experimental study and numerical modeling of arc and weld pool in stationary gta welding of pure...

ORIGINAL ARTICLE

Experimental study and numerical modeling of arc and weldpool in stationary GTAwelding of pure aluminum

Amir Hossein Faraji & Massoud Goodarzi &Seyed Hossein Seyedein & Mohammad Hasan Zamani

Received: 25 September 2013 /Accepted: 27 December 2013 /Published online: 31 January 2014# Springer-Verlag London 2014

Abstract In this study, a 2D mathematical model was devel-oped for both arc and weld pool in stationary GTAwelding. Inarc model, current continuity equation has been solved in botharc and cathode regions without any assumption of fixedcurrent density on the cathode surface which was essential inmost previous works. The results of arc model were presentedfor both copper and aluminum anodes to investigate the effectof anode material on arc properties. It was seen that aluminumanode has lower maximum anode current density and heatflux but the distributions are wider than copper anode.Furthermore, shear stress on anode surface is higher in thecase of aluminum anode. Also, calculated results of thisstudy were compared with other available theoretical andexperimental results. It has been shown that the agreementbetween calculated and experimental results was fairlygood. The necessary information to simulate the weldpool, including the anode current density and heat fluxto the workpiece were taken from the arc model. In thismodel, due to high thermal conductivity of pure alumi-num, fluid flow into the weld pool was ignored. Effects of

arc variables, i.e., arc length, applied current and weldingtime on the shape and size of the weld pool were inves-tigated as well. In order to check the validity of the weldpool model, a comparison between calculated results andthe results of our experimental tests was conducted.Generally, these comparisons reveal an acceptable agree-ment between calculated results and experimental data.

Keywords Numerical modeling . GTAwelding . Arc .

Weld pool . Pure aluminum

1 Introduction

Arc plasma has been applied in industrial processing ofmaterials, for example in surface treatment, arc furnaces,processing of minerals and in arc melting. Probably, mostimportant application in arc melting is arc welding.Among the arc welding processes, gas tungsten arcwelding (GTAW) process has been widely used in indus-trial welding applications [1–6]. The geometry and size ofthe formed weld pool are key characteristics for qualityweldments [7, 8].

Arc properties affect the weld characteristics intensively.Among the arc properties, heat flux to the workpiece andanode current density are mostly of concern because thesetwo determine heat flow into the weld pool and therefore thedepth and width of the weld pool [9–13]. So, it is importantand useful to understand the basic phenomena in arc plasma.But, it is very difficult to clarify these phenomena experimen-tally [4, 14, 15].

Therefore, mathematical modeling approaches for describ-ing these phenomena were extensively developed. The start ofsimulating the GTAW arc was performed by Hsu et al. in the

A. H. Faraji :M. Goodarzi (*) : S. H. Seyedein :M. H. ZamaniSchool of Metallurgy and Materials Engineering,Iran University of Science and Technology, Tehran, Irane-mail: [email protected]

A. H. Farajie-mail: [email protected]

A. H. Farajie-mail: [email protected]

S. H. Seyedeine-mail: [email protected]

M. H. Zamanie-mail: [email protected]

Int J Adv Manuf Technol (2014) 71:2059–2071DOI 10.1007/s00170-014-5651-8

year 1983 [16]. Afterwards, many studies were carried out tomodify this model; But, in lots of these studies, only the arccolumn region was modeled and the electrode region was notconsidered [17, 18]. Furthermore, it should also be empha-sized that in majority of previous studies on heat transfer andfluid flow in arc plasma, a predefined current density profilewas needed to be assumed over the surface plane of cathode[3, 4, 14, 17–22].

To describe the main objective of this study, it is necessaryto mention two points. The first one is that most of theprevious studies were concerned with iron and its alloys andmodeling of the weld pool in pure aluminum has received lessattention in literatures. The second one is that almost all of thefew studies related to pure aluminum, as in the study ofFarzadi et al. [23, 24], only modeled the weld pool assuminga normal Gaussian distribution of current density and heatinput from arc to the weld pool. However, there is almost nonumerical model to consider both the arc and weld pool inGTAwelding of pure aluminum. Moreover, since it has beenfound that the theoretical predictions are sensitive to thecurrent density in the cathode, the first aim of this paper is tomodel the arc including both arc column and electrode regionwithout any assumption of current density in cathode surface.In other words, the current density is also calculated in cathoderegion (electrode), in addition to arc column. Furthermore, inthis model, the influences of the anode material on arc prop-erties are simply studied. Aluminum and copper anodes areconsidered for modeling of arc.

The second aim of this paper is to develop a rather simpleweld pool model. This model provides an appropriate tool toclarify the validity of arc model with pure aluminum anode.The other purpose of this model is to investigate the effect ofarc current and length on depth and width of the weld pool.

2 Mathematical model

2.1 Arc model

In GTAW process, an electric arc is struck between atungsten electrode and a workpiece. The present modelis developed for a direct current electrode negative GTAwelding in stationary situation. So, tungsten electrode isthe cathode and the workpiece is the anode. Because ofthe symmetric condition in radial distance from the arcsymmetry axis, a cylindrical coordinate is used and thefollowing assumptions are made:

& The arc is assumed to be steady and in local thermody-namic equilibrium (LTE).

& The plasma is optically thin so that radiation energy fromthe arc will not be absorbed by plasma.

& The flow is assumed to be laminar.

& The weld pool surface is supposed to be flat.& The electrode is supposed to be a tungsten rod with flat

surface.

2.1.1 Governing equations

According to the above assumptions, the governing equationscan be expressed as follows:

Equation of mass continuity:

1

r

∂∂r

rρvð Þ þ ∂∂z

ρuð Þ ¼ 0 ð1Þ

Here r and z are radial and axial coordinates, respectively. ρrepresents the mass density, u and v represent the radial andaxial velocity components, respectively.

Conservation of radial momentum:

1

r

∂∂r

rρvvð Þ þ ∂∂z

ρuvð Þ ¼

−∂p∂r

þ 2

r

∂∂r

rμ∂v∂r

� �þ ∂∂z

μ∂v∂z

þ ∂u∂r

� �� −2μvr2

−J zBθ

ð2Þ

Conservation of axial momentum:

1

r

∂∂r

rρvuð Þ þ ∂∂z

ρuuð Þ ¼

−∂p∂z

þ ∂∂z

2μ∂u∂z

� �þ 1

r

∂∂r

rμ∂v∂z

þ ∂u∂r

� �� þ J rBθ

ð3Þ

Here P is the pressure, μ is the viscosity, Jr and Jz respec-tively represents the redial and axial components of currentdensity and Bθ represents the circumferential component ofmagnetic flux density. The last term in the radial and axialmomentum equations is due to the Lorentz force in the weldpool.

Conservation of energy:

1

r

∂∂r

rρvhð Þ þ ∂∂z

ρuhð Þ ¼ ∂∂z

k

Cp

∂h∂z

� �þ 1

r

∂∂r

rk

Cp

∂h∂r

� �

þ j2z þ j2rσ

þ 5kb2e

J zCp

∂h∂z

þ J rCp

∂h∂r

� �� − Sr

ð4Þ

Here, h is the enthalpy, Cp is the heat capacity underconstant pressure, k is the heat conductivity, σ is theelectrical conductivity, kb is the Boltzmann constant, ande is the elementary charge. The energy equation con-tains three source terms including the joule heating, the

2060 Int J Adv Manuf Technol (2014) 71:2059–2071

diffusive transport of enthalpy due to electron flux tothe anode and radiation loss (Sr).

Current continuity equation:

∂∂z

σ∂φ∂z

� �þ 1

r

∂∂r

σr∂φ∂r

� �¼ 0 ð5Þ

Here, φ is the electrical potential. Using Ohm’s law, thecurrent density components can be calculated as follows:

J r ¼ −σ∂φ∂r

J z ¼ −σ∂φ∂z

ð6Þ

Finally, the azimuthal component of self-induced magneticfield (Bθ) is computed by:

Bθ ¼ μ0

r

Z0

r

J z r dr ð7Þ

Here, μ0 is the magnetic permeability of the free space.The plasma properties including the density, heat capacity,

enthalpy, viscosity, thermal, and electrical conductivity aretreated as a function of temperature and are taken from Luet al. [2].

2.1.2 Calculation domain and boundary conditions

The calculation domain and boundary conditions are shown inFig. 1 and Table 1, respectively. A large calculation domain ofOEFIO, including the cathode, is used to solve the currentcontinuity equation. To solve other equations, a smaller do-main of ABCDEFIA excluding the cathode is used.

Zero velocities are assigned to anode (FI) and cathodesurfaces (AB, BC, and CD). Along the symmetry axis OI,zero gradients are assumed for all variables except for theradial velocity that is set to be zero. For the enthalpy equation,constant values were used for all boundaries except for thesymmetry axis.

Over the boundary OD, a uniform current density of J0defined as the input current divided by the area of cathodecross section (J0=I/(πRc

2)) is used. Here, I and Rc are electriccurrent and radius of the electrode, respectively.

Special attention is required to specify the heat fluxes at theanode and cathode surfaces.

Cathode An electrical sheath with the thickness of 0.1 mm[2, 11, 25, 26], was considered between the arc columnand the cathode surface. A positive source term could be usedto explain the energy used to ionize the plasma in this layer.

This heat source that causes a voltage drop can be expressed as[2, 17, 18, 25]:

Qioniz ¼ JCj jVC ð8Þ

Here JC is the cathode current density and VC is the cathodefall voltage which can be approximated by [2, 17, 18, 25]:

VC ¼ 5

2

kbTe

eð9Þ

Where Te is the temperature of the electrons in the vicinityof the cathode surface.

Anode In this study, three different mechanisms of heat trans-fer from arc to anode are considered. Conventionally, the heatflux to anode (Qa) can be expressed by:

Qa ¼ Qc þ Qr þ Qe ð10Þ

Where Qc is the local heat fluxes by conduction and con-vection and can be written as follows [11, 12]:

Qc ¼0:515

Prw

ρeμe

ρwμw

� �0:11 ρwμwver

� �0:5he−hwð Þ ð11Þ

Where the subscripts w and e denote the wall and the edgeof anode boundary layer, respectively. The wall temperature isassumed to be 1,000 k for copper anode and 500 k foraluminum anode. And Prw is the Prandtl number at the wall.

Fig. 1 Computational domain for the arc and weld pool models

Int J Adv Manuf Technol (2014) 71:2059–2071 2061

The heat flux due to electron flow (Qe) was calculated by[11, 12]:

Qe ¼ Ja ϕa þ 3:203kbTe

e

� �ð12Þ

Here Ja and ϕa are the anode current density and the workfunction of anode material, respectively.

Radiative heat transfer from arc to anode surface (Qr) wascalculated by means of approximation of the view factorscalculated as follows [11, 12, 17, 18]:

Qr ¼Z

V j

SR; j4πd2i; j

cosψ:ΔV j ð13Þ

Here, SR,j is the radiation losses per unit volume, di, j is thevector joining the surface of element on the anode and thevolume element in the arc (Vj), ψ is the angle between di, j andthe vector normal to the anode surface.

2.1.3 Numerical method

All mathematical representations were solved using thecontrol-volume method proposed by Patankar [27]. AFORTRAN code based on SIMPLEC algorithm wasemployed for computer simulation. In all cases of modeling,a non-uniform fixed-grid configuration with finer grid pointnear the cathode and anode surfaces was used.

2.2 Weld pool model

The domain of the numerical model to study the weld pool ofstationary DCGTAwelding is shown in Fig. 1. The weld pool

is assumed radially symmetric and thus the governing equa-tions are written in two-dimensional cylindrical coordinate.Furthermore, due to high thermal conductivity of pure alumi-num, fluid flow in the weld pool is ignored. As well, the weldpool surface is assumed to be flat and also the vaporizationfrom the free surface of molten pool is not considered. Asmentioned before, the anode current density and the heat fluxfrom arc to anode that are two main parameters in determiningthe weld pool shape, are taken from the arc model. These dataare used to develop a rather simple weld pool model.

2.2.1 Governing equations

Taking into account the above assumptions, the related con-servation equations are expressed as follows:

Current continuity equation is given by:

∂∂z

σ∂φ∂z

� �þ 1

r

∂∂r

σr∂φ∂r

� �¼ 0 ð14Þ

After solving the above equation, the current densitycomponents could be obtained according to Ohm’s lawas follows:

J r ¼ −σ∂φ∂r

ð15Þ

J z ¼ −σ∂φ∂z

ð16Þ

Energy conservation equation is represented as the follow-ing equation:

∂∂t

ρCpT� ¼ ∂

∂zk∂T∂z

� �þ 1

r

∂∂r

rk∂T∂r

� �þ 1

σJ 2r þ J 2z

� −∂∂t

ρ f lH f

� ¼ 0 ð17Þ

Here, T is the temperature, k is thermal conductivity, fl is theliquid fraction and Hf is the latent heat of fusion. The last two

terms in this equation are the joule heating and heat losscaused by melting the metal. Assuming that the liquid fraction

Table 1 Boundary conditions for the arc model

OD AB BC CD DE EF FI IO

v – V=0 V=0 V=0 V=0 ∂v∂r ¼ 0 V=0 V=0

u – u=0 u=0 u=0 ∂u∂z ¼ 0 ∂u

∂r ¼ 0 u=0 ∂u∂r ¼ 0

h – T=3,000 K Qioniz=|JC|VC T=3,000 K T=3,000 K T=1,000 K T=1,000 K T=constant ∂h∂r ¼ 0

φ Jz=J0 – – – ∂φ∂z ¼ 0 ∂ϕ

∂r ¼ 0 φ=0 ∂ϕ∂r ¼ 0


in the mushy region varies linearly with temperature, it can bedefined as [13, 28]:

f l ¼0 T < TsT−Ts

T l−TsTs≤T ≤Tl

1 T > Tl

8><>: ð18Þ

Here, Ts and Tl are the solidus and liquidus temperatures,respectively.

2.2.2 Calculation domain and boundary conditions

As shown in Fig. 1, the calculated domain for weld poolmodel is IFGHI. A non-uniform grid point system isemployed with finer grid sizes near the weld pool region.Due to radially symmetric of the domain, only half of theworkpiece is considered. Table 2 lists the related boundaryconditions for all variables.

The first row of this table demonstrates the boundaryconditions corresponding to current continuity equation. Atthe bottom of boundary GH, the electric potential is assumedto be zero. Along the boundary of FG and the symmetric axisof HI, zero gradients are used for the electric potential. At thetop surface of the workpiece IF, the distribution of currentdensity is calculated from arc model.

The second row of the table demonstrates the boundaryconditions corresponding to the energy conservation equation.For side surface FG and bottom surface GH, convection heattransfer to the surroundings is considered. The radial energyflux is set to be zero across the symmetric line HI. At the topsurface IF, the heat flux calculated from the arc model minusthe convection heat loss to the surroundings (q=qarc−hΔT) isapplied.

2.2.3 Numerical solution procedure

A FORTRAN code using the finite volume method (FVM)was developed to solve the transport equations. The dimen-sions of the calculation domain were 15×5 mm. A non-uniform rectangular grid system with finer grids near the heatsource was employed for calculations.

Computations have been performed for commercial purealuminum. The material properties used for modeling aresummarized in Table 3. Density, thermal conductivity, and

specific heat as a function of temperature were taken fromPehlke [29]. Other properties, except for electrical conductiv-ity, and equivalent convection heat-transfer coefficient, weredriven from Farzadi et al. [24]. The electrical conductivity wastaken from Hatch [30]. The equivalent heat-transfer coeffi-cient considering both convection and radiation heat loss wascalculated based on the approach presented by Holman [31].Practically, the equivalent heat-transfer coefficient varies withtemperature. However, since the results did not show highsensitivity to variation of that, a constant equivalent heat-transfer coefficient was taken in the computations.

Table 2 Boundary conditions for the weld pool model

IF FG GH HI

φ J=Jarc ∂φ/∂r=0 φ=0 ∂φ/∂r=0T q=qarc−hΔT q=hΔT q=hΔT ∂T/∂r=0

Table 3 Material properties used in the weld pool model

Properties Symbols Value

Density (solid) ρs 2700 kg m−3

Density (liquid) ρ l 2375 kg m−3

Liquidus temperature Tl 930 K

Solidus temperature Ts 916 K

Specific heat (solid) Cp,s (0.46 T+766.17) J kg−1 K−1

Specific heat (liquid) Cp,l 1086 J kg−1 K−1

Latent heat of fusion Hf 3.95×105 J kg−1

Thermal conductivity(solid)

Ks (0.028 T+65.32) W m−1 K−1

Thermal conductivity(liquid)

Kl (0.028 T+65.32) W m−1 K−1

Electrical conductivity σ 3.76×107 1Ω−1 m−1

Equivalent heat-transfercoefficient

h 35 W m−2 K−1

Boltzmann constant kb 1.38×10−23 J K−1

Elementary charge e 1.602×10−19 C

Fig. 2 Calculated current density vectors for a 6.3-mm-long arc at 200 Å


2.3 Experimental procedure

Stationary GTAwelds were performed on center of 40×40×5 mm plates of commercial pure aluminum. The weldingelectrode was made of EWTh-2 with 3 mm in diameter andhigh purity argon was used as the shielding gas. DCENpolarity at two different current levels, 100 and 130 Å wereused for welding. The arc lengths were selected to be 2 and4 mm. After welding, the welded samples were cut from thecenterline of plates and prepared by polishing to 1 μm finish.

Finally, to reveal the shape and size of the weld pool, thecross-sections of the weldments were etched chemically inKeller’s reagent.

3 Results and discussion

This section is divided into two parts. The first part presentsthe results of arc model for two different anode materials.Since most of the previous arc models were concerned with

0

0.002

0.004

0.006

0.008

0.01

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

Radial distance (m)

Axi

al d

ista

nce

(m

)

11000K (this study)12000K (this study)13000K (this study)14000K (this study)15000K (this study)17000K (this study)19000K (this study)21000K (this study)11000K (Hsu et al)12000K (Hsu et al)13000K (Hsu et al)14000K (Hsu et al)15000K (Hsu et al)17000K (Hsu et al)19000K (Hsu et al)21000K (Hsu et al)

Fig. 3 Calculated temperaturecontours in comparison withexperimental data [16], for a 10-mm-long arc at 200 Å with acopper anode

0

0.002

0.004

0.006

0.008

0.01

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

Radial distance (m)

Axi

al d

ista

nce

(m

)

11000K (Copper anode)12000K (Copper anode)13000K (Copper anode)14000K (Copper anode)15000K (Copper anode)17000K (Copper anode)19000K (Copper anode)21000K (Copper anode)11000K (Aluminium anode)12000K (Aluminium anode)13000K (Aluminium anode)14000K (Aluminium anode)15000K (Aluminium anode)17000K (Aluminium anode)19000K (Aluminium anode)21000K (Aluminium anode)

Fig. 4 Comparison of calculatedtemperature contours betweencopper and aluminum anodes fora 10-mm-long arc at 200 Å


copper anode, firstly an arc model is developed for copperanode to compare and verify the results of present arc modelwith previous studies data. Then, an arc model for aluminumanode is developed to compute the heat flux and currentdensity to aluminum anode. Subsequently, in the second part,the results of the weld pool model are presented. The effects ofwelding current and arc length on the weld pool geometry arealso considered. Finally, in order to check the validity of the

weld pool model, calculated results, and experimental datawould be compared.

3.1 Results of the arc model

Figure 2 shows current density distribution for the200 Å arc with 6.3 mm arc length. As shown, thewelding current travels from the surface of the anodeand enters the cathode spot along the arc column. Thecurrent density achieves its greatest value at the vicinity ofcathode spot.

The temperature contours predicted for a 10-mm-long arcat 200 Å with a copper anode are shown in Fig. 3 where theexperimental result of Hsu et al. [16] is also given for com-parison. This graph shows a fairly good agreement between

Fig. 5 Calculated velocity profile for a 6.3-mm-long arc at 200 Å

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

0 0.002 0.004 0.006 0.008Radial distance (m)

Axi

al d

ista

nce

(m

)

10Pa (Copper anode)

100Pa (Copper anode)




10Pa (Aluminium anode)





10Pa (Goodarzi results)





Fig. 6 Calculated pressurecontours for a 10-mm-long arc at200 Å in the case of copper andaluminum anodes andcomparison with results ofGoodarzi [11]

0

100

200

300

400

0 0.002 0.004 0.006 0.008 0.01

Axial distance (m)

Axi

al v

elo

city

(m.s

-1)

This study (copper anode)This study (aluminium anode)Hsu et al (calculated)Ramirez et al (calculated)Lago et al (calculated)

Fig. 7 Variation of axial velocity along the symmetry axis for a 10-mm-long arc at 200 Åwith copper and aluminum anodes and comparisonwithother calculation results [3, 16, 17]


calculated and experimental values except for the region closeto the electrodes.

Figure 4 demonstrates the effect of anode material ontemperature contours. As seen, temperature contours are alittle wider in the case of aluminum anode and the differencebetween these contours becomes lower in region near thesymmetry axis. But, generally, there is a little differencebetween temperature contours of copper and aluminumanodes.

The corresponding velocity vectors of plasma flow for a10-mm-long arc at 200 Å are displayed in Fig. 5. As seen,firstly the plasma flows downward along the symmetry axisand then due to the stagnation effect at the anode, deflectsand flows radially outward along the free surface of anode.The maximum calculated velocity of the plasma flow is272 m s−1.

In Fig. 6, the pressure distribution of plasma for copper andaluminum anodes for a 10-mm-long arc at 200 Å is comparedwith the results of Goodarzi [11] that is for copper anode. Aswould be expected, the maximum pressures are located at thefront of the electrode and near the weld pool surface. In total,there is a fairly good agreement between our results and theresults of Goodarzi. It is interesting to see that there is a littledifference between pressure contour of copper anode and

aluminum anode and this difference becomes lower close tothe symmetry axis.

In Fig. 7, the variations of axial velocity with axial distancefor two anode materials are compared with some calculatedresults [3, 16, 17]. There is mostly no difference between theplots related to copper and aluminum anodes. There is a betteragreement between our data with the results of Hsu et al. [16]rather than other results.

The radial variations of velocity along the anode surface forboth anode materials are presented in Fig. 8. As shown, radialvelocity in the case of aluminum anode is higher than copperanode.

The distribution of radial velocity along the surface of theanode is plotted in Fig. 9. As seen, the anode material has asmall effect on the variation of temperature along the symme-try axis. In addition, some other calculated results are present-ed for comparison so that all of them are related to a copperanode. The agreement is rarely good especially with theresults of Ramirez et al. [17].

The variations of pressure with axial distance and radialdistance compared with other calculated results [16, 17, 32]are indicated in Figs. 10 and 11, respectively. As a result, theanode material has a small effect on pressure distributions of

Fig. 8 Variation of radial velocity along the anode surface for a 10-mm-long arc at 200 Å for the case of copper and aluminum anodes

0

4000

8000

12000

16000

20000

24000

0 0.002 0.004 0.006 0.008 0.01

Axial distance (m)

Tem

pra

ture

(K

)

This study (copper anode)

This study (aluminium anode)

Hsu et al (calculated)

Ramirez et al (calculated)

Fig. 9 Variation of temperature along the symmetry axis for a 10-mm-long arc at 200 Å for the case of copper and aluminum anodes andcomparison with other calculation results [16, 17]

0

200

400

600

800

1000

0 0.002 0.004 0.006 0.008 0.01

Axial distance (m)

Pre

ssu

re (

Pa)



Hsu et al (calculated)Ramirez et al (calculated)

Lee and Na (calculated)

Fig. 10 Variation of pressure along the symmetry axis for a 10-mm-longarc at 200 Å for the case of copper and aluminum anodes and comparisonwith other calculation results [16, 17, 32]

0

100

200

300

400

500

600

0 0.002 0.004 0.006 0.008 0.01

Radial distance (m)

Pre

ssu

re (

Pa)



Ramirez et al (numerical)

Lee and Na (numerical)

Fig. 11 Variation of pressure along the anode surface for a 10-mm-longarc at 200 Å for the case of copper and aluminum anodes and comparisonwith other calculation results [17, 32]


plasma on the anode. It is also seen that the agreement is betterin the case of the results of Lee and Na [32] than in othercalculated results.

Figure 12 shows the variations of azimuthal component ofmagnetic field versus radial distance from the symmetry axis ofarc in different distances from the cathode surface. The resultsof Ramirez [18] are also illustrated for comparison. There is afairly good agreement, especially close to the anode surface.

Figure 13 presents the evaluations of radial component ofthe current density with radial distance from the symmetryaxis of the arc in different distances from the cathode surface.The results of Ramirez [18] are also illustrated for comparison.As seen, there is a fairly good agreement, especially close tothe anode surface.

Figure 14 represents the distribution of the anode currentdensity for a 6.3-mm arc at 200 Å. In this graph, the experi-mental results of Nestor [33] and some calculated results [17,18] are also presented for comparison. The results of Nestor arefor 1 % thoriated tungsten electrode having a pointed tip of 30°as the cathode and a water-cooled copper plate as the anode.

As seen, the maximum anode current density is a bit higherin the case of copper anode than aluminum anode. It is alsoobserved that the distribution of anode current density is widerin the case of aluminum anode than copper anode.

Figure 15 shows the anode total flux (heat transferred fromthe arc to the workpiece) for a 6.3-mm arc at 200 Å.Experimental results of Nestor [33] and some calculated re-sults [17, 26] are also represented for comparison. The resultsof Nestor are for 1 % thoriated tungsten electrode having apointed tip of 30° as the cathode and a water-cooled copperplate as the anode.

The anode total flux is the most important arc propertyneeded to simulate the weld pool. As seen in Fig. 15, our resultis closer to experimental result of Nestor [33] than previouscalculated results [17, 26]. As well, the maximum heat fluxand the distribution of heat flux are higher and wider in thecase of copper anode than aluminum anode, respectively.

In Fig. 16, the contributions of heat flux to anode for twodifferent anode materials are illustrated and compared withcalculated results of Goodarzi [11]. As shown, electron andconvection contribution of the heat flux is higher and radiationone is lower in the case of copper anode than aluminum anode.

Figure 17 shows the percentage of anodic heat flux contri-butions in the case of copper and aluminum anode. As seen,

-0.04

-0.03

-0.02

-0.01

0

0 0.002 0.004 0.006 0.008 0.01

This study (Z=0mm)This study (Z/L=0.25)This study (Z/L=0.5)This study (Z/L=1)Ramirez et al (Z=0mm)Ramirez et al (Z=0.25)Ramirez et al (Z=0.5)Ramirez et al (Z=1)

Radial distance (m)

B (

tesl

a)

Fig. 12 Radial distribution of azimuthal component of magnetic field fora 10-mm-long arc at 200 Å in the case of copper anode and comparisonwith results of Ramirez et al. [18]

-5

-4

-3

-2

-1

0

0 0.002 0.004 0.006 0.008 0.01Radial distance (m)

Rad

ial c

urr

ent

den

sity

(A

.mm

-2)

This study (Z/L=0.25)



Ramirez et al (Z/L=0.25)



Fig. 13 Radial distribution of radial component of current density for a10-mm-long arc at 200 Å in the case of copper anode and comparisonwith results of Ramirez et al. [18]

0

1

2

3

4

5

6

0 0.002 0.004 0.006 0.008 0.01

An

od

e cu

rren

t d

ensi

ty (

A.m

m-2

) Copper anodeAluminium anode

Nestor (experiment)Olsen (experiment)

Ramirez (calculated)

Radial distance (m)

Fig. 14 Distribution of anode current density for a 6.3-mm-long arc at200 Å for the case of copper and aluminum anodes and comparison withother calculation results [12, 13, 33]

0

10

20

30

40

50

60

70

0 0.002 0.004 0.006 0.008 0.01

Radial distance (m)

An

od

e to

tal f

lux

(W.m

m-2)

Copper anodeAluminium anodeNestor (experimental)Ramirez et al (calculated)Kim et al (calculated)

Fig. 15 Distribution of anode total flux for a 6.3-mm-long arc at 200 Åfor the case of copper and aluminum anodes and comparison with othercalculation results [17, 26, 33]


for both cases of anode material, the percentage of electronflux increases first and then decreases sharply until it reaches anearly constant value. But the percentages of convection andradiation flux change in reverse. The other important point isthat the radius of these sharp changes is about 0.007 m that isprobably related to the effective radius of the arc on the anodesurface.

Figure 18 reveals the variations of shear stress on anodesurface for a 6.3-mm-long arc at 200 Å and comparison withsome other theoretical results [11, 18]. As seen, the shearstress is higher for aluminum anode than copper anode.

3.2 Results of weld pool model

3.2.1 Calculated results

To check the arc model in the case of aluminum anode, thecurrent density and heat flux on the anode surface werecalculated from the arc model for 100- and 130-Å arcs atlengths of 2 and 4 mm. These results are shown in Figs. 19

and 20, respectively. As seen, as the electric current increasesand the arc length decreases, the maximum of current densityand heat flux at the anode increases. Moreover, distributionradius of current density and heat flux increases with increas-ing the electric current and arc length.

Figure 21 shows typical current density vectors in theworkpiece for 100 Å arc of 2 mm length. As shown, thecurrent density achieves its greatest value at the center pointof the weld pool surface where the arc is concentrated above.

The calculated temperature contours in the workpiece for a100-Å arc of 2 mm length at the fourth second of welding timeare shown in Fig. 22.

Figure 23 shows the effects of arc parameters included thearc current, the arc length and the welding time on the dimen-sions of calculated weld pool. As would be expected, bothdepth and width of the weld pool are increased by increasingthe welding time. In addition, by increasing the electric cur-rent, the depth and width of the weld pool increase. The reasonis that increasing the arc current results in an increase in heatinput to the workpiece, and besides, by increasing the currentdensity entered into the workpiece, heat produced due to jouleeffect will be increased. It can also be seen from this figure that

0

10

20

30

40


An

od

e fl

uxe

s (W

.mm

-2)

Electrons (copper anode)Electrons (aluminium anode)Electrons (Goodarzi)

Convection (copper anode)Convection (aluminium anode)Convection (Goodarzi)Radiation (copper anode)

Radiation (aluminium anode)Radiation (Goodarzi)

Fig. 16 Contributions of anode heat flux for a 6.3-mm-long arc at 200 Åin the case of copper and aluminum anodes and comparison with resultsof Goodarzi [11]

Fig. 17 Percentage of heat flux contributions for a 6.3-mm-long arc at200 Å in the case of copper and aluminum anodes

0

10

20

30

40

50

60

70


Sh

ear

stre

ss (

N.m

-2)

This study (copper anode)This study (Aluminium anode)Ramirez et al

GoodarziWesthofe

Fig. 18 Contribution of shear stress on the anode surface for a 6.3-mm-long arc at 200 Å in the case of copper and aluminum anodes andcomparison with other calculated results [11, 18]

0

5

10

15

20

0 0.002 0.004 0.006Radial distance (m)

An

od

e cu

rren

t d

ensi

ty (

A.m

m-2

)

I=100A, L=2mm

I=100A, L=4mm

I=130A, L=2mm

I=130A, L=4mm

Fig. 19 Distribution of anode current density in the case of aluminum anode


increasing the arc length decreases the weld depth but theresults did not show a distinguishable relation between thearc length and the weld width.

3.2.2 Comparison between the calculated resultsand the experimental data

Figure 24 shows comparison between calculated and experi-mental weld pool depth and width for 100 and 130-Å arcs of2 mm length. Furthermore, the percentage of difference be-tween calculated and experimental data is given in Table 4.There are some differences between calculated and experi-mental results. As reported in previous literatures [7, 8, 13,14], both heat conduction and fluid flow affect the weld poolshape. The effect level of each one is depends on the type ofmaterial and the welding parameters. As a result, the mainreason of these differences is probably due to the assumptionof ignoring the fluid flow in the weld pool model. However,the percentage differences are totally lower than 17 %. Itmeans that the agreement between the predicted and experi-mental results is fairly good. So, it can be guessed that for purealuminum in the range of applied welding parameters, the heatconduction is the dominant mechanism of heat transfer information of the weld pool. The reason can be caused by highthermal conductivity of pure aluminum.

4 Conclusions

This study can be divided into two parts. In the first part, a 2Dnumerical model was constructed to predict heat transfer andfluid flow in the arc for both cases of copper and aluminumanodes. In the second part, a 2D model considering only heatconduction was developed for the weld pool in pure aluminumto calculate the weld pool dimensions. The major conclusionstaken from these investigations are summarized as follows:

1. The calculated results are in a fairly good agreement withthe previous theoretical results and corresponding exper-imental data for both arc and weld pool model.

0

30

60

90

120

150

180

0 0.002 0.004 0.006Radial distance (m)

An

od

e to

tal f

lux

(W.m

m-2

)

I=100A, L=2mm

I=100A, L=4mm

I=130A, L=2mm

I=130A, L=4mm

Fig. 20 Distribution of anode total flux in the case of aluminum anode

Fig. 21 Calculated current density vectors in the workpiece for 100Å arcof 2 mm length

Fig. 22 Calculated temperature contours in the workpiece for a 100Å arcof 2 mm length at the fourth second of welding

0

0.5

1

1.5

2

1 2 3 4 5Time (s)

Dep

th o

f wel

d po

ol (m

m)

I=100A, L=4mm I=130A, L=4mmI=100A, L=2mm I=130A, L=2mm

1

1.5

2

2.5

3

1 2 3 4 5Time (s)

Hal

f w

idth

of

Wel

d p

oo

l (m

m)

I=100A, L=4mm I=130A, L=4mm

I=100A, L=2mm I=130A, L=2mm

(a)

(b)

Fig. 23 Effects of welding parameters on a weld pool depth and b halfwidth of weld pool


2. The effects of welding parameters and anode material onthe arc properties are studied. Some results are the samefor both copper and aluminum anode cases. However,radial velocity and shear stress on the anode surface werelager in the case of aluminum anode than copper one. Inaddition, regarding the anode current density and heat fluxto the anode, the maximum value is lower and the distri-bution is wider in the case of aluminum anode than copperanode.

3. The results show that both the depth and width of the weldpool increases with increasing arc current and weldingtime. Furthermore, increase in the arc length results indecrease in the weld pool depth.

4. It can also be guessed that for pure aluminum in the rangeof applied welding conditions, the heat conduction is the

dominant mechanism of heat transfer in the weld pool.The reason is probably high thermal conductivity of purealuminum.

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Fig. 24 Comparison between calculated and experimental depth and halfwidth of the weld pool for 100 and 130 Å arcs of 2 mm length

Table 4 Percentage of difference between calculated and experimentalweld pool dimensions for 100 and 130 Å arcs of 2 mm length

Welding time (s) Depth of weld pool (%) Width of weld pool (%)

I=100 Å I=130 Å I=100 Å I=130 Å

2 16.9 13.80 16.50 14.30

3 16.70 15.60 4.40 4.50

4 15.60 14.30 2.90 10.60


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experimental study and numerical modeling of arc and weld pool in stationary gta welding of pure...

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