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Numerical analysis of double-electrode gas metal arc welding process

C.S. Wu a,*, M.X. Zhang a, K.H. Li b, Y.M. Zhang b

a Institute for Materials Joining, Shandong University, 73 Jingshi Road, Jinan, Shandong 250061, Chinab Center for Manufacturing and Department of Electrical and Computer Engineering, University of Kentucky, Lexington, USA

Received 22 February 2006; received in revised form 17 March 2006; accepted 11 July 2006

Abstract

With consideration of process characteristics of the newly developed DE-GMAW (double-electrode gas metal arc welding), a finiteelement analysis (FEA) model is developed to numerically analyze this novel process. To this end, the authors have extended the func-tions of SYSWELD, a standard software package for numerical analysis of welding processes; simplified the method for processing theweld reinforcement; and proposed an appropriate mode for the welding heat source in this novel process. Based on the FEA results oftemperature profile in DE-GMAW, the weld dimension at cross section and temperature distribution are obtained. The predicted andexperimentally measured results match satisfactorily. The results show that DE-GMAW has advantages in terms of increasing depositionrate, lowering heat input to base metal, and reducing residual stress and distortion.� 2006 Elsevier B.V. All rights reserved.

Keywords: DE-GMAW process; Weld dimension; Residual stress and distortion; Prediction; Finite-element analysis

1. Introduction

In the conventional gas metal arc welding (GMAW), thearc is always established between the consumable electrodeand the base metal. The base metal is the cathode and thepart of the arc heat determined by the product of the weld-ing current and the cathode potential is directly absorbedby the base metal. Because this part of the heat directlymelts the base metal contributing to enlarging the weldpool and distortion, the increase of deposition rate viaincreasing the welding current is limited unless backing isused to support the large weld pool. Due to deposition isthe major application of GMAW, the fundamental charac-teristic of the arcing principle limits the further improve-ment of productivity in conventional GMAW. Forexample, for a half inch (12.7 mm) thick joint, five coverpasses are typically needed to fill the groove after the rootpass [1]. However, if the workpiece is not a terminal of thearc, so that the permitted amperage is not restricted, high

current can then be used to achieve high melting rate to fillthe groove in a single pass. A novel process, referred to asthe double-electrode GMAW, has been developed at theUniversity of Kentucky to decouple the base metal currentfrom the torch current in GMAW [2]. As shown in Fig. 1,adding a GTAW (gas tungsten arc welding) torch toGMAW torch constitutes the double-electrode GMAWsystem. The current supplied by the bypass control unitflows from the filler wire (GMAW torch) to the GTAW’stungsten electrode without going through the base metal.The corresponding arc is established between the filler wireand the tungsten electrode. This arc does not directly heatbase metal and is referred to as the bypass arc. The corre-sponding current is referred to as the bypass current Ibp.The part of the current which flows from the filler wire tothe base metal is referred to as the base metal currentIbm. The current which flows through and melts the fillerwire will be the sum of the bypass current Ibp and the basemetal current Ibm, and is referred to as the melting currentIm. Because two electrodes are used and the method is basi-cally similar to GMAW except for the current bypass, themethod is referred to as the double-electrode GMAW or

0927-0256/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.commatsci.2006.07.004

* Corresponding author.E-mail address: wucs1959@126.com (C.S. Wu).

www.elsevier.com/locate/commatsci

Computational Materials Science 39 (2007) 416–423

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pyDE-GMAW. This modified arc welding process has a fewadvantages including high deposition rate, low heat inputto base metal, and low residual stress and distortion. Asillustrated in Fig. 2, this process can be used for high-speedarc welding with good weld bead quality.

In order to better understand the DE-GMAW processand establish the knowledge base and foundations neededto support this novel process, the physical phenomenashould be studied by modeling and simulation. In thispaper, numerical analysis of the DE-GMAW is con-ducted to provide guidelines for optimizing the processexperimentally.

2. Formulation

SYSWELD, a software package for numerical analysisof welding processes, is applied to simulate the thermalprocess in DE-GMAW. Though extensive investigationshave been conducted on modeling and simulation of con-ventional GMAW, there still are unsolved problems. Forexample, the weld reinforcement was not considered [3];the weld reinforcement was not determined by taking theweld pool surface deformation into account [3–5]; andthe procedure for determining the weld reinforcementwas too complicated due to the coupling among arc pres-sure, droplet impact, fluid dynamics, pool surface depres-

sion, etc. [6–11]. To obtain an effective method to analyzeDE-GMAW process with satisfactory accuracy, theauthors have extended SYSWELD’s functions as describedbelow.

2.1. Processing of weld reinforcement

The main arc in DE-GMAW is a gas-metal arc andthere thus are phenomena of wire melting, droplet transfer-ring and weld reinforcement forming. To calculate thethermal process more accurately, the model must deal withthe weld reinforcement. The cross section area of weld rein-forcement can be easily calculated through dividing themelted amount of wire per unit time by the welding speed,i.e.,

A ¼ pd2f vf

4vw

; ð1Þ

where A is the cross section area of weld reinforcement, df

is the wire diameter, vf is the wire feed rate, and vw is thewelding speed. However, the geometry of weld reinforce-ment at the cross section is determined by combinedactions of arc pressure, droplet impact, weld pool gravity,and surface tension. An accurate determination of thisgeometry needs to deal with the weld pool surface deforma-tion which in turn is affected by complicated fluid dynamics

Fig. 1. Experimental system for double-electrode gas metal arc welding.

Fig. 2. DE-GMAW weld appearance (Ibm = 250 A, Ibp = 80 A, welding speed 1.27 m/min).

C.S. Wu et al. / Computational Materials Science 39 (2007) 416–423 417

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inside the weld pool [6–11]. To concentrate on the predic-tion of weld dimensions in DE-GMAW, a thermal conduc-tion model is developed to calculate the temperaturedistribution by finite-element-analysis (FEA) so that thefluid convection is only indirectly considered. Hence, a sim-plified method is employed to compute the weld reinforce-ment. In this model, the dimension and geometry of weldreinforcement at the cross section are determined first.Second, the weld reinforcement is added to the workpiecein advance. And then the mesh is automatically generated.During FEA, the elements associated with the weld rein-forcement are ‘‘activated’’ one by one as the weldingproceeds.

As shown in Fig. 3, the contour of weld reinforcement atthe cross section is assumed to be parabolic, i.e.,

y ¼ ax2 ða < 0Þ: ð2Þ

Along the parabola,

y ¼ �h when x ¼ �ffiffiffiffiffiffiffih�a

r: ð3Þ

Since

dydx

����y¼�h

¼ 2axjx¼�

ffiffiffiffi�h

a

p ¼ �2a

ffiffiffiffiffiffiffi� h

a

r¼ tgh:

Then

h ¼ � tg2h4a

ð4Þ

where h is the contact angle. When the material propertiesand welding conditions are known, h may be considered asa constant. Here h and h are predetermined based on somemacrophotograph of DE-GMAW weld cross sections.

Also,

A ¼ 2

Z ffiffiffiffi�h

a

p

0

ðax2 þ hÞdx:

Hence,

a2 ¼ 2vwtg3h

3pd2f vf

: ð5Þ

When a, h and h are known, the configuration of weld rein-forcement at the cross section is completely determined.

2.2. Mesh generation

The workpiece is mild steel sheet of length 120 mm,width 50 mm and thickness 2.5 mm. For mesh generationpurpose, the weld reinforcement is added onto the work-piece in advance. For the elements associated with the weldreinforcement ahead of the welding arc, they are ‘‘dead’’;i.e., they are not considered in FEA. For those elementsassociated with the weld reinforcement behind the weldingarc, they are ‘‘activated’’ and their influence is included inFEA. The whole workpiece is discretized into non-uniform8-node hexahedrons (Fig. 4).

To include the effect of arc pressure, droplet impact andweld pool surface depression indirectly, a simplifiedmethod is used to deal with the mesh structure for the frontand rear parts of weld pool. As aformentioned, the weldreinforcement is added to the workpiece in advance. Infact, the whole mesh structure and its cross section areshown in Figs. 4 and 5, respectively. To consider thedepressed weld pool surface indirectly, some elements atthe front of weld pool are treated as ‘‘dead’’ so that thecross section of mesh structure around the arc centerlineis actually like that shown in Fig. 6.

2.3. Heat source mode

Appropriate mode of heat source must be determined todescribe the practical physical phenomena in DE-GMAW.In this study, two types of heat sources are combinedtogether to describe DE-GMAW heat input. The wire ismelted and transferred into the weld pool so that the poolsurface at the rear of weld pool is humped and the weldreinforcement is formed after solidification. Because thetransferred droplets are overheated, they deliver some extraheat content into the weld pool [7]. To consider this part ofheat input, a volumetric heat source with uniform intensity

Fig. 3. Schematic of weld reinforcement at cross section. Fig. 4. Mesh generation.

418 C.S. Wu et al. / Computational Materials Science 39 (2007) 416–423

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is used for the humped region in the weld pool. A Gaussianheat source exerts heat flux on the weld pool surface. Thetotal power PT is the sum of two parts:

P T ¼ P S þ P V; ð6Þ

where PS and PV are the power of Gaussian and volumetricheat sources, respectively.

Let k represent the power percentage of Gaussian heatsource of all heat input, then

P S ¼ kðg1U bmIbm þ g2U bpIbpÞ;P V ¼ ð1� kÞðg1UbmIbm þ g2UbpIbpÞ; ð7Þ

where g1 and g2 are the power efficiencies of the main arcand the bypass arc, respectively, Ibm is the current flownto the base material, Ibp is the bypass current, and Ubm

and Ubp are the voltage of main arc and bypass arc, respec-tively. For a specific welding condition of DE-GMAW, asuitable value of k can be selected to obtain satisfactory re-sults in FEA. In this study, k, g1 and g2 are taken values of0.60, 0.65 and 0.30, respectively. It is assumed that the

effective radius of Gaussian heat source isffiffiffiffih�a

q.

2.4. Governing equations and boundary conditions

Under a moving coordinate system o-xyz with y-axisalong the welding direction, z-axis along the workpiecethickness direction (coinciding with the arc centerline),and the origin o at the workpiece surface, the governingequation for the temperature field on the workpiece is asfollows:

qCP

oTotþ ð�vwÞ

oToy

� �¼ o

oxkoTox

� �þ o

oykoToy

� �

þ o

ozkoToz

� �þ qVðx; y; zÞ; ð8Þ

where q is the density, Cp is the specific heat, vw is the weld-ing speed, T is the temperature, t is the time, k is thethermal conductivity, and qV(x,y,z) is the volumetric heatsource term of the weld reinforcement within the effectiveregion of welding arc.

On the upper surface of workpiece,

�koToz¼ arcðT � T1Þ þ merLb � qSðx; yÞ ð9Þ

where arc is the heat loss coefficient, T1 is the ambient tem-perature, mer is the evaporation coefficient, Lb is the latentof evaporation and qS(x, y) is the Gaussian heat sourceterm.

On the bottom surface of workpiece,

�koToz¼ arcðT � T1Þ: ð10Þ

At the symmetry plane (x = 0),

oTox¼ 0 ð11Þ

Initial condition,

t ¼ 0; T ðx; y; z; 0Þ ¼ T1 ð12Þ

3. Results

For a test case (Im = 330 A, Ibm = 250 A, Ibp = 80 A,Ubm = 32 V, Ubp = 20 V, vf = 232.83 mm/s, vw = 21.17mm/s, mild steel workpiece of length 120 mm, width50 mm and thickness 2.5 mm), finite-element analysis oftemperature field in DE-GMAW has been carried out.The specific heat and thermal conductivity are temperaturedependent [12,13]. Some physical properties are listedbelow, and others are summarized in Table 1.

Fig. 5. Cross section of mesh structure.

Fig. 6. The imaged mesh structure at the front of weld pool.

Table 1Other thermo-physical properties and parameters used in the calculation

Property or parameter Symbol Value

Density q 6900 kg m�3

Ambient temperature T1 293 KMelting point Tm 1773 KLatent of evaporation Lb 73.43 · 105 J kg�1

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Cp¼

513:76�0:335T þ6:89�10�4T 2

�10539þ11:7T

11;873�10:2T

644

354:34þ0:21T

8>>>>>>>>>>><>>>>>>>>>>>:

ðJ kg�1Þ

T 6 973 K

973 K6 T 6 1023 K

1023 K6 T 6 1100 K

1100 K6 T 6 1379 K

1379 K6 T

ð13Þ

k ¼

60:719� 0:027857T

78:542� 0:0488T

15:192þ 0:0097T

349:99� 0:1797T

8>>>><>>>>:

ðW m�1 K�1Þ

T 6 851 K

851 K6 T 6 1082 K

1082 K6 T 6 1768 K

1768 K6 T 6 1798 K

ð14Þarc ¼ 4:536� 10�8ð293:15þ T ÞðT 2þ 293:152Þ þ 25ðW m�2K�1Þ

ð15Þ

Fig. 7. Predicted and measured weld cross section in DE-GMAW. (a) Measured. (b) Predicted and (c) comparison between the predicted and measuredresults.

Fig. 8. Comparison of weld cross section. Condition 1: With bypass current. Condition 2: No bypass current. (a) Cross section of weld and (b) comparisonbetween predicted and measured weld cross section.

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lg mer ¼ 2:52þ 6:121� 18;836

T

� �� 0:5 lg T ðkg s�1m�2Þ: ð16Þ

Based on the numerically simulated temperature profile,the geometry and dimension of weld at cross section havebeen obtained and compared with experimental measure-ments. In Fig. 7, (a) is the macro-photography of DE-GMAW weld, (b) is the predicted weld cross section, and(c) is the comparison between the predicted and measuredweld cross section in DE-GMAW. It can be seen that thepredicted and measured weld cross section in DE-GMAWmatches well.

Two conditions are used to make a comparison (condi-tion 1: with bypass current, Im = 330 A, Ibm = 250 A,

Ibp = 80 A; condition 2: no bypass current (i.e., regularGMAW), Im=330 A, Ibm = 330 A, Ibp = 0 A). Asshown in Fig. 8, though the cross-section areas of weldreinforcement are similar because of the same wire feedrate for two conditions, but the workpiece is com-pletely penetrated in condition 2 because of the higherheat input to the base material (Ibm = 330 A). For condi-tion 1, the welding current flowing through the workpieceis only 250 A, so the weld penetration and weld volumeare much smaller because of the lower heat input(Ibm = 250 A).

The heat-affected zone (HAZ) is the portion of the basematerial that was not melted but whose properties (and,

Table 2Weld width, HAZ width and maximum penetration with and without bypass current

Weld width (mm) HAZ width (mm) Maximumpenetration (mm)Front Back Front Back

Condition 1: Measured 6.20 Non-penetration – – 1.80Condition 1: Computed 5.96 Non-penetration 7.84 7.27 1.70Condition 2: Computed 6.11 2.20 10.02 9.52 Full penetration

Fig. 9. Temperature field and weld bead. (a) Condition 1: with bypass current. (b) Condition 2: no bypass current.

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pyusually, structure) were altered by the heat of weldingthrough some phase transformation or reaction [14]. Inthis study a peak temperature 1073 K is defined as thetemperature at which the structure and properties of thebase material are altered by some metallurgical transfor-mation, and then the HAZ width is determined by thetemperature profile. As can be seen in Table 2, for condi-tion 2, the front and back widths of heat-affected zone(HAZ) are 28% and 24%, respectively larger than thoseunder condition 1. It is evident that the bypass currentdecreases the heat input to the base material in DE-GMAW, so dimensions of both weld and HAZ arelowered. Figs. 9 and 10, respectively compare their tem-perature fields on the workpiece and thermal cycles ofsome points at upper surface of workpiece under thesetwo conditions. The thermal distribution with bypass cur-rent is clearly lower than that without bypass current. Dueto the lower temperature profile, the resulted thermalstress, strain and distortion of the welded workpiece arelower. Fig. 11 demonstrates the thermal stress, strain

and distortion on some points at the upper surface ofworkpiece.

Fig. 10. Thermal cycles at workpiece upper surface points. (a) Condition 1:with bypass current. (b) Condition 2: no bypass current.

Fig. 11. Thermal stress, strain and distortion on some points at workpieceupper surface points under two conditions. (a) Mean value of stress. (b)Equivalent strain (c) thermal deformation.

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4. Conclusion

(1) Characteristics of DE-GMAW have been combinedwith function-extended SYSWELD to develop afinite-element model which is capable of simulatingthis novel process numerically.

(2) A simplified method for processing the weld rein-forcement is introduced and the corresponding modeof heat source in DE-GMAW is proposed. The tem-perature profiles and thermal stress and distortion inDE-GMAW are numerically analyzed.

(3) The computed weld dimensions are found in satisfac-tory agreement with experimental measurements.

(4) Because of the lower heat input to the base metal,both the weld geometry and HAZ of the welded mildsteel in DE-GMAW are much reduced. The thermaldistortion is also much reduced.

Acknowledgments

This study is supported by the National Science Foun-dation, Arlington, VA, USA under Grant DMI-0355324,

and the Specialized Research Fund for the DoctoralProgram of Higher Education in China (Grant No.20050422027).

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