Numerical Study of Localized Necking in the Strain Path of Copper Hydroformed Tube: Effect of Friction

1

Numerical study of localized necking in the strain path of copper hydroformed tube: effect of friction

A.Abdelkefi1,2,3,a,N.Guermazi1,b,N.Boudeau2,3,c*, P.Malécot2, 3, d, G. Michel2, 3, e 1Laboratoire de Génie des Matériaux et environnement(LGME), Ecole Nationale

d’Ingénieurs de Sfax (ENIS), B.P 1173-3038, Sfax, Université de Sfax, Tunisie.

2FEMTO-ST, Département Mécanique Appliquée, 24 rue Epitaphe, 25000

Besançon, France.

3 ENSMM, 26 rue Epitaphe, 25030 Besançon Cedex, France. [email protected],[email protected], [email protected], [email protected],

e [email protected] .

Abstract

The effect of the friction coefficient in the strain path of hydroformed tube is

discussed in this paper. A finite element simulation with the LS-DYNA/Explicit

software has been performed and experiments have been carried out. The

localized thinning can be related to necking and then, the use of the Forming

Limit Curve (FLC) and the analysis of the strain path can give some indications

on the risk of fracture in the hydroformed part. FE simulations have been

performed with different friction coefficients to study their effect on the resulting

strain path and to predict the localized thinning during tube hydroforming in a

square section die. Hydroforming experiments have been performed on

deoxidized copper (Cu-DHP) tubes to validate the finite element results. When

the pressure increases, the strain increases firstly in the transition zone, that next

leads to severe thinning in the corner zone and finally, in the straight wall. The

comparison between the results obtained with the finite element and experiments

confirms that the thickness reduction is more important in the transition zone

between the straight- wall and the corner radius and the localized necking occurs

in the transition zone. It is then possible to define the limits of the process and

enhance the necking prediction.

Keywords: Tube hydroforming; Friction effect; Strain path; Localized necking.

1. Introduction:

In recent years, there is an increasing demand for hydroformed parts dedicated

for aeronautical and automotive applications. This is because hydroforming

offers various advantages such as weight reduction, part consolidation, lower

tooling cost, improved structural strength and stiffness improvements, secondary

operations bypass and scrap reduction (Ahmetoglu and Altan 2000). In this

context, great efforts have been focused on tube hydroforming using analytical

models, numerical computations and experimental characterizations (Kridli et al.

2

2003; Hwang and Chen 2005). The success of such process depends on the

knowledge of the material properties of the tube, the dies geometries and the

friction conditions. The friction coefficient directly affects the flow of material in

the die, thus the thickness repartition over the final part. In the literature, many

researchers have been interested in the study of the strain path of the

hydroformed tubes (Bihamta et al. 2013; Li et al. 2012 ; Xu et al. 2009-a; Xu et

al. 2009-b). Indeed, to estimate if this thickness change is safe from fracture, the

forming limit diagram or curve (FLD or FLC) was generally used. Consequently,

in Ls-Dyna software the FLD for each section of the workpiece (after

hydroforming) was drawn. Bihamta et al., (Bihamta et al. 2013) have used the

FLC to control the hydroforming process and then to estimate the validity of this

technique in the case of hydroforming in complex dies. Li et al. (Li et al. 2012)

have also used this method to study the strain path and to predict the localization

of defects in elliptical section. In addition, FE simulations have been performed

with different friction coefficients to examine their effect on the resulting strain

path. Xu et al. (Xu et al. 2009-a) have investigated the (FLC) in a squares section

die to study the thickness variation for different points, indeed they have

concluded that the thinnest element of the tube wall occurs at the transition zone,

while the thickest element is located at the middle of the side wall. Xu et al., (Xu

et al. 2009-b) have investigated the (FLC) in a trapezoidal sectional die and they

have predicted the localized thinning.

2. Experimental procedure

2.1. Material:

In the present study the material used is deoxidized copper (Cu-DHP) tube with

outer diameter of 35mm and nominal thickness of 1 mm, and 250 mm of length.

In the meanwhile of bulging test, internal pressure and pole height of the tube

(also named the bulge height) are continuously measured resulting in a pressure–

bulge height curve. The previous curve with the analytical model proposed in the

literature (Boudeau and Malécot 2012) leads to obtain the curve of the true

stress-true strain curve as given in Fig.1.

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Fig.1. Typical true stress-true strain curve for the tested material.

The mechanical properties of the tested material are listed in Table1.

Table.1: Mechanical properties of the used copper.

Density (tonne/mm3) 8.49e-9

Rm (MPa) 440

Rp0.1 (MPa) 420

A10 (%)* 2

E (GPA) 132

Poisson coefficient υ 0.34

Strength coefficient K.(MPa) 263.63

Strain hardening coefficient n 0.287

Yield stress σ.(MPa) 50

Initial strain ε0 0.0043

*A 10: Elongation of drawn copper tubes on annealing temperature after cold

work.

2.2. Hydroforming procedure

In the present study, a modular tool has been designed to run tube bulging tests

in an open die or tube hydroforming in closed shape dies. This tool is installed in

a press. The experimental devices are illustrated in Fig.2. A multiplier pressure

cylinder creates the high pressure to bulge the tube and two vertical cylinders

clamp the tube at its two extremities by cone-cone contacts. The test proceeds as

following: (1) conical plungers come in contact with the ends of the tube; (2) the

hydraulic fluid is pumped into the specimen through the conical plungers

resulting in a slow increasing pressure inside the tube. (3) the tube deforms and

takes, little by little, the shape of the die. During the hydroforming process, the

internal pressure inside the tube and the tube deformation are measured. In the

0,00 0,05 0,10 0,15 0,2040

60

80

100

120

140

160

Tru

e S

tres

s (M

Pa)

True strain

σ� = 263.63(0.0043 + ε̅) .���

4

present test, the maximal internal pressure was 28 MPa that allows a tube

expansion without any risk of crack (Fig.3). This maximal pressure was

estimated through numerical simulations and optimization procedure. The tests

are conducted without specific lubricant, but the tools are oiled to avoid their

degradation.

Fig. 2: The modular tool installed on the press at FEMTO-ST lab (a) and the main dimensions of the square section die (b)

The copper tubes were hydroformed using a square cross-section die with

50 mm of length and 5 mm of corner radius .The geometry of a half tube is

considered and it is shown in Fig.4.

3. The finite element study

Because of the symmetry of the geometry, only a half tube is considered to

simulate the tube hydroforming in a square die via LS-DYNA/Explicit©

software (Hallquist 1989). The geometry is meshed with 51448 nodes and

51164 Belytschko-Tsay shell elements. The element size is based on the

smaller detail in the model, meaning the die corner radius r = 5 mm. The

Fig.3. Tube after hydraulic expansion with various internal pressures: experimental result.

Displacement sensor

Die emplacement

Conical machining for embedding (upper)

35

50

R5

(a) (b)

5

die is assumed to be a rigid elastic material. The tube material is assumed as

elastic-plastic and isotropic. In the plastic range, the Swift law

287.0)0043.0(63.263)( εσ +=MPa is considered. The Swift parameters

have been identified from experimental hardening curve obtained with the

tube bulging test (Boudeau and Malécot 2012). The tube is clamped at its

two ends. Finally, an internal pressure is applied on the inner surface of the

tube. Based on the experimental measurements, the maximum pressure

varies from 15 to 28 MPa, in a virtual period of 0.001s (Fig.4). We assume,

for the simulation, a contact "automatic one way surface-to-surface" and we

introduce various friction coefficients. Two friction coefficients (µ=0.05

and µ=0.1) between tube and die are considered and, then, the thickness

distribution in the final part is studied. Post-processing the numerical results

will consist in analyzing the evolution of thickness reduction, thickness

spatial repartition and die radius evolution in relation with the different

friction conditions.

Fig. 4. FE model (a) and typical FE results (b).

The dimensions of the cooper tube and the main results are summarized

Table.2.

Table.2: Dimensions of the tube and main results.

External radius (mm)

Half model length (mm)

Tube thickness (mm)

Friction Thickness reduction (%)

Final radius (mm)

17.5 125 1 0.05 20.5 5.32 17.5 125 1 0.1 21.5 5.23

4. Effect of friction on tube hydroforming and prediction of thinning

location

In this section, we are interested in thinning and its location in the

hydroformed tube (Fig.5). A quarter of the tube was considered due to the

geometrical symmetry.

(a) (b)

Tube

die

Bulged tube

a b

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Fig.5. Thickness reduction under different friction coefficient values and experimental result for several measurement points.

A profile is defined in the centered cross section of the tube and the thickness

reduction versus the points of measure defined along the transversal profile is

also shown in Fig.5. The values for the friction coefficient have been chosen

from experimental results obtained on pin-on-disk tribometer realized at the

University of Sfax (LGME) with samples corresponding to the two materials

in contact during tube hydroforming. The thickness reduction measured from

experiments presents a maximum value of 30% while FEM results lead to

exhibit 21.5% of reduction. Points 1 and 26 define the midline of the straight

wall while points 5 and 20 define the beginning of the transition zone. A

significant increase of the thickness reduction was obtained and this can be

ascribed to the increase of the friction coefficient, especially in the transition

zone. Whereas the friction coefficient was found to have a little effect on the

thickness reduction in both straight wall and corner zone. This finding is

consistent with that obtained in the literature (Orban and Hu 2007). Despite

the 9% of difference between numerical and analytical results, the two

approaches show similar evolutions. These differences can be linked to:i) the

friction coefficient is not characteristic of the real friction conditions during

tube hydroforming; ii) the 3D shell model is not sufficiently precise for

thickness evaluation. In addition, the FE simulations are certainly more

representative of the real process but, a model based on shell elements can

lead to an over estimation of the thickness. A 3D model with solid finite

elements would be more appropriate for the evaluation of the thickness

reduction.

5 10 15 20 25 30

10

15

20

25

30

Thi

nnin

g(%

)

measurement point

experimental µ=0,05(FE) µ=0,1(FE)

Straight

Wall

Straight

Wall

Transition

Zone

Transition

Zone

Corner

Zone

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Fig.6: Thinning localization in the hydroformed tube.

In order to validate the numerical results, a real hydroformed tube profile is

examined as shown in Fig.6. As it can be seen exactly the location of the

thinning is in the transversal profile of the hydroformed tube. This confirms

again that the severe thinning occurs in the transition zone and thus a good

correlation was obtained between the numerical and experimental studies.

5. Effect of the friction on the strain path and the study of the localized necking:

The localized thinning can be related to necking and then, the use of the

Forming Limit Curve (FLC) and the analysis of the strain path can give

some indications on the risk of fracture in the hydroformed part. Two

friction coefficient values were used: µ=0.05 and µ=0.1. Three zones are

considered: the straight wall (S343), the transition zone (S3790) and the

corner area (S3787) illustrated in Figs.7 and 8 .The strain evolution on the

FLC diagram reveals, in particular when the final pressure is 28MPa, that

no risk of necking to be detected (Fig.7).

Transition zone Corner zone

Straight wall

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Fig.7. Experimental/FE results obtained under different friction coefficients and a pressure value of 28 MPa.

On the other hand, another simulation with a maximum pressure of 36

MPa, corresponding to crack formation during experiments, has been post-

processed with the same way as previously described. As illustrated in Fig.

8, the main results indicated that a severe thinning takes place in the

transition zone. In addition, when the pressure increases from 28 to 36

MPa, the strain increases firstly in the transition zone, that next leads to

severe thinning in the corner zone and finally, in the straight wall.

Therefore, both of experimental and numerical results (Figs.7 and 8) let us

to believe that the localized necking occurs in the transition zone.

-40 -30 -20 -10 0 10 20 30 40 50

0

20

40

60

80

100

120

Maj

or s

trai

n [ ε

1] (%

)

Minor strain [ε2](%)

% FLC Safety margin severe thinning wrinkle S343 (µ=0.1) S3790 (µ=0.1) S3787 (µ=0.1) S343 (µ=0.05) S3790 (µ=0.05) S3787 (µ=0.05)

Corner zone Straight Wall

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Fig.8. Experimental / FE results obtained under different friction coefficients and a pressure value of 36 MPa.

6. Conclusion

In this work, we have focused our attention on the study of the friction

effect on the strain path using the forming limit curve (FLC). The

prediction of the localized thinning for hydroformed tube was alos

investigated. During tube hydroforming experiments a square die was used.

Numerical simulations have been performed with LS-DYNA/Explicit

software. The correlation between the numerical and experimental results

was discussed. Through the finite element simulations, one can conclude

that, the predicted FLC matches well with the obtained experimental data.

Therefore, such correlation emphasizes the accuracy and the validity of our

numerical approaches. Finally, it is equally important to note that the

-40 -30 -20 -10 0 10 20 30 40 50

0

20

40

60

80

100

120

Μaj

or s

trai

n[ε 1] (

%)

Minor strain [ ε2] (%)

% FLC Safety margin severe thinning wrinkle S343 (µ=0.1) S3790 (µ=0.1) S3787 (µ=0.1) S343 (µ=0.05) S3790 (µ=0.05) S3787 (µ=0.05)

Transition zone

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localized thinning occurs firstly in the transition zone, then in the corner

zone and finally in the straight wall.

References

(Ahmetoglu and Altan 2000) Ahmetoglu M., Altan T. (2000), Tube hydroforming: state-of-the-art and future trends, Journal of materials Processing Technology, 98 (2000) 25-33. (Kridli et al. 2003) Kridli G.T., Bao L., Mallick P-K., Tian Y., Investigation of thickness variation and corner filling in tube hydroforming, Journal of Materials Processing Technology, 33 (2003) 287-296. (Hwang and Chen 2005) Hwang Y.M ., Chen W-C ., Analysis of tube hydroforming in a square cross-sectional die, International Journal of Plasticity, 21 (2005) 1815-1833. (Bihamta et al. 2013) Bihamta R., D’Amours G., Bui Q.H., Guillot.M., Rahem A., Fafard M., Numerical and experimental studies on the new design concept of hydroforming dies for complex tubes, Materials and Design, 47 (2013) 766-778. (Li et al. 2012) Li S., Chen X., Kong Q., Yu Z., Lin Z., Study on formability of tube hydroforming through elliptical die inserts, Journal of Materials Processing Technology, 212 (2012) 1916-1924. (Xu et al. 2009-a) Xu X., Li S., Zhang W., Lin Z., Analysis of thickness distribution of square-sectional hydroformed parts, Journal of Materials Processing Technology, 209 (2009) 1397–1403. (Xu et al. 2009-b) Xu X., Lin Z., Li S., Zhang W., study of tube hydroforming in a trapezoid-section die, Journal of Materials Processing Technology, 209 (2009) 158–164. (Boudeau and Malécot 2012) Boudeau N., Malécot P., A simplified analytical model for post-processing experimental results from tube bulging test: Theory, experimentations, simulations, Journal of Mechanical Sciences, 65(2012)1-11. (Hallquist 1989) Hallquist J.O., LS-DYNA3D User Manual v970, LSTC, Livermore, 1989. (Orban and Hu 2007) Orban H., Hu S.J., Analytical modeling of wall thinning during corner filling in structural tube hydroforming, Journal of Materials Processing Technology, 194 (2007) 7–14.