S

Sa

b

a

ARRAA

KFTBEFE

1

ffiispihtld1iplttwe

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Journal of Materials Processing Technology 212 (2012) 1916– 1924

Contents lists available at SciVerse ScienceDirect

Journal of Materials Processing Technology

journa l h omepa g e: www.elsev ier .com/ locate / jmatprotec

tudy on formability of tube hydroforming through elliptical die inserts

huhui Lia,∗, Xianfeng Chena, Qingshuai Konga, Zhongqi Yua, Zhongqin Lina,b

Shanghai Key Laboratory of Digital Autobody Engineering, Shanghai Jiao Tong University, Shanghai 200240, ChinaState Key Laboratory of Mechanical System and Vibration, Shanghai 200240, China

r t i c l e i n f o

rticle history:eceived 21 November 2011eceived in revised form 23 March 2012ccepted 21 April 2012vailable online xxx

a b s t r a c t

This paper proposes a novel experimental approach to evaluate the formability for tube hydroformingunder biaxial stretching through elliptical bulging. The idea comes from the hydraulic stretch-drawingtests with elliptical dies for the right hand side of forming limit curve (FLC). Based on the deformationtheory and the classical Hosford yield criterion, an analytical model is constructed for the elliptical bulgingof tube hydroforming. Then the novel experimental device is designed with five upper elliptical dieinserts and one lower die insert used to produce ellipsoidal bulged domes and some experiments are

eywords:ormabilityube hydroformingiaxial stretchinglliptical bulgingorming limit curve (FLC)

performed. The linear strain paths in different strain states are verified and the right hand side of FLCfor roll-formed QSTE340 seamed tube is determined through the proposed experimental approaches.Finally, a comparison between the theoretical results and experimental data is performed. The theoreticalpredictions show good agreement with the experimental results.

© 2012 Elsevier B.V. All rights reserved.

lliptical die inserts

. Introduction

Due to increasing demands for lightweight parts, tube hydro-orming has been widely used to manufacture parts in variouselds, such as automobile, aircraft, aerospace, and ship building

ndustries (Dohmann and Hartl, 1996). During tube hydroforming,everal forming parameters, including the loading path, materialroperties, die design, and friction at the tube-die interface, signif-

cantly influence the results. So the finite element method (FEM)as been widely used to predict and estimate the formability of theube hydroforming process recently (Kang et al., 2005). The formingimit curve (FLC) or the forming limit diagram (FLD), which intro-uced by Keeler and Backofen (Keeler and Backofen, 1963) in the960s, is an important input for FEM simulation of parts. The exper-

mental measurement of FLC has become common practice in therocess of evaluating the formability of sheet metal. Test methods

ike Nakazima and Marciniak are frequently used as standardizedest methods. But now there are not standardized and authorita-ive test methods used for the FLC of tube hydroforming in thehole forming modes. Therefore it is important to investigate the

xperimental approaches to obtain the curve.The important problems of establishing the FLC are the deter-

ination of various linear strain paths and the suitable apparatus.n sheet metal tests, various strain states are achieved by adjustingifferent parameters like the lubrication conditions between the

∗ Corresponding author. Tel.: +86 21 34206304; fax: +86 21 34206304.E-mail address: lishuhui@sjtu.edu.cn (S. Li).

924-0136/$ – see front matter © 2012 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.jmatprotec.2012.04.016

sheet metal and the punch and the sheet width, and a hemispher-ical punch or a cylindrical punch is used. In tube hydroforming,several research studies have been reported concerning the loadingpaths or the forming limit of tubes. Asnafi (1999) constructed ana-lytical models to determine the loading paths for force-controlledtube free hydroforming. Asnafi and Skogsgardh (2000) also stud-ied stroke-controlled tube free hydroforming theoretically for thelinear strain paths. Chu and Xu (2008) investigated the predictionof FLD for tube hydroforming from the perspective various combi-nations of loading paths based on plastic instability. Davies et al.(2000) proposed a tooling and experimental apparatus to establishthe FLC for AA6061 tube based on the free-expansion tube hydro-forming with axial compression and internal pressure. Hwang et al.(2009) carried out bulge tests to establish the FLC of tubular mate-rial AA6011. A self-designed free bulge forming apparatus of fixedbulge length and a hydraulic test machine with axial feeding wereused to carry out the bulge tests. Kim et al. (2005) performed aseries of free bulge tests to evaluate the forming limit of the hydro-forming process. The test tube is supported between a lower and anupper die. The lower part of the tube is fixed in movement, whilethe other is free to be able to move in the axial direction for pro-viding axial feeding. Song et al. (2010) also executed a series of freebulge tests to the forming limit curve for tubular material in thetube hydroforming process with the same experimental apparatus.

All the investigations known in literature so far are concentrated

on the free bulge tests with axial compression and internal pres-sure. So only the left hand side ( ̌ < 0) of FLC could be obtainedfrom experiments. To obtain the right hand side ( ̌ > 0) of FLC,both ends of tube are subjected to different loading histories

sing Technology 212 (2012) 1916– 1924 1917

itaucKbaiaedstra

booCs(fuptosapamo

sfatudTdftld

2

2

sfstts

sdSbds

Fig. 1. Simulation results for tube free bulge test.

S. Li et al. / Journal of Materials Proces

nvolving axial tension and internal pressure. The difficulty iso clamp both ends of tube with internal pressure. Yoshidand Kuwabara (2007) constructed the FLC for a steel tube fromniaxial to equibiaxial tension regions using a self-designed servo-ontrolled tension/compression-internal pressure testing machine.orkolis and Kyriakides (2008) investigated the inflation andurst of Al-6260-T4 tubes under combined internal pressure andxial tension/compression load through a combination of exper-ments and modeling and observed that localized wall thinningnd burst can be very sensitive to the constitutive descriptionmployed for the material. Chen et al. (2011) designed a novelevice requiring the simultaneous application of lateral compres-ion force and internal pressure to control the material flow underension–tension strain states. But the suitable loading paths for theight hand side of FLC are calculated by FEM simulations and theccuracy is not high.

In sheet metal forming, the right hand side of FLC can be obtainedy hydraulic stretch-drawing tests with elliptical dies. Rees (1999)utlined a theory of diffuse instability for ellipsoidal bulging ofriented, orthotropic rolled sheet metals under biaxial tension.omparisons are made with the limiting strains and the peak pres-ure is observed from experimental pole failures. Giuliano et al.2005) performed bulge tests using elliptical shape dies with dif-erent aspect ratios to predict the limit strains of PbSn60 alloynder biaxial stress at the room temperature and at constant gasressure. Altan et al. (2006) used biaxial bulge tests to determinehe material properties (flow stress, anisotropy and formability)ver a large strain/deformation range. Abu-Farha et al. (2008) pre-ented a detailed systematic methodology for assessing formabilitynd limiting strains by pneumatic sheet metal stretching. The pro-osed approach is demonstratively applied to the AZ31 magnesiumlloy at elevated temperatures. Since the biaxial bulge test for sheetetal has not been standardized yet, the biaxial bulge test has its

wn specific field of application due to biaxial tension strain paths.In this study, it is attempted to propose a novel approach to

tudy the formability of tube hydroforming under biaxial stretchingrom the biaxial bulge test for sheet metal. The principle is describednd an analytical model is developed for the elliptical bulging ofube hydroforming. An experimental setup is designed with fivepper elliptical die inserts and one lower die insert used to pro-uce ellipsoidal bulged domes with different biaxial strain ratios.hen some experiments are performed. The linear strain paths inifferent strain states are verified and the right hand side of FLCor seamed tube is determined. Finally, a comparison between theheoretical results and experimental data is performed. Good corre-ation is observed between the theoretical results and experimentalata.

. Analysis for tube elliptical bulging

.1. Principle description

In order to observe the material deformation behaviors of theimplest tube free bulge hydroforming, FEM simulation is per-ormed with both tube ends fixed. The simulation results for thetrain ratio of the node with the lowest thickness value at theop of the bulge are shown in Fig. 1. In order to achieve theension–tension strain states, the free expansion length is relativelyhort.

The simulation results show that the materials are difficult to betrained under tension states in longitudinal direction. The plasticeformation is primarily under plane strain state at the initial stage.

o in order to study the formability of tube hydroforming underiaxial stretching, an approach must be proposed to improve theeformation in longitudinal direction under tension–tension straintates.

Fig. 2. Principle diagram for tube hydrofroming under biaxial stretching.

In sheet metal bulge test, different elliptical aspect ratios insertsare used to produce ellipsoidal bulged domes with different strainratios. These geometrical aspect ratios represent the ratios betweenthe minor and major axes of the elliptical die inserts, and do notnecessarily equal the biaxial strain ratio at the apex of the bulgedellipsoidal dome.

So in tube hydroforming, different elliptical aspect ratios(� = L2/L1) die cavities are used for different biaxial strain ratios( ̌ = ε2/ε1). In tube elliptical bulging, both ends of tube are fixed.And as shown in Fig. 2 L1 is the major axis in circumferential direc-tion and L2 is the minor axis in longitudinal direction. The decreaseof L2 is benefit for the deformation in longitudinal direction undertension–tension strain states. The upper die faces are designed withdrawbead and without drawbead. The use of the drawbead is tocontrol the material flow along larger biaxial strain ratios with thesame elliptical aspect ratio.

In order to verify the principle for tube hydroforming underbiaxial stretching, FEM simulation is used before the experimen-tal setup manufactured. The test seamed tube with 58 mm outsidediameter, 2.5 mm wall thickness and 210 mm long, is produced byroll forming and welding the QSTE340 sheet metal. Micro-hardnessprofile (Chen et al., 2011) indicates that a seamed tube is composedof weld metal, heat affected zone (HAZ) and base metal, and theweld metal and HAZ width is approximately 4 and 6 mm. The stress-strain relations for three parts of seamed tube are fitted to the flowcurve as �̄ = K(ε0 + ε̄)n. Material properties for each part are listedin Table 1.

The FEM model of tube hydroforming is set up in FEM programLS-DYNA, which is composed of a rigid upper die, a rigid lowerdie and a deformable seamed tube. The deformable seamed tube is

modeled using the 4-noded Belytschko–Tsay shell elements with7 integration points through the shell thickness, and the MAT 036-model of LS-DYNA “Mat 3-Parameter Barlat” is used. The contact

1918 S. Li et al. / Journal of Materials Processing Technology 212 (2012) 1916– 1924

Table 1Material properties of three parts of seamed tube.

Material Strengthcoefficient K(MPa)

Hardeningexponent (n)

Initialequivalentstrain (ε0)

Anisotropycoefficient (R)

Base metal 680 0.145 0.040 1.17HAZ metal 699 0.126 0.023 1.00

idia

alc

FsFm

Weld metal 721 0.091 0.011 1.00

nteraction is modeled using Coulomb’s law: friction coefficient forie-tube and die-punch are both 0.05. The FEM model is shown

n Fig. 3. Fig. 4 shows the simulation results for different ellipticalspect ratios � die cavities under different biaxial strain ratios ˇ.

From the simulation results, different biaxial strain states can bechieved through different elliptical aspect ratios die cavities. Theinear strain paths for establishing the FLC under biaxial stretchingan be obtained through the elliptical bulging.

In order to observe the influence of pressure, experiments andEM simulations for two types of loading paths with different pres-

ures are performed. The two loading paths are shown in Fig. 5 andig. 6 shows the hydroformed parts for the two loading paths. Theeasured strains are basically the same.

Fig. 4. Simulation results under dif

Fig. 3. FEM model under biaxial stretching.

Fig. 7 shows the strain paths for the two different loading paths.The results show that the biaxial strain paths are only related tothe elliptical aspect ratios. The effect of the pressure on the forminglimit strain and strain ratios is not obvious. So the FLC is less sen-sitive to the forming parameters. Compared with the free bulgingand our prior research, our current approach has the advantage

of control of material flow using the mold surface accurately andprecisely.

ferent biaxial strain ratios ˇ.

S. Li et al. / Journal of Materials Processing T

Fig. 5. Two loading paths with different pressures.

Fig. 6. Hydroformed parts for the two loading paths.

Fig. 7. Strain paths for the two different loading paths.

echnology 212 (2012) 1916– 1924 1919

2.2. Equilibrium analysis

Consider a tube with both ends fixed which is subjected to inter-nal pressure Pi in Fig. 8. For an element at the pole of this tube, thefollowing equilibrium equation can be written:

Pi = ti

(�1

�1+ �2

�2

)(1)

where Pi is the instantaneous internal pressure, ti is the instanta-neous tube wall thickness, �1 and �2 are stress components in thecircumferential and the longitudinal directions, and �1 and �2 arethe instantaneous circumferential and the longitudinal radii.

Assume now that the expansion occurs in the profile shown inFig. 9. During free forming, tube free bulging area can be approxi-mated as elliptic profile (Hwang and Lin, 2006). During the ellipticalbulging, tube bulging area also can be approximated as ellipticprofile. Therefore, elliptic functions can be used to describe the lon-gitudinal and circumferential profiles of bulging area. Fig. 9 showsthe instantaneous geometry of tube elliptical bulge. In Fig. 9, a0and b0 are the lengths of major and minor axes of the elliptical die,rd is the die profile radius, and �1 and �2 are the instantaneouscircumferential and the longitudinal radii.

In the longitudinal elliptical cross-section, the elliptic functioncan be denoted as

z2

�21

+ x2

b2= 1 (2)

where �2 and b is the lengths of major and minor axes of the lon-gitudinal elliptical cross-section.

Considering the point of contact with the die fillet: (�0, rd + b0)is on the longitudinal elliptical arc, one obtains

b = (rd + b0)�1

(�21 − �2

0)1/2

(3)

In the circumferential elliptical cross-section, the elliptic func-tion can be denoted as

z2

�21

+ y2

a2= 1 (4)

where �1 and a is the lengths of major and minor axes of the cir-cumferential elliptical cross-section.

Considering the point of contact with the die fillet: (0, �0) is onthe circumferential elliptical arc, one obtains

a = �0 (5)

And

�1 = �0

[�

2(eε1 − 1) + 1

](6)

ti = t0eε3 (7)

where ε1 and ε3 are strain components in the circumferential andthe radial directions, �0 is the initial tube radius, and t0 is the initialtube wall thickness.

And

�2 =(

b

a

)2

�1 = (rd + b0)2�31

(�21 − �2

0)�20

(8)

Substituting Eqs. (6)–(7) and (8) into Eq. (1) leads to

Pi = t0eε3

�0[

�2 (eε1 − 1) + 1

] ·[

�1 +�2

(�2

1 − �20

)(rd + b0)2[�

2 (eε1 − 1) + 1]2

](9)

1920 S. Li et al. / Journal of Materials Processing Technology 212 (2012) 1916– 1924

Fig. 8. The stresses acting on an ele

Fig. 9. Geometrical description of the elliptical bulging.

2

cSigrsiit

f

wi

l

P

Fig. 10. Schematic of the M–K model on prediction of FLC.

.3. Analytical model

To develop a model for the right hand side of FLC, the soalled Marciniak–Kuczynski (M–K) model is modified and applied.chematic of the M–K model is shown in Fig. 10. In this model, its assumed that there is an initial imperfection or a local hetero-eneity on material surface which generates a weak region. Thisegion is interpreted as a long groove perpendicular to the highertress direction (see Fig. 10). The indexes a and b are used to des-gnate the groove in the outer and inner regions, respectively. Thenitial imperfection factor of the groove f0 is defined as the materialhickness ratio

0 = tb0

ta0(10)

here ta0 and tb0 are the groove’s initial thickness at outer andnner regions.

During the entire tube elliptical bulging process, the force equi-ibrium equation can be written as follows:

a = Pb (11)

ment at the pole of the tube.

where Pa and Pb are the internal pressures of a and b regions.The compatibility requirement assumes that the minor strain

increment is equal in both regions as follows:

dε2a = dε2b (12)

From Eq. (9), the internal pressures of a and b regions can bewritten as follows:

Pa = ta0eε3a

�a0

[�

2(eε1a − 1) + 1

] ·

[�1a +

�2a

(�2

1a− �2

a0

)(rd + b0)2

[�

2(eε1a − 1) + 1

]2

]

Pb = tb0eε3b

�b0

[�

2(eε1b − 1) + 1

] ·

[�1b +

�2b

(�2

1b− �2

b0

)(rd + b0)2

[�

2(eε1b − 1) + 1

]2

] (13)

where �a0 and �b0 are the initial tube radius of a and b regions,�1a and �1b are the instantaneous circumferential radius of a andb regions, ε3a and ε3b are radial strains of a and b regions, ε1a andε1b are circumferential strains of a and b regions, �1a and �1b arecircumferential stresses of a and b regions, and �2a and �2b arelongitudinal stresses of a and b regions.

Substituting Eq. (13) into Eq. (11) leads to

ta0eε3a

�a0[

�2 (eε1a − 1) + 1

] ·[

�1a +�2a

(�2

1a − �2a0

)(rd + b0)2[�

2 (eε1a − 1) + 1]2

]

= tb0eε3b

�b0

[�2 (eε1b − 1) + 1

] ·[

�1b +�2b

(�2

1b− �2

b0

)(rd + b0)2[�

2 (eε1b − 1) + 1]2

](14)

Assume that the tube material obeys the Swift’s hardening law:

�̄ = K(ε0 + ε̄)n (15)

where K is the strength coefficient, �̄ is the equivalent stress, ε0 isthe initial equivalent strain, ε̄ is the equivalent strain and n is thestrain hardening exponent.

Then the equivalent stresses of a and b regions can be writtenas follows:

�̄a = Ka(εa0 + ε̄a)na

�̄b = Kb(εb0 + ε̄b)nb(16)

where Ka and Kb are the strength coefficients of a and b regions, �̄a

and �̄b are the equivalent stresses of a and b regions, εa0 and εb0 arethe initial equivalent strains of a and b regions, ε̄a and ε̄b are theequivalent strains of a and b regions, and na and nb are the strainhardening exponents of a and b regions.

Defining ϕ and ̨ as the ratio between the equivalent stress and

the major stress and between the minor and major stresses.

ϕ = �̄

�1, ̨ = �2

�1(17)

S. Li et al. / Journal of Materials Processing Technology 212 (2012) 1916– 1924 1921

wtb

ˇ

rns

|wa

ϕ

ˇ

te

3

iJ

Fig. 12. Elliptical bulging test setup.

Fig. 11. Hydroforming machine.

Combining Eqs. (14) and (16)–(17), one can write

Ka · eε3a (εa0 + ε̄a)na

�a0[

�2 (eε1a − 1) + 1

]· 1ϕa

·[

1 +˛a

(�2

1a − �2a0

)(rd + b0)2[�

2 (eε1a − 1) + 1]2

]

= f0Kbeε3b (εb0 + ε̄b)nb

�b0

[�2 (eε1b − 1) + 1

]· 1ϕb

·[

1 +˛b

(�2

1b− �2

b0

)(rd + b0)2[�

2 (eε1b − 1) + 1]2

](18)

here ϕa and ϕb are the ratios between the equivalent stress andhe major stress of a and b regions, and ˛a and ˛b are the ratiosetween the minor and major stresses of a and b regions.

Defining ̌ as the strain increment ratio

= ε2

ε1(19)

Graf and Hosford (1990) proposed that the Hosford yield crite-ion is an appropriate yield criterion for predicting the localizedecking in conjunction with the M–K method under in-planetretching. And they also suggested the value of m = 6 for BCC metal.

So the Hosford yield criterion can be written as,

�1|m + |�2|m + R|�1 − �2|m = (R + 1) �̄m (20)

here m is the stress exponent of crystal structure and R is thenisotropy coefficient.

Combining Eqs. (17) and (20), one can write

=[

1 + ˛m + R(1 − ˛)m

R + 1

]1/m

(21)

The flow rule leads to

= ˛(m−1) − R(1 − ˛)m−1

1 + R(1 − ˛)(m−1)(22)

Finally, one can predict the right hand side of FLC for tube ellip-ical bulging under biaxial stretching by solving the non-linearquation math problems of Eq. (18).

. Experimental investigation

In this study, all experiments are performed on the hydroform-ng machine designed in Auto Body Technology Center of Shanghaiiaotong University, as shown in Fig. 11. The maximum allowable

Fig. 13. Schematic for elliptical bulging test.

working pressure of the machine is 200 MPa and the maximumallowable axial force is 1000 kN.

3.1. Experimental setup and procedure

An experimental setup based on the concept of tube ellipticalbulging is manufactured to implement the tube bulge test, shownin Fig. 12. It is composed of an upper die, a lower die, two axialpunches, one lower die insert and five elliptical upper die inserts.During tube elliptical bulging, the tube with both ends fixed issubject to an internal pressure Pi. Fig. 13 shows the simplifiedschematic of experimental tooling.

The experimental procedure includes four steps: (i) the tubesare made-up for experiments. The tubes are cut into 210 mm long.Additionally, circular grids with a diameter of 2.5 mm are etchedon the tube surface before the experiments; (ii) the tube is placedinto the die, the dies are clamped and the punches are pushed forsealing; (iii) axial compressive force is assigned with the corre-sponding internal pressure under different linear strain paths tothe tube until the tube has burst; (iv) the etched grids on the tubesurface closely at the fracture location are chosen to measure. Themeasured engineering major and minor strains are transformed tothe true major and minor strains. These true strains are plotted onthe ε1 − ε2 Cartesian plane and labeled accordingly. Then the righthand side of FLC is determined.

3.2. Verification of the linear strain paths

In order to verify the material flow along biaxial stretching lin-ear strain paths through the experimental setup, experiments at

1922 S. Li et al. / Journal of Materials Processing Technology 212 (2012) 1916– 1924

Fig. 14. Hydroformed parts for seamed tube with weld zone attached to die.

Fz

dTzweTs

tpTlatd

4

4

nFa

tt

to deform. Due to the constraints of the weld zone, base zone nearthe weld zone shows “abnormal” deformation behavior in a seamedtube hydroforming (Chen et al., 2011). So the location of weld zoneaffects the formability of seamed tube. Bursting for seamed tube is

ig. 15. Hydroformed parts for seamed tube with weld zone located to the bulgeone.

ifferent pressure levels are performed for QSTE340 seamed tube.he selected elliptical aspect ratio � is 0.8 with drawbead. The weldone of seamed tube is located at two different limit positions,hich is attached to die and located to the bulge zone. During

xperiments, different levels of internal pressure are scheduled.he hydroformed parts at different internal pressure levels arehown in Fig. 14 and Fig. 15.

A three dimensional image processing system is used to measurehe major strains and minor strains of the deformed grids at theole of the forming tube surface closely at the fracture location.he strain paths will be plotted on the e1 − e2 Cartesian plane andabeled accordingly. As shown in Fig. 16 and Fig. 17, the strain ratiosre kept as a constant value. The linearity of the strain paths showshat different elliptical aspect ratios die cavities can be used forifferent biaxial linear strain paths for tube hydroforming.

. Results and discussions

.1. Experimental results

The hydroformed products after the elliptical bulging with inter-al pressure for different strain ratios are shown in Fig. 18 andig. 19 for the test seamed tube with weld zone attached to diend weld zone located to the bulge zone.

The major strains and minor strains of the deformed grids athe pole of the forming tube surface closely at the fracture loca-ion are measured. And the values of the true strain (ε2, ε1) are

Fig. 16. Validation of the linearity of the strain path for seamed tube with weld zoneattached to die.

transformed from (e2, e1) and used to construct the experimentalpoints in Fig. 20.

4.2. Forming limit prediction

From a macroscopic point of view, a seamed tube is composedof weld zone (including weld metal and HAZ metal) and base zone.The plasticity and toughness of weld zone is poor, and it is difficult

Fig. 17. Validation of the linearity of the strain path for seamed tube with weld zonelocated to the bulge zone.

S. Li et al. / Journal of Materials Processing Technology 212 (2012) 1916– 1924 1923

Fig. 18. Hydroformed parts for seamed tube with weld zone attached to die.

Fig. 19. Hydroformed parts for seamed tube with weld zone located to the bulgezone.

dltl

iTizi

Table 2Material properties of the base zone and weld zone.

Material Strengthcoefficient K(MPa)

Hardeningexponent (n)

Initialequivalentstrain (ε0)

Anisotropycoefficient (R)

Fig. 20. Theoretical FLC of a seamed tube and experimental data.

ifferent under biaxial stretching bulge test when the weld zone isocated at different positions. In this study, the weld zone of seamedube is located at two different limit positions for upper and lowerimit strains, which is attached to die and located to the bulge zone.

When the weld zone is attached to die, the model has an initialmperfection on material surface which generates a weak region.

he material properties of a and b regions are the same. And thenitial imperfection factor of the groove f0 is 0.986. When the weldone is located to the bulge zone, the model has a local heterogene-ty on material surface which generates a weak region. The initial

Base zone 680 0.145 0.040 1.17Weld zone 695 0.123 0.021 1.00

imperfection factor of the groove f0 is equal to 1. And the materialproperties of a and b regions are different. The indexes a and b areused to designate the weld zone and base zone. Material propertiesfor each zone material are listed in Table 2.

Then one can predict the right hand side of FLC for tube ellipticalbulging under biaxial stretching by solving the non-linear equationmath problems of Eq. (18). The principle is as follows:

At a biaxial stress state, a strain increment dε1a is set, and thenthe strain increment dε1b can be obtained from the force equi-librium equation. If the ratio of dε1b/dε1a is less than f (where fis the constant of failure criterion), then the tube does not reachthe bursting state and the program goes through to the next strainincrement dε1a. The calculation is iterated until the constant of fail-ure criterion f = 10 is reached. Then the limit strain of a seamed tubein bursting state is obtained. Repeat all steps for different biaxialstress states and the right hand side of FLC for tube elliptical bulgingunder biaxial stretching is constructed in Fig. 20.

4.3. Comparison of FLC

In Fig. 20, the solid thick curve “1” indicates the upper forminglimit for seamed tube. The lower forming limit is determined as thesolid thick curve “2”. The forming limit values for seamed tube withweld zone attached to die are much larger than those for seamedtube with weld zone located to the bulge zone. This is because theplasticity and toughness of weld zone for seamed tube is poor, andit is difficult to deform. Due to the constraint of the weld zone in aseamed tube hydroforming, the forming limit strains of base metalnear HAZ are much smaller than those without the constraint.

Fig. 20 also shows a comparison between the theoretical FLC andexperimental data for QSTE340 seamed tube. The theoretical FLCmatches well with the experimental data. The reasonable correla-tion shows that the theoretical model can reflect the forming limitbehavior of a seamed tube. The FLC for a seamed tube hydroformingcan be obtained based on the theoretical model.

5. Conclusions

A new theoretical model is developed for the elliptical bulgingfor tube hydroforming. The model uses the M–K theory and theclassical Hosford yield criterion, which helps to predict the FLC fortube hydroforming. It is demonstrated that the theoretical model isfeasible and effective for the elliptical bulging of tube hydroform-ing. The predicted FLC matches well with the experimental data,which demonstrates the accuracy and validity of the theoreticalmodel.

A novel experimental approach is proposed to evaluate theformability for tube hydroforming under biaxial stretching. Thenthe novel experimental tool set is designed, which can be usedto control the material flow under tension–tension strain statesthrough five elliptical upper die inserts with different ellipticalaspect ratios. Some experiments are performed for the right handside of FLC of QSTE340 seamed tube hydroforming. The experimen-

tal approach is simple and appropriate for industrial use. The FLCobtained through the approach is accurate by the precise controlof material flow using the mold surface and is less sensitive to the

1 sing T

ft

A

NB

R

A

A

A

A

C

C

924 S. Li et al. / Journal of Materials Proces

orming parameters. Using the novel tool set, engineers can obtainhe right hand side of FLC for tube hydroforming.

cknowledgments

The authors gratefully acknowledge the financial support ofational Natural Science Foundation of China (No. 51075267) andaosteel Group for the supply of test materials.

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