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Int. J. Mechatronics and Manufacturing Systems, Vol.

Copyright 2011 Inderscience Enterprises Ltd.

Experimental and numerical study ofhydroforming aptitudes of Welded Tubes

M. Ayadi and M.A. Rezgui*

LMSSDT-ESSTT,

5 Av Taha Hussein,

Montfleury 1008 Tunis, Tunisia

E-mail: [email protected]


*Corresponding author

A. Cherouat

UTT-Projet GAMMA INRIA,

Domaine de Voluceau-Rocquencourt,

B.P. 105, 78153 Le Chesnay, France


N. Mezghani

LMSSDT-ESSTT,

5 Av Taha Hussein,

Montfleury 1008 Tunis, TunisiaE-mail: [email protected]

Abstract: This paper presents an experimental/numerical methodology,to improve 3D Welded Tube (WT) behaviour by hydroforming process.This process, used for manufacturing complex structures, allows improving theweight saving and quality of finished parts. The experimental study is dedicatedto the identification of stressstrain flow of the Base Metal (BM) and theHeat-Affected Zone (HAZ) from the global measure and nanoindentation testof hydroformed tube state. Workpiece behaviours models show the combinedeffects of the inhomogeneous behaviour of BM and HAZ, and the geometricalsingularities found in the WT. From the simulations carried out, it is clear theinfluence of the plastic flow behaviour of the WT final state.

Keywords: hydroforming; WT; welded tube; anisotropic plastic flow;

nanoindentation; numerical simulation; experimental study; manufacturing,mechanical behaviour; ductile damage; HAZ; heat-affected zone.

Reference to this paper should be made as follows: Ayadi, M., Rezgui, M.A.,Cherouat, A. and Mezghani, N. (2011) Experimental and numerical studyof hydroforming aptitudes of Welded Tubes, Int. J. Mechatronics and Manufacturing Systems, Vol.


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Experimental and numerical study of hydroforming aptitudes 75

Biographical notes: Mahfoudh Ayadi received his PhD Thesis in Applied

Mechanics from Facult des Sciences Universit de Bordeau I, France, in1986. He is an Associate Professor of Mechanical Engineering atEcole Suprieure des Sciences et Techniques de Tunis (ESSTT), Tunisia.His research area includes hydroforming process and friction stir welding.He is a Researcher in Laboratoire de Mcanique des solides et des Structureset du Dveloppement Technologique (LMSSDT), Tunisia.

Mohamed Ali Rezgui received his PhD Thesis in Mechanical Engineeringfrom Ecole Centrale de Lyon (ECL), France, in 1994. He was a temporaryattached of teaching and research at ECL, in 1994. Currently, he is anAssistant Professor of Mechanical Engineering at Ecole Suprieure desSciences et Techniques de Tunis (ESSTT), Tunisia. He joined theLaboratoire de Mcanique des solides et des Structures et du DveloppementTechnologique (LMSSDT), Tunisia, in 2006. His research areaincludes forming process, friction stir welding and material behaviour

(composite, steel, etc.).

Abel Cherouat received his PhD Thesis in Mechanical Engineering Sciencefrom Franche Comte University, France, in 1994. In 1995, he was aPostdoctoral Associate in the Department of Mechanical Engineering at HighSchool of Engineering ENSAM Paris. He joined the Laboratory of MechanicalSystems and Concurrent Engineering CNRS of University of Technology ofTroyes (UTT) France in 1997. Currently, he is a Professor at the MechanicalDepartment in the University of Technology of Troyes. His main researchinterests are the numerical simulation and method, non-linear mechanicalstructure, material behaviour (composite, foam, steel, etc.), and adaptiveremeshing procedure in forming process and industrial systems.

Najeh Mezghani received her PhD Thesis in Mechanical Engineeringfrom Ecole Nationale des Arts et Mtiers de Paris (ENSAM), France.

She is an Associate Professor in Institut National des Sciences Appliquesde Tunis (INSAT), Tunisia. She is a Researcher in Laboratoire de Mcaniquedes solides et des Structures et du Dveloppement Technologique (LMSSDT),Tunisia.

1 Introduction

Owing to the increasing demands for the manufacturing of complex and lightweight parts

in various fields, the welded tubes (WTs) hydroforming process, considered

as an alternative to stamping for obtaining the hollow tubular structures, occupies

an increasingly significant place in automotive aircraft and aerospace industries(Dohmann and Hertl, 1997; Jae-Bong et al., 2001; Shin et al., 2002). However,

the effective use of the hydroforming technology in the manufacturing industry has

triggered new challenges in terms of the technological parameters specified for the

forming process and particularly the material properties of the WT (Natal Jorge et al.,

2007; Liu et al., 2007). The latest studies are devoted to the mechanical and numerical

modelling of the hydroforming processes using the Finite Element Analysis (FEA)

(Abrantes et al., 2005; Lang et al., 2004; Ayadi et al., 2008; Liu et al., 2007; Mezghani

et al., 2009), allowing the material flow prediction and hydroforming parameters

optimisation (Imaninejad et al., 2004b; Ray and Mac Donald, 2004; Neffussi and


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76 M. Ayadi et al.

Combescure, 2002; Johnson et al., 2004; Yuan et al., 2006; Ko, 2003; Fann and Hsiao,

2003; Manabe et al., 2006; Hama et al., 2006).In addition, the accuracy of the numerical prediction remains linked to the fidelity

models representing the WT behaviour and particularly the BM and the welded joint

(WJ) zone mechanical properties (plasticity metal flow, anisotropy effect and damage

initiation and growth) (Natal Jorge et al., 2007; Cherouat et al., 2002). The welded

structures characteristics comes from the significant transformations (shaping,

calibration, bending, rolling, welding ) undergone by the tube throughout its

production cycle. All these operations induce complex evolutions of hardening flow and

material anisotropy; those are amplified by the presence of the WJ along the tube. This

material imperfection is characterised by an HAZ singular by its geometry and properties.

This fact shows that oriented tensile tests are not adapted to identify the total behaviour

of the tubes with regard to the loading paths generated by the hydroforming process

(Imaninejad et al., 2004a; Bortot et al., 2008).This paper presents a computational-based numerical and experimental methodology

to adequately study and simulate the WT formability. The experimental study is

dedicated to the identification of material properties (in BM and HAZ) from the global

measure of thickness evolution, radial displacement and tube expansion. In the numerical

simulation, two types of behaviour (homogeneous and inhomogeneous) are proposed to

model the WT behaviour. In the homogeneous case, free expansion tests are carried out

on fixed ends tubular test-tubes subjected to an internal pressure, are exploited to

determine the hardening model of BM and HAZ as well as the geometrical singularities

found in the WT. In the inhomogeneous case, the BM part and the HAZ are characterised

by different plastic strain flows. The BM zone is modelled using isotropic elastoplastic

behaviour (Swift model) whereas the HAZ is modelled by analysing indentation

load-depth curves to evaluate stressstrain flow. Applications are made to the simulation

of the WT hydroforming to show the efficiency of the proposed methodology.

The confrontation between the numerical (estimates for the two approaches)

and experimental results has proved to be of great tool to the improvement and

optimisation of WT formability.

2 Experimental procedure

The swelling tests carried out until bursting showed that all the fissures are initiated

on the central area of the expanding zone not far from the weld zone (see Figure 2).

The defect pressure recorded is ranged between 30.5 MPa and 32 MPa. This failure of

WT can be attributed to diverse causes. This work is specifically focused on the study of

geometrical singularities found in the WJ

the inhomogeneous behaviour of the BM and the HAZ of the tube formability.

The weld tubes made of stainless steel (AISI 304) have 250 mm initial length,

48 mm inner diameter and 49.2 mm outer diameter (1.2 mm initial thickness).

The controlled process parameters are the axial load of the two ends of the tube fixed

and the internal fluid pressure is applied as a uniformly distributed load to the tube inner

surface and is introduced as a linearly increasing function of time. Comparator is used

to measure the external diameter of tubular parts in the middle of their length.


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Seventeen samples have been tested until the bursting step. For each of the tested tubes,

the bulge height, the radius of curvature along the longitudinal direction and the wallthickness were measured. The schematic configuration of the free expansion test is

shown in Figure 1.

Figure 1 Configuration of swelling device (see online version for colours)

Five representative experiments were made during hydroforming tests. The bursting

pressures recorded are ranged between 30.5 MPa and 32 MPa so that the weld properties

may have a significant effect on the deformation and the formability of the tube blank

(see Figure 2).

Figure 2 Tube ductile rupture from experiments (see online version for colours)

The ultrasonic technique is very useful for non-destructive measurement of the

mechanical properties of materials. It based an ultrasonic source to measure the

wall thickness variation by transmission of wave mechanics in the material through a

piezoelectric transducer. The transducer is placed on each point of the grid tube and the

values are directly displayed on the screen of the device and stored with an accuracy

of a 1000 (0.001 mm). The schematic representation of measuring method is shown in

Figure 3. The measurements obtained to estimate the tube thinning along the middle

contour and the axis line can be seen in Figure 4. On the tube contour, nine measures


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78 M. Ayadi et al.

of the thinning are made using ultrasound, and fluctuation around an average value of

about 0.855 is deduced.

Figure 3 Ultrasonic measurement set-up (see online version for colours)

Figure 4 Thinning along the middle contour and the weld tube axis: (a) Tube middle contourand (b) Weld tube axis

(a) (b)

In recent years, indentation techniques have been used extensively to determine directly

the material hardness or, indirectly, the bulk mechanical properties when other methods

have proven to be unsuitable. In particular, as indentation techniques have improved,

nanoindentation has become the most popular method for studying the mechanical

properties of thin films, joints and coatings.

Compared with the BM, the volumic fraction of the HAZ or the WJ is relativelyweak; consequently, the contribution of the WJ would be unperceivable with radial

displacement measurements on test-tubes (global approach). Thus, it is essential to use

not classic techniques to characterise the local material properties. This justifies

nanoindentation tests exploitation to determine the local behaviour of the weld tube.

In this study, the nanoindentation with a pyramidal BERKOVICH indenter has been used

as an effective tool to characterise the mechanical properties of WJ and HAZ.


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The geometrical singularities introduced by the WJ are revealed by scanning optical

electronic microscope on the cross-section of the wall. This geometrical defect modifiesthe wall thickness as observed on the notch profile on the tube internal wall as shown in

Figure 5. The measured dimensions of this notch indicate an average depth of about

0.115 mm and a width varying between 3.0 mm and 4.2 mm.

Figure 5 Optical image of the cross section and indents location of WT (see online versionfor colours)

Results obtained from 20 indents on the HAZ (Figure 6) show that the relative variations

recorded between the representative points A, B and C do not exceed 15%. It allows

admitting that mechanical properties of the HAZ are homogeneous on few micronsdepths.

Figure 6 Depth-indentation force graphs of representative indents A, B and C (see online versionfor colours)


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3 Numerical modelling

3.1 Mechanical characteristic of welded tube behaviour

Taking into account the ratio thickness/diameter of tube, the radial stress is considerably

small compared with the circumferential and longitudinal stresses z. In addition,the principal axes of the stress tensor and the orthotropic axes are considered coaxial

(see Figure 7). The transverse anisotropy assumption represented through the yield

criterion proposed by Hill (1950) can be written as:

2 2 2 2( )z zF G H = + + (1)

with (F, G,H) are the parameters characterising the current state of anisotropy.

Figure 7 Stress state at bulge tip

If the circumferential direction is taken as a material reference, the anisotropy effect

can be characterised by a single coefficient R (Fann and Hsiao, 2003) and equation (1)

becomes:

22 2 21 ( ) .1

z zRR

= + + +

(2)

The assumptions of normality and consistency lead to the following equations:

dd

1

dd

1

z

z z

R

R

R

R

=

+

= +

(3)

where is the effective plastic strain and ( , )z are the strains in the circumferentialand the axial directions. The effective strain for anisotropic material can be derived from

equivalent plastic work definition, incompressibility condition and the normality

condition:


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2 2 2 21 2 1d d d (d d ) 1 d11 2 1 2

z z

R R RR RR R

+ += + + = + + ++ +

dwith .

d

z

=

(4)

Taking into account the relations expressing strain tensor increments, the equivalent

stress of equation (2) becomes:

2 2 1 21 .1 1

R R

R R R

+

= + + + + + (5)

In the studied case, the tube ends are fixed. As a consequence, the longitudinal increment

strain d 0,z = and then relations (4) and (5) become:

2

3

2 3 1 1d d .

(1 ) 1 2

R R R

R R

+ + + = = + +

(6)

The knowledge of the two unknown strain and stress needs the establishmentof the final geometrical data linked to the tube (diameter and wall thickness):

0

lnd

d

=

and

2

Pd

t = (7)

wherePis the internal pressure, (d, d0) are the respective average values of the current

and initial sample diameter and tis the current wall thickness obtained according to thefollowing relation:

(1 )

0e .t t += (8)

Finally, the material characteristics of the tube (BM) are expressed by the effective stress

and effective strain according to the following equation (Swift model):

0( ) .nK = + (9)

The values of the strength coefficientK, the strain hardening exponent n, the initial strain

0 and the anisotropic coefficient R in equations (2) and (9) are identified numerically.

For the determination of the stressstrain relationship using bulge test, the radial

displacement, the internal pressure and the thickness at the tube centre are required.

A three-dimensional FEA has been performed using the finite element code Abaqusto investigate the WJ geometrical singularities effect and the inhomogeneous behaviour

of the BM and the HAZ on the tube formability. The model uses tri-linear hexahedral

eight-node elements in modelling the initial tube. Special fine mesh is used in the weld

zone area. For validation, comparisons between numerical and experimental results

are done. They concern the hardening laws (homogeneous and inhomogeneous),

the anisotropy effect, the wall thickness and the thickness variation along length and

middle circumference of bulged part.


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3.1.1 Homogeneous behaviour with geometrical singularities

In this case, the BM with geometrical singularities found in the WT is supposed

orthotropic transverse, whereas its behaviour is represented by Swift model. The optical

microscope observation on the cross section of the wall is used to build the geometrical

profile of the notch generated by the welded junction (see Figure 8). By considering

the assumptions relating to an isotropic thin shell (R = 1) with a uniform thickness,

the previously established relations (6), (7) and (9) allow to build the first experimental

hardening model using measurements of internal pressure/radial displacements.

This model is then proposed, as initial solution, to solve the inverse problem of required

hardening law that minimises the following objective function:

2

exp num

1 exp

1 p

p

i im

F i

i

F F

m F

=

=

(10)

where expi

is the experimental value of the thrust force corresponding to ith

nanoindentation depthHi, numi

F is the corresponding simulated thrust force and mp is the

total number of experimental points.

Figure 8 Profile of the geometrical singularities of the Heat-Affected Zone (see online versionfor colours)

Table 1 Swift parameters of different hardening evolution

Hardening model K(MPa) N

Initial 0.025 1124.6 0.2941

Intermediate 0.055 692.30 0.2101

Optimal 0.080 742.50 0.2359

Different flow stress evolutions of isotropic hardening (initial, intermediate and optimal)

are proposed to estimate the best behaviour of the BM with geometrical singularities

found in the WT. Figures 9 and 10 show the effective stress vs. plastic strain curves


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and the associated pressure/radial displacement for these three cases. As it can be seen,

there is a good correlation between the optimal evolution of Swift hardening and theexperimental results. Table 1 summarises the parameters of these models.

Figure 9 Stressstrain evolutions for different hardening laws (see online version for colours)

Figure 10 Internal pressure vs. radial displacement (see online version for colours)

The anisotropy factor R is determined only for the optimal hardening evolution.

In the problem to be solved, there is only one parameter, which initial solution exists,

that it corresponds to the case of isotropic material (R = 1). The numerical iterations

were performed on the WT with non-uniformity of the thickness (see Figure 8), and the

obtained results are shown in Figure 11. A good improvement in the quality of predicted

results is noted ifR corresponds to the value of 0.976.


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Figure 11 Radial displacement for different values of anisotropy coefficientR (see online version

for colours)

3.1.2 Inhomogeneous behaviour

In this case, the WT behaviour is based on the behaviour of the BM and the HAZ.

The BM with geometrical singularities behaviour is represented by optimal law

hardening withR = 0.976. The plastic flow behaviour (stress/strain) of the WJs and the

HAZ is identified numerically using Abaqus solver from global results (force/depth) of

nanoindentation tests (see Figure 12). The pyramid indenter is supposed as rigid body and

the interaction between material and indenter is characterised by a sliding friction with

a coefficient equal to 0.15. Figure 13 shows the effective stress distribution and indenter

print morphology, respectively, at the end of the penetration sequence and after

total removal of the indenter. The identified hardening coefficients are introduced by

Swift model. The predict results (force/indentation depth) obtained with iterativecomputational inverse method using equation (10) are given in Figure 14 in comparison

with the experimental values. For the characterisation of the welded tube properties with

inhomogeneous behaviour, two stages are proposed. In the first stage, the obtained

hardening coefficients (strength coefficient K, strain hardening exponent n and initial

strain 0) of BM and HAZ are used as an initial comparison, the successive iterations led

to identify the new values of the hardening by minimisation of the error between

numerical and experimental measurements of tube displacements using the least mean

square methods. Table 2 summarises the material properties of HAZ and BM.

Figure 12 Nanoindentation model set-up (see online version for colours)


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Figure 13 3D simulation of the indentation: (a) end of stage and (b) after indenter remove

(see online version for colours)

(a) (b)

Figure 14 Force vs. indenter depth comparison between experimental and numerical simulation(see online version for colours)

Table 2 Identified hardening parameters of BM and HAZ

Homogeneous Inhomogeneous BM Inhomogeneous HAZ

K[MPa] 928.4 845.5 1345

0 0.025 0.13 0.015

Swift modelcoefficients

N 0.284 0.331 0.265

3.2 Metal forming with anisotropic behaviour3.2.1 Localisation of the bursting zones

The comparison between the experimental results and the numerical prediction, using the

identified model (Table 1), emphasised the WJ geometrical singularities effect as well as

the mechanical characteristics of the HAZ on the WT formability. Indeed, it seems that

the geometrical singularities of the WJ are not the single indicator, which locates the

bursting zones. Figure 15 shows, for the same profile of geometrical singularities, the

effects of the inhomogeneous mechanical properties of BM and HAZ, on the initiation

and growth of ductile rupture. Initially, the sample is inflated so that the test section


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remained uniform. However, eventually it developed an axisymmetric bulge followed

by localised thinning along a generator of tube in the WJ that led to ductile rupture.

Figure 15 Effective stress in BM and HAZ: (a) homogeneous and (b) inhomogeneous(see online version for colours)

Figure 16 illustrates the effective stress profile (forR = 0.965 and R = 1.035) on the

internal half contour in the symmetry plane z= 0 of homogeneous and inhomogeneous

case. For this result, the local maximum effective stress values are max700 820.

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