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The numerical simulation of heat transfer during a hybrid laser–MIG

welding using equivalent heat source approach

Issam Bendaoud a,n,Simone Matte?a,Eugen Cicala a,Iryna Tomashchuk a,

Henri Andrzejewski a,Pierre Sallamand a,Alexandre Mathieu a,Fréderic Bouchaud b

a Laboratoire Interdisciplinaire Carnot de Bourgogne,UMR6303CNRS/Universitéde Bourgogne,IUT-12,rue de la Fonderie,Le Creusot71200,France

b Centre de Recherche des Matériaux du Creusot,Arcelor Mittal France/Industeel,56rue Clémenceau,Le Creusot71200,France

a r t i c l e i n f o

Article history:

Received4April2013

Received in revised form

14August2013

Accepted9September2013

Available online5October2013

Keywords:

Hybrid laser-arc welding

Numerical simulation

Heat transfer

a b s t r a c t

The present study is dedicated to the numerical simulation of an industrial case of hybrid laser–MIG

welding of high thickness duplex steel UR2507Cu with Y-shaped chamfer geometry.It consists in

simulation of heat transfer phenomena using heat equivalent source approach and implementing in

?nite element software COMSOL Multiphysics.A numerical exploratory designs method is used to

identify the heat sources parameters in order to obtain a minimal required difference between the

numerical results and the experiment which are the shape of the welded zone and the temperature

evolution in different locations.The obtained results were found in good correspondence with

experiment,both for melted zone shape and thermal history.

1.Introduction

The hybrid laser/MIG welding method allows achieving a syner-

getic effect from the use of two heat sources.The aim is to combine

the advantages of arc welding with those of laser to overcome the

limitations of individual processes.The hybrid laser arc welding is

reported as having the potential to increase penetration depth,

width and so welding speed,whilst improving tolerance and

controlling weld pool chemistry by means of?ller addition.In our

study,the work piece has a thickness of20mm.In this case,the

laser role is welding the root of the work piece and the MIG process

provides for the?lling the chamfer.The development of a simula-

tion of this process that would take into account the main involved

physical phenomena would be very useful industrial tool for

estimating the welding effects(temperature?eld and melted zone

shape)for a given set of operational parameters.Unfortunately,each

process alone is not already completely mastered or understood,nor

is their combination.Nevertheless,the precise knowledge of ther-

mal history is essential for accurate prediction of the distortions and

residual stresses.In order to access to the thermal history in the

solid part of the work piece,a method consists in treating the heat

transfer by the equivalent heat sources approach.This method does

not require the description of all phenomena that occur in the weld

pool:it consists in the de?nition of the heat sources that provide

the predetermined geometrical characteristics of the fusion zone.

A main dif?culty in this numerical approach is the choice of the heat

sources which will give an adequate representation of each process

and the identi?cation of parameters for these sources.This

approach is called“equivalent heat source approach”.Somme works

can be found in the literature using this approach.For instance,

Reutzel et al.[1]have proposed a three dimensional thermal?nite

element model using a volumetric double ellipsoidal heat source to

represent both laser and MIG.Le Guen et al.[2]have presented a3D

quasi-steady thermal model for hybrid laser/MAG welding which let

to calculate the temperature?eld in the solid and predicts the melt

pool surface by taking into account the addition of?ller metal and

the effects of surface tension.In the same way,Bidi et al.[3]using

this same approach,have determined the thermal?eld,in the case

of a hybrid laser/MIG welding process.The studied process is used

to obtain a straight weld bead on a stainless steel plate,in?at

position.In their work,the equivalent heat source approach is

associated to numerical exploratory designs method in order to

estimate the unknown parameters of the analytical sources.

In the last years,the multiphysical approach to the modeling of

hybrid welding starts to develop.In opposite to equivalent source

approach,that describes only thermal?eld in the work piece,

multiphysical approach is based on detailed description of various

phenomena taking place in the weld pool.First,very complete VOF

two-dimensional models dealing with metal transfer and melted

zone dynamics were proposed:Zhou and Tasi[6]solved thermo-

hydraulic problem in the transversal cut of melted zone when Gao

et al.[5]solved this problem on the joint line.Then,Cho and Na[4]

proposed three dimensional model providing the information on

Contents lists available at ScienceDirect

journal homepage:https://www.wendangku.net/doc/ea17290101.html,/locate/optlastec

Optics&Laser Technology

https://www.wendangku.net/doc/ea17290101.html,/10.1016/j.optlastec.2013.09.007

n Corresponding author.Tel.:t33385731115;fax:t33385731120.

E-mail addresses:issam.bendaoud@u-bourgogne.fr,

issam.bendaoud@yahoo.fr(I.Bendaoud).

Optics&Laser Technology56(2014)334–342

temperature ?eld,pressure balance,melt ?ow,and free surface evolution.However,these early studies contain very few compar-isons with experimental results and are not yet applied to complex welding geometries.

In spite of simpler description of heat transfer phenomenology,equivalent source approach is widely used for industrial applica-tions dealing with complex welding geometries due to shorter calculation times and smaller quantity of enter parameters,.

In this paper,a numerical simulation using the equivalent source approach is applied to the case of hybrid laser/MIG welding in a complex geometry.This model is able to determine the temperature ?eld out of the weld pool and to reproduce the shape of the melted zone.The heat source parameters are calibrated using a numerical exploratory designs method.The numerical results are compared with weld crosscut shapes and thermocouple measurements.

2.Welding experiment 2.1.Welding con ?guration

The experimental con ?guration is shown in Fig.1.The experi-ments consist in the realization of a one pass hybrid laser/MIG welding of duplex steel UR2507Cu (Euronorm 1.4507-X2CrNiMo-CuN25.6.3)in Y-shaped chamfer geometry.UR2507Cu is a super duplex stainless steel with 25%Cr having austeno-ferritic micro-structure with a ratio γ/αclose to balance.The chemical composi-tion is given in Table 1.

The ?ller wire Sandvik s 4L-25-10with a diameter of 1.2mm is used.It is chosen because of chemical composition (Table 2)close to that of the super duplex but containing more Ni,which allows maintaining the recommended quantity of ferrite (43%)in the melted zone of MIG.

The experimental work is carried out using a TRUDISK 6002Yb:YAG laser with a maximum output power of 6kW,and a FRONIUS torch arc.A FRONIUS head design holds the laser and the MIG torch.In this case,the laser focus position is in front of the arc,this position is de ?ned by two parameters:laser –MIG distance (D 2)and angle between the laser beam and the vertical axis (301)(Fig.1).The welding parameters are shown in Table 3.

A high speed camera PHANTOM V9.1with Cavilux laser diode illumination is used for the visualization of interaction zone.It is positioned in front of the laser,close to the welding axis,and has an inclination of 301to the surface of work piece.The camera provides 60frames per a second at full resolution of 1632?1200active pixels.Such shooting frequency was chosen due to the laser illumination characteristics,which is pulsed in a frequency of 60frames par a second.Fig.2shows an example of the frame obtained from a case having the distance laser/MIG of 21mm.Two separated operating zones can be observed (Fig.2):the laser weld pool followed by the MIG weld pool.The distance between two melted zones is estimated to 13mm.

It was found that the distance between laser and MIG sources is a key-parameter for avoiding weld pool collapse.An experi-ment carried out with laser/MIG distance changed from 21mm to 15mm showed that the formation of common weld pool leads to the collapse (Fig.3).The enhanced synergy of two heat sources increases the volume of melted material and therefore the bath does not support its own weight.Liquid metal ?ows down through the root created by laser.So,for full penetration welding of high thickness pieces,it is needed to keep suf ?cient distance between heat sources allowing the formation of separate melted zones.

In order to reveal the synergetic effect between laser and MIG sources distanced by 21mm comparing to the situation when each source is operating separately,a comparison was made between present hybrid welding con ?guration and standalone laser and MIG welding in two steps,(Fig.4).During two step welding,?rst the root of the work piece is welded by focused laser beam and then,

after

Fig.1.Joint geometry and laser/MIG layout.

Table 1

Chemical composition of the duplex stainless steel.C Cr Ni Mo N Cu 0.03

6.5

3.5

0.25

1.5

Table 2

Chemical composition of ?ller wire Sandvik s

4L-25-10.

C Si Mn P S

Cr Ni Mo N 0.02

0.3

0.4

0.02

0.015

9.5

0.24

Table 3

Operational parameters.Parameters

Values Laser power [kW]

6Laser beam diameter [mm]0.2Wire speed [m/min]12MIG power [kW]12.6Wire diameter [mm] 1.2Speed welding [m/min]

0.4Distance laser –MIG D 2[mm]

21Distance MIG torch-work piece surface D 1[mm]18Shielding gas ?ow in the nozzle:ARCAL 129[L/min]18Shielding gas ?ow in the saddle:ARCAL 129[L/min]30Shielding gas ?ow back side:Argon [L/min]

Fig.2.Front view of interaction zone by high speed camera.

I.Bendaoud et al./Optics &Laser Technology 56(2014)334–342335

cooling the work piece to ambient temperature,the ?lling of the “V ”chamfer is provided by the MIG process.The comparison of width and full depth penetration of MIG melted zone is made.The measurement results (Table 4)show the difference in melted zone dimensions compared to hybrid welding.The main difference is observed for full depth penetration of the MIG melted zone (p):the average penetration in the hybrid case is equal to 10.3mm,whereas in the two-step welding the penetration is 7.8mm.In fact,in hybrid welding,laser passage provides the preheating of “V ”chamfer area and therefore facilitates the fusion of chamfer bottom under action of falling metal droplets.For the width (w ),a difference of 1mm is observed.So,in spite of laser –MIG distance of 21mm,the effect of laser heat source on the development of MIG melted zone still exists.However,the laser melted zone remains stable and similar for both welding cases,which means that it is unaffected by MIG heat source.

2.2.Weld shapes characteristics end temperature measurements The welding experiment carried out with operating parameters shown above in Table 3resulted in full penetration defect free joint.Fig.5shows top and bottom surfaces of the weld bead.No defects or humping effect were observed.

In order to verify the constancy of the weld shape,?ve transversal cuts were prepared (Fig.6).Although the general appearance of the melted zones shapes remains coherent,we observe some ?uctua-tions in MIG melted zone;however the melted zone due to the laser is stable.These ?uctuations phenomena can be attributed on the one hand,to the adjustment of the experimental materials,the MIG torch

misalignment towards the welding axis can cause a deviation a the fusion zone,and on the other hand,?uid dynamics of the liquid metal may involve instability in the form of the weld pool.Six measurements shown on Fig.6b (L 1,L 2…)are made to char-acterize the geometry of the melted zone.To obtain the temporal evolution of temperature at different points around the melted zone,ten K-type thermocouples (maximal work temperature of 11001C)have been inserted into holes (0.5mm diameter,50mm deep)machined by electrical discharge.The thermocouples are inserted at the end of the holes and ?xed with a heat conducting silver pad.The layout of thermocouples (TC)(Fig.6a)has been de ?ned in order to record thermal gradients located around and closer to the limit of the melted

zone.

Fig.3.Weld pool collapse in case of D 2?15mm:(a)top view,(b)bottom

view.

Fig.4.Transversal cut of the weld performed by (a)two-steps welding,(b)hybrid welding.

Table 4

MIG melted zone dimensions in case of two-step and hybrid welding.

Two step welding

Hybrid welding w (mm)16.870.417.970.2p (mm)

7.870.3

10.37

0.9

Fig.5.Hybrid weld bead:(a)top surface,(b)bottom surface.

I.Bendaoud et al./Optics &Laser Technology 56(2014)334–342

336

3.Numerical modeling 3.1.Assumptions

The present model was developed using COMSOL Multiphy-sics s [7].The numerical model setup is based on the following assumptions:

Quasi-steady-state conditions:the heat equation is written for a moving coordinate system which moves with the same velocity as the heat source.

The ?ller material is supposed to have the same properties that UR2507Cu steel,and the latent heat of fusion is taken into account using the apparent heat capacity formulation [8]as shown in expression (1).

c eq p ?c p tL f

exp

T àT m eT2ΔT ?????????????πΔT 2

p e1T

where c p is the speci ?c heat capacity,L f is the latent heat of fusion,T m is the melting temperature and ΔT is the difference between solidus and liquidus temperature.

Fluid ?ow in the weld pool is not considered,but thermal conductivity of the liquid phase is enhanced to take in account convective heat transfer in the weld pool.

Metallurgical phenomena are not taken into consideration.The values of the latent heat of the metallurgical phase change are generally small compared to solid-liquid latent heat of fusion.

The weld pool surface is assumed to be in a static equilibrium under action of arc pressure,gravity and surface

tension.

Fig.6.Transversal cuts with thermocouples layout (Tc 0–Tc 9)and geometrical characteristics of the melted zone (L 1–L 6).

Table 5

Data used for calculation.Physical property

Value

Liquidus temperature,T l (K)1748Solidus temperature,T s (K)1612Fusion temperature,T f (K)

1680

Density of liquid metal,ρl (kg/m 3)à0.6779T t8113Density of solid metal,ρs (kg/m 3)

à0.3391T t7876Thermal conductivity of solid,λs (W/m K)

0.016T t8.4557Equivalent thermal conductivity of liquid,λl (W/m K)70

Speci ?c heat of solid,cp s (J/kg K)(T o 1119K )0.5046T t279.2(T r 1119K )0.1596T t459.52Speci ?c heat of liquid,cp l (J/kg K)0.0646T t691.14Latent heat of melting,L f (kJ/kg)

195

Fig.7.Coordinates system for q surf1

Fig.8.Flowchart of adjustment of heat source parameters.

I.Bendaoud et al./Optics &Laser Technology 56(2014)334–342337

The effect of ?uid ?ow induced by Marangoni phenomena or electromagnetic forces is neglected.

Only half of the work piece is considered since the weld is symmetrical along the joint centerline.The temperature ?eld is determined by solving the heat Eq.(2)where Q is a sum of volume heat sources.ρT eTc p eT TV s

?div eλT eTgrad !T TtQ e2T

Finally,to avoid the discontinuity in material properties

(thermal conductivity,speci ?c heat capacity and density)dur-ing phase transition the smoothed Heaviside function has

been used:

A ?A s teA l àA s T:f lc 2hs eT àT m ;ΔT T

e3T

where A s ,A l are respectively the properties of solid and liquid phase such as λ,ρand cp and ΔT is the temperature interval of smoothing (100K).

The data used for calculation are given in Table 5:3.2.Choice of the equivalent heat sources

The development of numerical model is divided in three steps.First,the sources which represent laser alone are de ?ned.Then

the

Fig.9.Diagram of effects of in ?uencing factors.

Table 6

Optimized parameters of heat sources.A 1(%)r surf1(m)dz (m)ηv (%)r 0(m)a r (m)a f (m)b (m)247?10à4

7?10à4

2.4?10à3

7?10à3

2?10à37?10à5c (m)λeq (W/m K)r 1(m)r surf2(m)A 2(%)η(%)D 2(m)h m (mm)9?10à3

1.45?10à3

7?10à3

25.5

2.25?10à2

2?10à3

I.Bendaoud et al./Optics &Laser Technology 56(2014)334–342

338

heat sources corresponding to MIG process are identi ?ed.And ?nally,all of these sources are introduced into the hybrid laser \MIG model.

https://www.wendangku.net/doc/ea17290101.html,ser sources

The focused laser beam is used in a keyhole mode.The energy contribution of laser is assumed by a combination [3]of Gaussian source with parietal supply:

q surf 1?P L A 12πr 2surf 1e àx 2tv 22r

2surf 1

e àw 2dz 2 e4Tand volumic Goldak conic source:

Q 1?9P L ηv 00r 11e à3x 2ty 2

r z

1àu ez th T??e5T

where r z ?r 0tr 0àr 1

z ,r 0melted zone radius when z ?0,h depth penetration,r 1melted zone when z ?àh and u (z th )Heaviside function.(v,w )are coordinate system for q surf1position is de ?ned as follows (Fig.7).

v ?z sin βty cos βw ?ày sin βtz cos βe6T

In Eq.(4)en (5)unknown parameters to be identi ?ed are A 1,r 0,r 1,r surf 1,dz ,and ηv .

3.2.2.Metal inert gas (MIG)sources

The power distribution of MIG [11]is modeled in following way.On the one hand,we consider that volumic energy is due to the heat input from melted droplets which is represented by

https://www.wendangku.net/doc/ea17290101.html,parison between calculated and experimental geometries of the melted zones.

Table 7

Statistical treatment of characteristic dimensions measured on experimental melted zones and their comparison with equivalent source model results.

L 1

L 2L 3L 4L 5L 6i (measurement)8.84 3.62 1.97 2.12 1.14 1.54s eL i T0.970.550.730.350.180.40s eL i T

0.260.150.190.090.050.1172?t α?s eL i T 1.230.700.920.170.080.50L i t2?t α?s eL i T10.07 4.32 2.89 2.28 1.22 2.05L i à2?t α?s eL i T7.62 2.93 1.05 1.95 1.05 1.04L i (modeling)

8.80

3.50

1.38

1.86

1.1

1.38

I.Bendaoud et al./Optics &Laser Technology 56(2014)334–342339

double-ellipsoid source proposed by Goldak et al.[9,10]

Q 2f

ex ;y ;z T?f f 6???3p ηU I f ???πp e à3x àD 2

a f 2

e à3y b eT2e à3z àh m c àá2ex 40T

Q 2r ex ;y ;z T?f r 6???3p ηU I r ???π

p e à3x àD 2a r àá2e à3y b eT2e à3z àh m c àá2

ex r 0T

e7T

As a second point the surface energy is associated to the arc.This heat source is assumed to have a Gaussian heat

distribution [8]:

q surf 2?

A 2U I

2πr surf 2

x àD 2eT2ty 2

2r surf 2

e8T

Parameters to be identi ?ed are a r ,a f ,b ,c ,η,r surf2,h m ,D 2and A 2.3.2.3.Hybrid laser/MIG sources

The setup of hybrid numerical model is based on both previous cases.The heat sources chosen for laser alone and MIG alone

were

https://www.wendangku.net/doc/ea17290101.html,parison between measured and calculated thermograms.

I.Bendaoud et al./Optics &Laser Technology 56(2014)334–342

340

used for the hybrid case and the heat parameters were identi?ed by using the numerical exploratory designs method.In this case we consider a prede?ned geometry for a?ller metal with a?xed inclination of?ller front.This geometry was determined from experimental macrographies.

4.Identi?cation of equivalent heat source parameters

The identi?cation process is applied in the same way for three numerical models.We use a method of parameter optimization, simple to implement and robust,founded on the numerical exploratory designs method[12].From the numerical model,we

de?ne a list of in?uencing factors(IF)and response functions(RF) which allow to determine all possible combinations(a design matrix)of input parameters and to organize the https://www.wendangku.net/doc/ea17290101.html,ing a limited number of calculations,we evaluate the effects of IF (parameters of analytical expressions of equivalent heat sources) on RF(geometrical characteristics of the melted zone).The analysis of response direction and amplitudes allows to make adjustments of the IF values in order to attain the?xed limit of relative error between the experiments and calculations.The procedure can be represented by the following diagram(Fig.8).

5.Results and discussion

A sensitivity study of equivalent heat source parameters is used to determine the in?uence of each parameters(a f,a r,b,c….) on the geometric dimensions(L1,L2,L3..)which describe the shape of the weld macrographs in transverse direction,as shows Fig.9. For the numerical design matrix we use a fractional design25à2 (which contains all combinations between the two values of the three analyzed factors).As an example,Fig.9shows the effect diagrams in the case of MIG only,which represent the amplitude and the direction of the in?uencing factors on each of response functions.

The analysis of these effects indicates that:

The RF L

is strongly in?uenced by the position of Goldak heat source relatively to chamfer bottom(h m).

The increase of arc heat source spread(R

surf2

)leads to the increase of L1et L2.

surf2

has an inverse effect on L1and L2:if R surf2increases L1and L2decrease.

Laser-arc distance(D

)also affects L1and L2:if D2increases L1 and L2increase.

x-axis spread of Goldak heat source(a

)has a low in?uence on all object functions.

The identi?cation of heat source parameters in hybrid case is based on models of laser and MIG.These parameters are given in Table6.

Fig.10shows calculated and experimental crosscuts of the welds for hybrid(c),laser(b)and MIG(a)cases.

The dimensions of the fusion zone obtained from the heat transfer study have been compared to the measured values.As it can be seen in Fig.10,the melted zone shape obtained from the numerical modeling correlates well with the experimental results. Table7gives an example of results obtained in hybrid welding case after?tting heat source parameters.

It can be observed that all the calculated values enter in the con?dence interval determined for experimental values.

The temperature?elds calculated in the work piece were compared with thermocouple measurements and show good con-cordance(Fig.11).It can be seen that in function of thermocouple position,it responds on MIG or laser heat source passage.The TC1 situated close to the top of the work piece responds only on MIG source passage without detecting the laser source.TC2and TC3 placed in the middle of work piece register two pikes(Fig.11):the ?rst one induced by laser and the second one induced by MIG. The shift between two pikes re?ects the distance between the laser head and the MIG torch.The TC4,TC5and TC6situated in the lower half of the work piece are mostly sensible to laser passage:they show one pick due to laser followed by a plateau corresponding to the diffusion of heat from MIG.

The comparison of pick values of experimental and calculated thermograms(Table8)showed r5%relative error.

We notice that the thermal levels are found by using the parameters de?ned before for the model conception which was initially validated by experimental macrographs.The difference between measured and calculated thermograms can be linked from one hand to the model errors as the numerical model does not take into account thermocouples holes and,in another hand, from the simplifying assumptions which present partially physical phenomena involved.

6.Conclusion

In the present study,a3D quasi-steady state model of heat transfer for welding duplex steel UR2507Cu with Y shaped chamfer is developed to analyze hybrid laser/MIG https://www.wendangku.net/doc/ea17290101.html,ing the numerical experimental designs method associated to the numerical model,the equivalent heat source parameters were estimated and adjusted to reproduce the characteristics of the melted zone. The model results are satisfying since we obtain low difference (o9%)between model and measurements for the melted zone dimensions and also for the temperature inside the work piece. These results allow us to validate to choice of equivalent heat sources for heat supply of hybrid welding process.This information can be used to solve thermomechanical problem.In the following, we look for developing a methodology based on the experimental designs which gives the possibility to link the operating parameters (laser power,welding velocity…)to simulated geometrical values of the melted zone.

Acknowledgement

The authors are grateful for the funding provided by the A.N.R for“SISHYFE”project.

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Table8

The comparison experimental and calculated maximum temperatures.

TC T max mes[K]T max num[K]ΔΤ[K]

Laser MIG Laser MIG Laser MIG

1–1144–1084–60

2–1119–1145–à26 389910539101069à11à16 410929*********à34à6 586987284588324à11 692785090187326à23

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