A thermo-fluid Analysis of the Friction Stir Welding Process

D. Jacquina, C. Desrayaudb, F. Montheillet c

Ecole Nationale Supérieure des Mines de Saint-Etienne, CNRS UMR 5146, Centre SMS, 158 cours Fauriel, 42023 Saint-Etienne Cedex 2, France

ajacquin@emse.fr, bcdesray@emse.fr, cmontheil@emse.fr

Keywords: Friction Stir Welding, analytic model, plastic power dissipation, friction law, relative slip

Abstract.

The thermo-mechanical simulation of Friction Stir Welding focuses the interest of the

welding scientific and technical community. However, literature reporting material flow modeling

is rather poor. The present work is based on the model developed by Heurtier [2004] and aims at

improving this thermo-fluid simulation developed by means of fluid mechanics numerical and

analytical velocity fields combined together. These various velocity fields are investigated

separately and especially according to the power dissipated during the flow. Boundary conditions

are considered through a new approach based on the kinematic analysis of the thread of the pin. An

equilibrium is established between the vertical motion of the bulk material dragged in the depth of

the metal sheet, and its partial circulation around the pin. The analyses of the obtained velocity

fields enable the understanding of the welded zone asymmetry and highlights the bulk material

mixing between the welded coupons in the depth of the sheet. A regression is performed on the

relative sliding velocity of the aluminium according to the surface of the tool: shoulder and pin.

Two dimension flow lines in the depth of the metal sheet are then obtained and successfully

compared with the results obtained by Colegrove (2004) [1].

Introduction

The basis of this work consists in studying separately the velocity fields used as components

by Heurtier in his model published in [2]. This model aims at representing the material flow

generated by the FSW process through a combination of analytical and numerical velocity fields.

These velocity fields are chosen to fit as well as possible the very complex boundary conditions of

the Friction Stir Welding process. The introduction of the thermal and tribologic boundary

conditions is presently discussed, and the expressions of the velocity fields are completed to

account for the bulk material dragging by the tool rotation and the probe unscrewing effect due to

the presence of a thread on the pin. The equilibrium between the orthoradial dragging and vertical

dragging is also discussed in this paper. Furthermore a comparison of the mean power dissipated by

each of these velocity fields is performed to highlight the origin of the heating power generated

during the process.

Modelling of the process

Three different velocity fields are used to describe the process. These velocity fields are based

on an analysis of the friction stir welding process. Remind that the process consists in the

displacement along the interface of the clamped parent material coupons, of a rotative tool

composed of a shoulder in which a threaded probe is inserted. The kinematics of the tool generate a

bulk material flow around the probe as “water around a bridge pile”. This flow is of course affected

by the thermal and tribologic boundary conditions generated by the rotation of the tools. This

rotation through the contact with the shoulder and the probe implies a dragging of the bulk material

Materials Science Forum Vols. 539-543 (2007) pp 3832-3837Online available since 2007/Mar/15 at www.scientific.net© (2007) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/MSF.539-543.3832

All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,www.ttp.net. (ID: 132.198.50.13, University of Vermont, Burlington, United States of America-28/09/13,16:34:30)

orthoradial to the probe axis (under the shoulder and along the probe) and vertically due to the

presence of the thread on the pin.

Constitutive equations

In the present work the bulk material constitutive equation is considered to fit with a Norton

Hoff law, the parameters of which were determined from a regression performed on hot torsion

testing. Nevertheless the value obtained is an average of the flow stress values over the range of

temperature, which the bulk material is subjected to during the FSW process. Results obtained on a

AA7449 in the T79 state are considered here : mkεσ &=0 with k = 100 MPas

-1 and m=0.12

an average value of the consistency k is chosen over the range of temperature from 100°C to

450°C

Circumventive velocity field

The model is based on the displacement of a cylindrical tool ended by a screw shaped probe

around which the bulk material flows like the water around a bridge pile. The classic circumventive

velocity field defined for perfect fluids is used in this case.

This first field was at the basis of the model developed by Heurtier [2] and describes the bulk

material flow around the pin. Since the work developed by Jacquin [3] this field now includes a

circulation Γ of the material around the pin to account for rotative dragging of the bulk material by

the probe.

2

0

2(1 ) cos( )r

rv v

r r

ϕθ∞

∂= = −∂

Vur

= (1)

2

0

2(1 )sin( )

2

rv v

r r rθ

ϕθ

θ π∞

∂ Γ= = − + −

∂

The introduction of the circulation value enables to keep the incompressibility properties of

the field. The value chosen for the circulation will be discussed in the results section and depends

strongly on the friction conditions of the probe with the bulk material. This dragging of the bulk

material located in an horizontal plane is a cause of the dissymmetry of the welded zone, as shown

in figure 1.

Figure 1 : aspect of the flow lines in the circumventive velocity field. Kinematics of the tool indicated by arrows

Materials Science Forum Vols. 539-543 3833

Torsion velocity field

The friction power dissipation used to heat the bulk material before joining is at the centre of

the patent describing the process. Friction occurs between the shoulder and the surface of the parent

metal sheets. It develops in the subsurface a shear strain. The torsion velocity field aims at

describing this shearing effect of the shoulder on the subsurface, called the flow arm zone. Its

influence is limited to an average thickness h of 2mm. It was clearly developed by Heurtier [2] for

the FSW modelling. Although the flow arm zone presence is linked to the friction effects of the

shoulder, the power dissipated in this zone has to be considered as plastic power dissipation.

Nevertheless a part of the heating power issues from the surface friction with the shoulder, at the

level of which a discontinuity of the velocity may appear. These aspects are described with the

boundary conditions.

The vortex velocity field

The third field is purposed to describe the vertical dragging of the bulk material by the thread

of the probe enabling the homogeneity of the weld even for high thickness aluminium alloy sheets.

This field was discussed by heurtier and its description was improved by Jacquin [3] through

axisymmetric FEM calculations, especially close to the pin where velocity gradient values are high.

location of the vortex m= 0.05 m=1 (liquid)

Figure 2 : aspect of the axisymmetric vortex velocity field generated by the vertical dragging of the probe thread

For a low (m=0.05) and high (m=1) value of the strain rate sensitivity of the bulk material.

Figure 2 features the effect of the bulk material strain rate sensitivity m (for a viscous

material) on the shape of the vortex and especially its size, intensity (velocity amplitudes) and

distance of the vortex centre from the probe.

Boundary conditions and friction power dissipated.

Till now the formula proposed by Grong [4] to quantify the friction power dissipation, was

used in the model developed by Heurtier :

3 2 32 4

3 3s Grong sQ p R pN Rπµ ω π µ= = & (2)

With sR the radius of the shoulder, µ the local Coulomb friction coefficient and p the

normal pressure. ω , or GrongN•

is the rotative velocity between the tool and the bulk material, i.e.

the rotation velocity value of the tool from which the welded material surface velocity is

substracted :

3834 THERMEC 2006

Grong tool weldedmaterialN N N= −& & & (3)

In the present work the TRESCA formulation for the shear stress is used :

maxmτ τ= 0max

3

στ = (4)

m is the tresca coefficient providing the ratio of bulk material flow stress, required to strain

the subsurface. This model is adapted to the description of elasto-plastic bodies contacts, due to the

consideration of a maximum shear stress value identified as a fraction of the bulk material flow

stress. In the present case m is set to 0.3 due to the high chemical reactivity of the aluminium in

contact with the shoulder. This formulation leads to a somewhat different form of the friction

dissipated power :

1

3 3

02

33

m

m m mglis

friction

N R rW mk

L m

π+•

+ + − = +

(5)

with glis Grong tool weldedmaterialN N N N= = −& & & &

Note that this formula contains the Flow stress of the bulk material contained in the flow

arm zone. L is the thickness of the flow arm zone. The radius of the probe and the shoulder being

respectively r0 = 6 and R = 15 mm, the vertical load : 80 kN.

The comparison of the power obtained with both assumptions for the shearing stress

highlights the overestimation of the COULOMB model due to the fact that if τ = µP, the shearing

stress may increase proportionally to the pressure, whereas the flow stress of the viscoplatic plastic

bulk material imposes a limit for this value in the TRESCA model. The power estimated with the

Coulomb model is 50 times the value obtained with the TRESCA formulation.

Dissipated plastic power

The plastic power dissipated by each of the velocity fields considered separately is

calculated using the rheology previously defined and applying the formula :

0 .V

W dVσ ε= ∫ & (6)

with )~:~(32 εεε &&&= (7)

ε&~ being the strain rate tensor, symmetric part of the velocity gradient.

The volume over which the integration is performed is a 30 mm diameter cylinder (because

of the axisymmetric frame chosen) with a 10 mm thickness. The plastic power dissipated out of

this cylinder is neglected due to the low value of the velocity values far from the probe.

For the torsion velocity field the power is integrated as follows : 1

3 3

1 022

33

m

m mr rNW Lk

mL

ππ

+•+ + − =

+

(r1 = R, shoulder radius) (8)

Materials Science Forum Vols. 539-543 3835

for the circumventive velocity field with circulation we obtain :

2 22 2 2

0 0

3 2 5,

2 sin( )2 4

3 3 2ij

i j

r v r v

r r r

θε ε

π π

• •∞ ∞

ΓΓ = = + −

∑ (9)

leading to an expression of the power that cannot be integrated analytically, this expression

is computed numerically. For the vortex the power calculation is obtained from the finite element

code used to calculate the velocity field.

Results and discussion

All the power values can be plotted as a function of the relative slip of the welded material

with respect to the tool. In the present paper this relative slip is considered to be equal under the

shoulder and along the probe in the orthoradial direction. Due to the effect of the probe thread the

vertical dragging velocity turns out to be the complementary of the orthoradial dragging. One can

easily understand that if the bulk material is fully dragged in rotation by the pin then the effect of

the thread is zero and no vertical motion occurs. At the opposite if no dragging occurs in the

orthoradial direction by the pin the vertical reaction of the fillet and thus the vertical velocity will be

maximum. This remark enables to parameter all the calculated powers through a unique value of

relative slip α, equal to 0 if the bulk material is slipping on the tool with no shear stress, and 1 if

sticking occurs. Figure 3 shows the evolution of the dissipated power values for each velocity field

considered separately.

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

0 0,1 0,2 0,3

α : relative slip velocity, tools / bulk material

Dissipated power (w)

Plastic power of thecircumventive velocity field

Plastic Power of the torsionfield

Plastic power of the vortexfield

Thermal power dissipated byfriction (boundary layer)

Figure 3 : comparison of dissipated power values in the various zones of the friction stir weld

One can observe that as α increases the friction power decreases due to the fact that when

α=1 no relative slip remains and no friction power is left. However the value of the friction power

remains quite low according to the values of the power dissipated plastically and especially through

the torsion velocity field. This observation points out the fact that the heating source may not be

essentially localized “in” the contact between the shoulder and the welded material but rather in the

subsurface (i.e. flow arm zone). Note that this result is due to the use of the TRESCA friction model

leading to much smaller value of the shear stress. The authors of this paper claim that shear stress

are actually strongly overestimated through the COULOMB Model commonly used for elastic

bodies contact.

3836 THERMEC 2006

The orthoradial dragging of the bulk material (circulation Γ) appears to be of major

importance if we consider the power dissipated. Its occurrence will considerably modify the

temperature and velocity field profiles. Furthermore, as observed on the flow lines plotting, this

velocity field is at the basis of a significant mixing of the parent material in the depth of the metal

sheet. Such a velocity field should be considered for a global model of the FSW process.

If we now consider the low value of the power dissipated through the vortex velocity field

one could say that ignoring this velocity field may simplify the formulation of a global model of the

FSW process. However the vertical bulk material flow may be at the origin of significant heat

convection phenomena especially in the present case where the heating source is located in the

upper part of the weld (surface and subsurface). The vortex velocity field may in fact homogenize

the temperature distribution in the depth of the sheet and thus increase the homogeneity of the weld.

The regression performed on the α parameter enables to classify the various components of

the global velocity fields relevant to describe the bulk material flow around the probe. This

parameter has now to be calculated as a consequence of the thermal equilibrium considering

conduction and convection (through the global velocity field) and minimizing the power dissipated

in the system.

Conclusions

In the present paper a comparison is made on the power dissipated through the various

velocity fields required to describe the bulk material flow around the probe during the FSW process.

This comparison enables to classify the respective weight of each velocity field component on the

thermo-mechanical history of the bulk material during the process. The shearing of the bulk

material in the flow arm zone appears to be powerfull and may be the major heating source in the

process. Although the power dissipated by the vortex velocity field appears to be low, the intensity

of the velocity generated along the probe may be the cause of a vertical heat convection enabling

the temperature homogenisation in the depth of the sheet. Compared to the Coulomb law, the

TRESCA model is more suitable to quantify the shear stress in the contact that appears to be much

smaller than the values calculated by Grong.

Acknowledgements

The authors wish to thank the European community for its financial support to the

DEEPWELD project in the context of which this work was performed. The DEEPWELD project

deals with the multiphysic modelling of the friction stir welding process. DEEPWELD (AST4-CT-

2005-516134) is a 36 month Specific Targeted Research Project (STREP) co-funded by the 6th

Framework Programme of the European Community. N.B. this publication reflects only the author's

views the European Community is not liable for any use that may be made of the information

contained therein.

References

[1] P.A Colegrove, H.R. Shercliff. Two-dimensional CFD modelling of flow round profiled FSW

tooling. Science and technology of welding and joining 9 (6): pp. 483-492 (2004).

[2] P. Heurtier, M.J. Jones, C. Desrayaud, F. Montheillet, D. Allehaux and J. Driver. Mechanical

and thermal Modeling of Friction Stir Welding. Journal of Material Process and Technology. Vol

172, issue 1, pp 152-158 (2006).

[3] D. Jacquin. Training period report : Master “Material and Science Engineering”, Ecole

Nationale Supérieure des Mines de Saint Etienne (September 2005)

[4] O. Grong. Metallurgical modelling of welding of Aluminium alloys, in Mathematical

Modelling of Weld phenomena 3, The Institute of Materials, p. 313-356 (1997).

Materials Science Forum Vols. 539-543 3837

THERMEC 2006 10.4028/www.scientific.net/MSF.539-543 A Thermo-Fluid Analysis of the Friction Stir Welding Process 10.4028/www.scientific.net/MSF.539-543.3832

DOI References

[1] P.A Colegrove, H.R. Shercliff. Two-dimensional CFD modelling of flow round profiled FSW tooling.

Science and technology of welding and joining 9 (6): pp. 483-492 (2004).

doi:10.1179/136217104225021832 [2] P. Heurtier, M.J. Jones, C. Desrayaud, F. Montheillet, D. Allehaux and J. Driver. Mechanical and thermal

Modeling of Friction Stir Welding. Journal of Material Process and Technology. Vol 172, issue 1, pp 152-158

(2006).

doi:10.1016/j.jmatprotec.2005.07.014