 30 shows the experimental and numerical punch force–displacement curves for the case of constant 4uid pressure of 2758 kPa (400 psi), up to the failure point. Besides the obvious improvement in the failure punch depth, the pressurized 4uid also forces the sheet to better conform to the shape of the punch, resulting in a better-formed part and a possible reduction in the springback, as shown in Fig. 31 (Fig. 32).

M. Zampaloni et al. / International Journal of Mechanical Sciences 45 (2003) 1815 – 1848

1841

Fig. 27. Plastic strain contours, predicted with a solid model, for a 3003-H14-aluminum sheet alloy after the pressure pro;le in Fig. 26 was applied to its topside. (a) Topside of the sheet, (b) bottom side of the sheet. Results clearly match the failure location observed in the experiment, Fig. 25.

Numerical Punch Force vs. Displacement for 3003-H14 Aluminum Sheets Under a Constant Fluid Pressure Applied From One Side of The Material 45000 2758 Kpa (400psi)

40000

Punch Force (N)

35000 2069 Kpa (300psi)

30000

1370 Kpa (200psi)

25000

690 Kpa (100psi)

20000

0 Kpa (0psi) 15000 10000 5000 0 0

5

10

15

20

25

30

35

Punch Displacement (mm)

Fig. 28. Numerical punch force–displacement results for 3003-H14-aluminum alloy sheet at constant 4uid pressures applied to the topside of the sheet.

1842

M. Zampaloni et al. / International Journal of Mechanical Sciences 45 (2003) 1815 – 1848 Failure Depth Vs. Pressure 35

30

Failure Depth (mm)

25

Poly. (Numerical) Poly. (Experimental) 20

15

10

5

0 20

520

1020

1520

2020

2520

3020

Pressure (Kpa)

Fig. 29. Failure depth versus pressure results for 3003-H14-aluminum alloy sheet. Comparison between experiment and numerical results.

5.3. Varying 3uid pressure In the case of varying 4uid pressure, the pressure was applied to the top surface of the sheet incrementally up to 14:4 MPa (2080 psi). In the numerical simulation, the punch was given a velocity pro;le (Fig. 20), since in the experiments the punch was not stopped during the process of applying the 4uid pressure. The 4uid pressure pro;le applied in the numerical analysis was taken from the experimental data (see Fig. 5b). The timing of the pressure pro;le was changed in order for it to be applied in the numerical analysis. Fig. 30 shows the predicted punch force, before failure, matching the experimental values very well (3% error). 5.4. Draw-in results Fig. 33 shows the resulting part when hydroforming experiments with draw-in were performed. It is clear from Fig. 33, that the material is anisotropic and wrinkling occurs along the rolling direction of the sheet. Initially in the numerical analysis, the von Mises isotropic material model (material number 18 in Ls-Dyna: ∗MAT POWER LAW PLASTICITY) was used. Fig. 34 shows the resulting deformed shape of the sheet using this material model. From this ;gure the isotropic nature of this material model is clear, since the wrinkles occur along both axes of the material.

M. Zampaloni et al. / International Journal of Mechanical Sciences 45 (2003) 1815 – 1848

1843

Punch Force Vs. Punch Displacement 45000 40000

Punch Force (N)

35000 30000 25000 20000 15000 10000 Experimental

5000

Numerical

0 0

5

10

15

20

25

30

35

40

Displacement (mm)

Fig. 30. Punch force versus punch displacement for the 400 psi constant 4uid pressure.

Fig. 31. Part shape comparison between: (a) conventional stamping (no 4uid pressure), and (b) a hydroformed sheet with a constant 4uid pressure of 2758 kPa (400 psi) applied to its topside. Besides improved formability, the hydroformed part conforms to the shape of the punch more closely too, possibly resulting in a reduced springback.

Barlat and Lian [16] developed an orthotropic material model for anisotropic sheet metals with plane stress conditions. This material model uses the Lankford parameters (R0 ; R45 and R90 ) for the de;nition of anisotropy as follows: ! = a|K1 + K2 |m + a|K1 − K2 |m + c|2K2 |m − 2 Q m ;

(21)

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M. Zampaloni et al. / International Journal of Mechanical Sciences 45 (2003) 1815 – 1848

where x + h y ; 2 

x + h y 2 K2 = + p2 +2xy : 2

K1 =

(22)

The anisotropic material constants (a; c and h) are obtained through the R0 ; R45 and R90 as follows (17):  R0 R90 ; a=2−2 (1 + R0 )(1 + R90 ) c = 2 − a;  R0 (1 + R90 ) h= : R90 (1 + R0 )

(23)

The anisotropy parameters (R0 ; R45 and R90 ) are determined from uniaxial tensile tests performed in 0◦ , 45◦ and 90◦ measured from the rolling direction of the sheet. An iterative method is used to ;nd the “p” value. This particular material model is used in Ls-Dyna to simulate the anisotropic behavior of the material (Material #36 in Ls-Dyna: ∗MAT 3-PARAMETER BARLAT). The material properties for the AA3003-H14 used in this simulation are shown in Table 4 below.

Punch Force vs. Displacement

Experimental, Variable Numerical,Variable

120000

Punch Force (N)

100000

80000

60000

40000

20000

0 0

5

10

15

20

Displacement (mm)

Fig. 32. Punch force versus punch displacement for varying 4uid pressure.

M. Zampaloni et al. / International Journal of Mechanical Sciences 45 (2003) 1815 – 1848

1845

Fig. 33. Experimental results for the draw-in case with 4uid pressure of 70 psi applied to the topside of the sheet.

Fig. 34. Numerical draw-in simulation using an isotropic material model in LS-Dyna.

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M. Zampaloni et al. / International Journal of Mechanical Sciences 45 (2003) 1815 – 1848

Table 4 Material properties for 3003-H14 using Barlat model 3003-H14

y (yield stress)

E

& (Poisson ratio)

150:6 MPa

69 GPa

0.33

k

n

Thickness (t)

202:2 MPa

0.0476

1 mm

R0

R45

R90

0.500

0.550

0.650

Fig. 35. Numerical draw-in simulation using an anisotropic material model (Barlat YLD-89) in LS-Dyna. A better comparison with the experiments (Fig. 33) could be seen.

Fig. 35 shows the resulting deformed shape of the sheet using this anisotropic material model. It is clear that the numerical model correctly predicts the wrinkling behavior of the aluminum sheet when utilizing Barlat’s material model.

M. Zampaloni et al. / International Journal of Mechanical Sciences 45 (2003) 1815 – 1848

1847

6. Conclusions A total of nine di7erent combinations of experiments were conducted to evaluate the sheet hydroforming process. These experiments included studying the e7ect of boundary condition (i.e., pure-stretch, draw-in and their combinations) and pressure loading (i.e., constant and varying 4uid pressure and a localized pressure applied using a vinyl sheet) on the deformation of 3003-H14aluminum sheet alloy. Overall, the experimental results show that the sheet hydroforming process is a viable processing method that deserves some additional attention based on the signi;cant advantages that it provides in potential cost savings (no female die needed), improved formability and part shape accuracy. Further experimentation is needed, however, in order to validate the die design that accounts for the dual 4uid pressures applied to the upper and lower surfaces of the sheet. In addition, the investigation into the wrinkling and rupturing characteristics needs to be continued and a characteristic punch stroke/4uid pressure path should be determined to minimize the occurrence of these instabilities. The numerical analysis of the hydroforming process with the commercial ;nite element code Ls-Dyna 3D seems to capture the failure and wrinkling characteristics of the 3003-H14-aluminum sheet alloys very well. The accuracy of the numerical predictions, however, is very sensitive to the material properties of the sheet metal. Accurate material characterization methods are required to ensure that the model can accurately capture the deformation behavior of the material. Acknowledgements The authors wish to thank the Manufacturing Research Consortium at Michigan State University and its member companies GM and Ford for providing the funding support for this research work. References [1] McClintock FA. A criterion for ductile fracture by the growth of holes. Journal of Applied Mechanics 1968;35: 363–71. [2] Rice JR, Tracey DM. On the ductile enlargement of voids on triaxial stress ;elds. Journal of Mechanical Physics and Solids 1969;17:201–17. [3] Clift SE, Hartley P, Sturgess CEN, Rowe GW. Fracture prediction in plastic deformation process. International Journal of Mechanical Science 1990;32(1):1–17. [4] Hartley P, Pillinger I, Sturgess C. Numerical modeling of material deformation processes research development and applications. Berlin: Springer; 1992. [5] Youssef Y, Denault J. Thermoformed glass ;ber reinforced polypropylene: microstructure, mechanical properties and residual stresses. Polymer Composites 1998;19(3):301–9. [6] Tirosh J, Yossifon S, Eshel R, Betzer A. Hydroforming process of uniform wall thickness products. ASME Journal of Engineering for Industry 1977;99:685–91. [7] Yossifon S, Tirosh J, Kochavi E. On suppression of plastic buckling in hydroforming processes. International Journal of Mechanical Science 1984;26:389–402. [8] Yossifon S, Tirosh J. Rupture instability in hydroforming deep-drawing process. International Journal of Mechanical Science 1985;27:559–70. [9] Yossifon S, Tirosh J. Buckling prevention by lateral 4uid pressure in deep drawing. International Journal of Mechanical Science 1985;27:177–85.

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M. Zampaloni et al. / International Journal of Mechanical Sciences 45 (2003) 1815 – 1848

[10] Yossifon S, Tirosh J. On the permissible 4uid-pressure path in hydroforming deep drawing processes—analysis of failures and experiments. Journal of Engineering for Industry 1988;110:146–52. [11] Lo SW, Hsu TC, Wilson WRD. An analysis of the hemispherical-punch hydroforming process. Journal of Materials Processing Technology 1993;37:225–39. [12] Hsu TC, Hsieh SJ. Theoretical and experimental analysis of failure for the hemisphere punch hydroforming processes. Journal of Manufacturing Science and Engineering 1996;118:434–8. [13] Pourboghrat F, Zampaloni M, Benarad A. Hydroforming of composite materials. October 2003. United States Patent No. 6631630. [14] Pourboghrat F, Chu E. Springback in plane strain stretch/draw sheet forming. International Journal of Mechanical Sciences 1995;36(3):327–41. [15] Hill R. The mathematical theory of plasticity. Oxford: Clarendon Press; 1950. [16] Barlat F, Lain J. Plastic behavior and stretchability of sheet metals. Part I: a yield function for orthotropic sheets under plane stress conditions. International Journal of Plasticity 1989;5:51–66. [17] Hallquist JO. Ls-Dyna user’s manual. Livermore Software Technology Corporation, 1999.

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distributed memory computers, provided that the number of dipoles per processor is large enough. The size of the dipoles was varied in the range λ/11 – λ/8 for ...

Simulation and experimental study of spray pyrolysis of ...
Department of Chemical Engineering, Graduate School of Engineering, Hiroshima University, .... Healthcare Co., Ltd., Tokyo, Japan). Droplet size distri-.

Experimental Study of Internet Stability and Backbone ...
the stability of major paths between Internet Service ... both telephony and circuit switched data networks. ... Backbone service providers participating in the In-.

Experimental and theoretical study of 1-(2-ethylamino ...
which was controlled by CorrWare and Zplot software. The cell assembly ... distilled water and analytical reagent-grade hydrochloric acid, 0.5 M HCl, were used ...

A Numerical Study of the Sensitivity of Cloudy-Scene ... - Sites
Jun 28, 1996 - Our civilization has been the single most important force in recent ... The solar energy absorbed and reflected by the earth occurs .... The design strategy of the experiment incorporated both old and new technology concepts.

Using eyetracking to study numerical cognition-the case of the ...
Sep 23, 2010 - Their results. revealed a significant negative correlation between reaction. time and number of errors and the numerical difference. between the two numbers. In other words, the larger the. numerical difference is between two numerical

numerical study of the behaviour for elastic- viscoplastic ...
Abstract : The variation of stress during creep convergence of a horizontal circular galleries excavated in rock salt is studied. Examples are given for rock salt by N. Cristescu ([1], [2]). A non-associated elasto-viscoplastic constitutive equation

A numerical study of a biofilm disinfection model
Derive a model from (1)–(6) that takes into account the fact that some bacteria ... Free Open Source Software for Numerical Computation. http://www.scilab.org/.

Using eyetracking to study numerical cognition-the case of the ...
Whoops! There was a problem loading more pages. Retrying... Using eyetracking to study numerical cognition-the case of the numerical ratio effect.pdf. Using eyetracking to study numerical cognition-the case of the numerical ratio effect.pdf. Open. Ex

Experimental Study of Fractional Order Proportional ...
Simulink [software (s/w) mode] and finally experimental verification and comparisons in .... in degrees of the respective sinusoidal output is noted at steady state. .... The master controller uses water level in tank 2 as process variable by varying

Minority vs. Majority: An Experimental Study of ...
Jan 11, 2008 - reason, you wish to vote for project 2, write 1 in the second cell in the first row and write 0 in the other two. You can choose only one project, that is there must appear a 1 and two zeros as your votes in every row. Choose your vote

Cross-situational learning: an experimental study of ...
Spoken forms were produced using the Victoria voice on the Apple Mac OS X speech synthe- ... .ac.uk/research/˜mtucker/SlideGenerator.htm), and participants were tested ... or 8 non-target referents co-present with the target referent on each ...

An Experimental Study of Security Vulnerabilities ... - Semantic Scholar
Networked systems, such as large web server farms and .... host. A user logon to an FTP server authenticates itself by user name and password and then ...