Arc characteristics in gasmetal arc welding of aluminum using argon as theshielding gasP. G. Jönsson, R. C. Westhoff, and J. Szekely Citation: Journal of Applied Physics 74, 5997 (1993); doi: 10.1063/1.355213 View online: http://dx.doi.org/10.1063/1.355213 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/74/10?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Effects of Shielding Gas on Absorption Energy of NdYAG Laser for Aluminium Welding AIP Conf. Proc. 899, 327 (2007); 10.1063/1.2733169 Synthesis of aluminum nitride films by plasma immersion ion implantation–deposition using hybridgas–metal cathodic arc gun Rev. Sci. Instrum. 75, 719 (2004); 10.1063/1.1646741 Modeling of temperature field and solidified surface profile during gas–metal arc fillet welding J. Appl. Phys. 94, 2667 (2003); 10.1063/1.1592012 Welding of ship structural steel A36 using a Nd:YAG laser and gas–metal arc welding J. Laser Appl. 12, 185 (2000); 10.2351/1.1309549 Analysis of arc pressure effect on metal transfer in gasmetal arc welding J. Appl. Phys. 70, 5068 (1991); 10.1063/1.349014

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Arc characteristics in gas-metal arc welding of aluminum using argon as the shielding gas

P. G. J6nsson Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

FL C. Westhoff The Aerospace Corporation, PO. Box 92957, Los Angeles, California 90009-2957

J. Szekely Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

(Received 30 November 1992; accepted for publication 20 July 1993)

A mathematical model has been developed describing transport phenomena in gas-metal arc welding. In the statement of the model a cylindrical electrode was considered and attention was concentrated on representing the electrodynamic, heat-transfer, and fluid-flow phenomena in the plasma column. Solutions were generated for the axisymmetric Maxwell’s equations, Navier- Stokes equations, and thermal-energy balance equation for variable properties. The specific system considered involved the use of an aluminum electrode and argon as the shielding gas. Several current levels were explored and the theoretical predictions of temperatures were found to be in good agreement with spectroscopically measured temperatures. This appears to have been the first time that gas-metal arc-welding problems were treated in such a fundamental manner.

I. INTRODUCTION

The purpose of the work described in this article is to present a comprehensive description of the electromag- netic, heat-flow, and fluid-flow phenomena that are en- countered in gas-metal arc-welding (GMAW) systems. It will be shown that in contrast to the quite-explored field of gas-tungsten arc-welding (GTAW) operations gas-metal arc-welding systems have been much less studied and that intrinsic differences exist between these operations.

In GTAW systems, sketched in Fig. 1, the arc is struck between an inert tungsten cathode and the weld pool, which serves as the anode. The cathode is inert, it retains its shape, and the thermal emission of electrons is thought to occur from a “cathode spot” the size and properties of which are usually computed from empirical relationships. The literature describing GTAW systems is quite extensive and in recent years quite comprehensive mathematical models have become available representing this operation.‘-’ More specifically, it has been shown that one may model these systems by writing down Maxwell’s equa- tions, coupled to the differential momentum and thermal- energy balance. The numerical solution of these equations then yields expressions for the spatial distribution of the potential, the current, heat generation, the velocity and the temperature profiles. Several studies have shown good agreement between the measurements and the theoretical predictions.“” The computations have been greatly aided by both the availability of fluid-flow software packages and a more ready access to a thermophysical data base for the property values. The principal fundamental problems that are not yet fully resolved pertain to the boundary condi- tions in the vicinity of the cathode and the anode regions. Clearly a rigorous account would have to represent the

non-thermal-equilibrium phenomena that take place in the anode and the cathode sheaths. Up to today, only a few analyses have dealt with these phenomena, in a one- dimensional manner.‘“14

Gas-metal arc welding, sketched in Fig. 2, is funda- mentally different from these systems, because here the consumable metal electrode is the anode and the metal pool serves as the cathode surface. This arrangement is predicated by the need to provide a rapid melting of the electrode, which is facilitated by the high rate of heat gen- eration in the near-anode area. Examination of the com- puted or measured temperature and velocity profiles for GTAW systems shows that the anode and the cathode regions behave in a totally different way. It follows that the reverse polarity employed in GMAW should provide ma- jor differences in behavior. In GMAW the situation is fur- ther complicated by the fact that rather than having a fixed cathode spot (or at least having a cathode spot that is confined to a relatively small region) found in GTAW systems, the cathode spots will move around the much larger surface of the weld po01.‘~~‘~ A further major differ- ence is that an essential feature of the GMAW systems is that we have to deal with a consumable electrode, the shape of which is continually changing. Indeed, fmding ways to control this change in shape and the droplet for- mation mechanism would be the ultimate objective of this research.

In the following we present a mathematical represen- tation of the transport phenomena in GMAW systems, together with the numerical solution of the resultant dif- ferential equations and a comparison of the theoretical pre- dictions with measurements.

5997 J. Appl. Phys. 74 (IO), 15 November 1993 0021-8979/93/74(10)/5997/10/$6.00 @ 1993 American Institute of Physics 5997 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

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?lectrode (cathode)

work&w weld pool (anode)

FIG. 1. A sketch of the GTAW system.

II. STATEMENT OF THE PROBLEM

Figure 3 shows a schematic sketch of the system, which is seen to consist of the anode, the arc column, and the cathode. The domain is so defined that allowance is made for the entrainment of the surrounding gases and also for a general interaction with the gaseous environ- ment.

In a physical sense we may consider the system such that current is passed from the anode to the cathode and that the resultant joule heating of the intervening gaseous medium will give rise to the plasma column. The actual temperature distribution in the plasma column will depend of the spatial rate of (joule) heat generation and on the convective and radiative heat transfer. In the first instance the anode is assumed to have a 6xed shape, thus electrode taper, droplet formation, and the like are not considered in this instance. While recognizing that such transient shape changes will modify the current density and the tempera-

- consumable electrode

P’a Cd

l- I

FIG. 2. A sketch of the GMAW system.

I anode Bi

j plasma j column

I H cathode

E

E

~ C

AIlf lOW

*

;

FIG. 3. Region of integration for arc model.

ture distribution, the modeling of the simplified case was thought to be an important intermediate step.

In the statement of the model we consider that surface AD is isopotential, while the current density is specified at surface IH.

A. Mathematical formulation of the arc

The following assumptions are made in the statement of the mathematical model.

(i) The arc is axially symmetric, so the governing equations can be written in two-dimensional cylindrical coordinates.

(ii) The operation of the arc is independent of time (i.e., steady state).

(iii) The arc is in local thermal equilibrium (LTE) (i.e., the electron and heavy-particle temperatures are very similar). Hsu and co-workers3.4 show that this assumption is accurate through most of a gas tungsten arc, except near the anode and cathode surfaces and in the fringes.

(iv) The arc plasma is pure argon at one atmosphere. (v) The gas flow is laminar. This can be justified in a

similar way used by McKelliget and Szekely for a GTAW system on the basis of laminar-turbulent transition of a free jet.’

TABLE I. Boundary conditions for the arc.

Figure 3 u W h cp

BC,CD,A D

DE

0 0 h.a WAD)

0 apw 4 a* -“---GO az --24j a2

EG apu -&-=O aw Yg=o

hi (inllow) ah -=Q ar

(outflow)

a4, ----co ar

IH Q 0 h,i Given by Eqs. (7), (91,

and (10)

HG 0 0 h $0 0

5998 J. Appl. Phys., Vol. 74, No. IO, 15 November 1993 Jl)nsson, Westhoff, and Szekely 5998

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(vi) The plasma is optically thin so that radiation may be accounted for using an optically thin radiation loss per unit volume.

(vii) The consumable electrode is cylindrical and the tip of the electrode and the workpiece surfaces are flat.

(viii) The influence of metal droplets is neglected. (ix) The consumable electrode is in a quasisteady

state.

B. Transport equations for the arc

According to the above assumptions the governing transport equations for the arc may be expressed in cylin- drical coordinates as

conservation of mass:

1 J(P~) ) d(pw)-O I- r & 2lz ’ (1)

where p is the mass density, r is the radial distance, z is the axial distance, and u and w are the radial and axial velocity components, respectively;

conservation of radial momentum:

1 a(pru”) +d(puw) E- r &

-=-$+[t$(pr$)-p; az

+g [(g+$)]) -JA (2)

where P, p, J,, and Be are the pressure, viscosity, axial current density, and self-induced azimuthal magnetic field, respectively;

conservation of axial momentum:

(3)

where J, is the radial current density; conservation of thermal energy:

1 a(pruh) d(pzuh) r dr +-a-

where h is the enthalpy, k is the thermal conductivity, Cp is the specitic heat at constant pressure, o, is the electrical conductivity, SR is the radiation loss term, kb is the Bolt- zmann constant, and e is the elementary charge;

conservation of charge continuity:

+.rg)+g (dg)=o, (5)

where @ is the electrical potential. The momentum equations consist of, from left- to

right-hand side, the two convective terms, the pressure gra- dient term, the diffusive term, and the electromagnetic body force term. The following energy equation consists of,

from left- to right-hand side, the two convective terms, the two diffusive terms, the Joule heating term, the radiation loss term, and the transport of enthalpy due to electron drift (Thompson effect). Finally, the charge continuity equation consists of two diffusive terms. The current den- sity J can be obtained from

J,=-q$, (7)

while the self-induced azimuthal magnetic field Be is de- rived from Ampere’s law as

where p. is the magnetic permeability of free space. The integration constant is assumed zero for Be-0 as r+O, since the integrand approaches zero as r-0.

C. Boundary conditions for the arc

A complete listing of the boundary conditions for the arc is presented in Table I.

D. Anode region (BC, CD, and DA)

A no-slip boundary condition is imposed for the mo- mentum boundary conditions. The enthalpy boundary con- dition h, is assumed to be the enthalpy corresponding to the melting temperature of pure aluminum, 933 K. From a practical point of view it is clear that the temperature in the anode varies, but this variation will not affect the stud- ied arc characteristics. Also, initial sensitivity calculations, using anode temperature values ranging between 300 and 933 K, showed that the calculated maximum velocities and temperatures within a 224 A arc differed by less than 0.5%. The only equation solved within the electrode region is the equation for the conservation of charge. Here, the region DA is taken to be isopotential (Q, =O) . This is based on the assumption that the conductivity in the metal is much higher than in the plasma and that the variation of the electric potential in the metal is much less than in the arc.

E. Anode region inflow (DE)

At the inflow region the momentum boundary condi- tions are straightforward. The expression a( pw)Gz is the gradient of mass flow and is assumed to be zero. This is analogous to the expression dw/az=O, except that the den- sity term is included in the former expression to ensure mass conservation, since the density of gas is temperature dependent. Also, the inlet gas enthalpy hi is assumed to be the enthalpy corresponding to a temperature of 300 K. Initial sensitivity analyses of the temperature of the inlet gas within a range of 300-1000 K show that the arc be- havior is not significantly affected. This has also been con- cluded by Hsu and co-workers.3

5999 J. Appl. Phys., Vol. 74, No. 10, 15 November 1993 JLinsson, Westhoff, and Szekely 5999 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

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O= Experiments

0 0 2 4 6 0 1 2 3 4 5 6

Radial distance (mm) Radial distance (mm)

20000 1111,11~1,11~1,11l1,l~~~,~~~~.

f = Calculations

0 = Experiment?

i

0 0 1 2 3 4 5 6

Radial distance (mm)

F. Cathode region (GM)

The no-slip conditions are used for the momentum equations at the solid boundaries. The cathode surface temperature is assumed to be the melting temperature of pure aluminum, 933 K, within the cathode spot region (weld pool region). The cathode surface temperature out- side the cathode spot region is arbitrarily assumed to be 600 K. This value is based on results from a sensitivity calculation, where it was shown that the calculated maxi- mum velocity and temperature values varied with less than 0.1% for temperature values of 300-933 K. Based on these temperatures the boundary conditions for the enthalpy within (IH), hc,i, and outside (HG), hc,o, the cathode spot region are taken at temperature values of 933 and 600 K, respectively. The radius of the cathode spot R, is defined as an average value representing the movement of the cathode spot. Theoretical calculations of the weld pool profiles showed that the weld pool radius is 3.2-3.5 mm for weld- ing currents of 150-220 A. 17,18 Based on these values of the weld pool radius, a sensitivity calculation was done to study the effect of the cathode spot radius on the calculated arc characteristics. It was shown that the calculated max- imum velocity varies less than 1.7% and the maximum

FIG. 4. Temperature as a fonction of radial position at three different heights above the workpiece: (a) 2.5 mm; (b) 5.0 mm; and.(c) 7.5 mm. The current is 150 A and the arc length is 10.0 mm.

temperature varies less than 0.1% for a 2.7-4.5 mm range of the cathode spot radius. Therefore, R, was chosen as 2.7 mm in this investigation.

It is assumed that a single value of the current density is valid within the cathode spot (weld pool) region and that the current density is zero outside the cathode spot region. This assumption is based on the strong dependence of the current density on surface temperature; the temper- atures in the weld pool region are substantially higher than in the rest of the work piece. Therefore, the current-density conditions at the cathode are given by

I Jc=a, r<Rcr

e (9)

J,=O, r> R,, (10)

where J, is the cathode current density and I is the welding current.

The electric potential boundary conditions at the cath- ode are derived using Bq. (7). The value of the axial cur- rent density in Eq. (7) is taken as the cathode current density given by Eqs. (9) and ( 10).

6000 J. Appl. Phys., Vol. 74, No. 10, 15 November 1993 Jbnsson, Westhoff, and Szekely 6000

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s 42

2 10000 i% E E

5000

+= Calculations *= Experiment8

I otf’l”,‘t”l’lt”“,i

0 2 4 6 6

Radial distance (mm)

(4 25ooopat, I,,, III, ,,,I I,,, I(,,

+ = Calculations c= Experiment8’

0 1 2 3 4 5 6

Radial distance (mm)

(b)

0. Arc column (Sf)

At the axis of symmetry, the following accepted boundary condit ions are used: zero radial velocity at the axis, and zero gradients of all other variable condit ions normal to the axis.

H. Arc, inflow, and outflow (EG)

Since it is not clear where outflow and inflow will oc- cur, zero radial mass flow [a( pu)/dr] and electric potential gradients are specified at the boundary. The boundary con- dition for enthalpy representing mass flowing into the sys- tem is taken as hi, which corresponds to a temperature value of 300 K. Although this value is arbitrary, initial calculations have shown that the arc behavior is not af- fected significantly by the choice of the enthalpy value. In fact, Hsu and co-workers found that the computed arc behavior does not change significantly whether enthalpies corresponding to temperature values of 1000 or 2000 K are u~ed.~ This is because the specitlc heat variation outside the arc column is very small (520 J/kg K at 1000-6000 K compared to 9310 J/kg K at 15 000 K) and does not rep-

,IIIf i ,“‘T”’ ,, I , I , , t

+ = Calcuiations O= ExDeriments3’ -

g 15000

0 1 2 3 4 5 6

Radial distance (mm)

(4

FIG. 5. Temperature as a function of radial position at three different heights above the workpiece: (a) 2.5 mm; (b) 5.0 mm; and (c) 7.5 mm. The current is 250 A and the arc length is 10.0 mm.

resent a large change to the energy equation. F inally, for outflow, the expression ah/& is assumed to be zero.

I. Source terms used at the cathode and the anode regions

1. Cathode

At the cathode boundary layer a nonlocal thermal- equil ibrium (non-LTE) condit ion is bel ieved to exist. This non-LTE condit ion is caused by a difference in tempera- ture between electrons and heavy partic1es.l’ For thermi- onic cathodes found in GTAW, a positive source term is used to approximate the energy used in the cathode bound- ary layer to ionize the plasma (thereby causing a drop in the electric potential). This term is expressed as’

a= IJCI vc, (11) where V, is the cathode fall voltage. However, in GMAW of aluminum the cathode is nonthermionic2’ and the cath- ode region is under high pressure due to the impinging plasma jet. The physics of the cathode fall region and the thermal balance at a nonthermionic cathode are not very well understood.21 Therefore, we have chosen to use a sim-

6001 J. Appl. Phys., Vol. 74, No. 10, 15 November 1993 JBnsson, Westhoff, and Szekely 6001

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6.0

1 loom 2 llcm

i 12ooo 13000

[mm] 5.0 4.0 3.0 2.0 1.0 0.0

(a)

6.0

[mm] 5.u 4.0 3.0 2.0 1.0 0.0

(b)

FIG. 6. Contour plots of the gas temperature at (a) 150 A (T,,,,- -21 510 K) and (b) 250 A (T-,-=26 410 K).

ilar treatment of the energy source term at the cathode boundary as is used in GTAW. This will be an approxi- mation, but initial sensitivity calculations showed that it will not affect the conditions in the arc column or in the anode region, where the highest temperatures exist. The following expression is used for the cathode fall voltage:’

(12)

where T,, is the decrease in electron temperature at the cathode g&en as

Tc,e= Tcg-- Teat,

The thermal-energy loss in the arc at the anode bound- ary is in general due to conduction, convection, radiation, and vaporization. In this investigation the heat loss due to radiation and vaporization is neglected; however, vaporiza- tion will be dealt with in a future study, as it has been shown by Dunn and Eagar that the metal-vapor content in the arc significantly affects the thermal and electrical con- ductivity for argon plasmas.‘3’”

The heat loss in the arc at the anode boundary is due to the Thompson effect and the combined effect of conduction and convection. This heat loss is represented by the follow- ing expression:

with Teat being the temperature of the cathode and Tc,* the temperature in the gas at a distance 0.1 mm from the cath- ode. This distance is the maximum experimentally ob- served thickness of the cathode fall region.22

Qa=;: LJr( Tag-- Tan> +A( Tas- Tan) 1

Toa-- Tan +ks 6 ’ ( 14)

2. Anode

The energy lost by the arc in the area close to the anode is due to electrical and thermal energy. The electri- cal energy is mainly transferred to the plasma (by making atoms vibrate faster) through joule heating. The effect of joule heating is accounted for in Q. (4), describing the conservation of thermal energy. The enthalpy of the elec- trons are accounted for in the form of the Thompson effect.

where the thst term is due to the Thompson effect and the second term is due the combined effect of conduction and convection. A single source term is used to account for the Thompson effect in the bulk and at the anode boundary given by Eq. (4). In Eq. ( 14)) T, is the temperature of the anode and Ta,g is the temperature in the gas at a distance 0.1 mm from the anode. This distance 6 is the maximum experimentally observed thickness of the anode fall

6002 J. Appl. Phys., Vol. 74, No. 10, 15 November 1993 JBnsson, Westhoff, and Szekely 6002

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3.75 -- Wm2.

l%w

-s

.

\

,

.- .

i I i 1 1 I I x \ 1 -. . . b . , % \

x \ . . . I > I - I I , . , l ,

1 3

1 8

k t

L %

. I

B I

L 1

1 I

1 d

* I

I I

. ,

s I I

c J

. ,

r .e

c -

- c

c c

- .a.

- c

I: ;, 4.0

I 1 \ i . . \ \ t 1 , \ . \ \ L \ \ \ 1 \ 1 3 I \ \ 1 b 1 I x 1 3 \ i i i b b L I I 1 1 1 I 1 : t t 1 f 1 I 4 l I I I l J

4 I

r /

.- /

- c

cc

cc

C I

iid

3.0

(4

8.0

6.0

- -4

6.31 hii rm2-

FIG. 7. Mass flow vector plots at (a) 150 A and (b) 250 A.

ra,,+ TarI Lg=---y--- *

8.0

6.0

region.” Furthermore, kg is the thermal conductivity taken at an average temperature of the gas TaVg given by

This approach is, of course, an approximation, since the parameters in Fq. (14) are dependent on the grid size; however, sensitivity analyses showed that in combination, the parameters are less dependent on the grid size. As a specific example, if the distance 6 is taken as 0.05 mm, the axial temperatures in the arc core are changed by 1.5%- 2.3% at locations 2.5-1.0 mm from the anode. It is also important to bear in mind that a LTE condition is assumed in the arc. Therefore, it is only an approximation to allow for non-LTE regions, and these are not truly dependent on grid size since we are not allowing for non-LTE effects. Actually, the approach is comparable to what is used in turbulence modeling, where approximate models are used to mimic the actual behavior of stress fields in wall regions.“‘.

As a practical matter, in the numerical solution of the equations the Thompson effect, conduction, and convec- tion were added as source term in the first cell bordering the anode. The Thompson effect was accounted for as a

source term, throughout the computational domain, but its formal inclusion in Fq. (14) serves to emphasize its im- portance, also at the phase boundary.

111. METHOD OF SOLUTION

The solution of the governing equations and boundary conditions was obtained using a modified version of ~/E/FIX. ~/E/FIX is a two-dimensional steady-state code , based on a finite-volume scheme.26 During a calculation the difference equations were solved by iteration until the difference of the residuals was less than 1%. Satisfaction within 1% was also met for all current balance calcula- tions. Since the nonlinear equations are highly temperature dependent, the relaxation parameters were continuously increased from values of 0.1 in the earlier iterations to values of 0.4 at later iterations.

A typical calculation used a 54 x 38 nonuniform mesh and required 9-12 hours of CPU time on-a VAX station 3 100. The properties for density, molecular viscosity, ther- mal conductivity, specific heat, and electrical conductivity were taken from tabulated data by Liuz7 (T < 25 000 K) and Devote” ( T > 25 000 K). The radiation loss S’, , was taken from experimental data by Evans and Tankin.29 The value of the electrical conductivity of aluminum, necessary

6003 J. Appl. Phys., Vol. 74, No. IO, 15 November 1993 Junsson, Westhoff, and Szekely 6003

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--4

2540 N/m2

-----* 750 N/m2

L 3.0

(4

. . . . _ . . r * _ ,~_,".~,,

. . .

.

.

. .

.

. * .

, *

.

.

.

Lml : :

5.0 4.0 3.0

(b)

. . .

. .,

. .,

. . .,

-. .,

. * .,

, ..,

. ..,

. . a,

. .,I

. .I,

. . .I . .,I . . I, . .I, . * * , . * * , . t 2 4 . .I,

. .I

. .I t., - ., . .*

. . .., L -WC F --.-

i4Lz 2.0

8.0

6.0

FIG. 8. Momentum flux vector plots at (a) 150 A and (b) 250 A.

for the solution of the equat ion of current continuity, was taken from Touloukian3’ as 9.26X lo6 (a m) -r at 933 K.

IV. RESULTS

Actual calculations were performed for argon arcs, us- ing currents ranging from 150 to 400 A. Aluminum was the electrode material, the electrode diameter was chosen as 1.2 m m , and the arc length as 10 m m . The argon shield- ing gas was assumed to enter the system at a linear velocity of 1 m /s. These values were chosen to correspond to the condit ions under which the experimental measurements were made, which are used to test theoretical predictions.31

current is 150 A. F igure 4(b) shows that the agreement between experimental and calculated temperature values is quite good at a location that is halfway between the elec- trode and the workpiece. The agreements at locations 2.5 and 7.5 m m above the workpiece [Figs. 4(a) and 4(c), respectively] are also good.

Smars and Acinger3* used time-resolved spectroscopic measurements to study the temperature in the arc. They measured the radial distribution of the relative intensity of a single neutral argon line at different distances from the workpiece. By using a relation between the time intensity and temperature, they calculated the temperature distribu- tion. The welding currents studied were 150 and 250 A, and the measurements were done at three different heights above the workpiece: 2.5, 5.0, and 7.5 mm.

Similarly, the experimental and calculated temperature values for a case where the current is 250 A are plotted in F igs. 5(a)-5(c). Here the agreement between measured and calculated values is quite good both at a 2.5 and 5.0 m m location above the workpiece. Although not as close in agreement as the lower height comparisons, the tempera- ture values at 7.5 m m height above the workpiece still represent reasonable agreement.

In F ig. 4 the temperature is plotted as a function of radial position at three different heights above the work- piece: (a) 2.5 m m ; (b) 5.0 m m ; and (c) 7.5 m m . Both the experimental values reported by Smars and Acinger3r and calculated values are given for a case where the welding

Additional temperature measurements in an argon/ a luminum arc, using a similar methodology as Smirs and Acinger, 3* have been rep or-ted by King and Howes.32 They measured the temperature at welding currents of 200 and 300 A at a location m idway between the electrode and the workpiece. Unfortunately, the authors did not report the arc length and diameter of the electrode that were used in the experiments; however, the measured temperatures at 200 and 300 A were reported as 15 000 and 23 000 K, respectively. Assuming an electrode diameter of 1.2 m m and an arc length of 10 m m the calculated values halfway between the electrode and the workpiece are 16 700 and

6004 J. Appl. Phys., Vol. 74, No. 10, 15 November 1993 Jtinsson, Westhoff, and Szekely 6004

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1-l

10.0

9.0

8.0

7.0

6.0

------I 3.0

10 /----

/-- ~-,' --I 1.0

.’ f” 11

---- 1 * I ,/I -c--I I 7-i 0.0

[mm1

10.0

8.0

6.0

[mmJ 5.0 4.0 3.0 2.0 1.0 0.0 bnJ 5.0 4.0 3.0 2.0 1.0 0.0

(a) (b)

FIG. 9. Contour plots of the electric potential at (a) 150 A (EP,,= - 11.70 V) and (b) 250 A (EP-= - 15.03 V).

20 600 K at 200 and 300 A, respectively. This is a reason- able agreement and it gives added credibility to the math- ematical model.

The temperature contours for two cases where the val- ues of the currents are 150 and 250 A are illustrated in Figs. 6(a) and 6(b). The shape of the contours looks sim- ilar to what can be seen in GTAW.2-” However, contra- dictory to GTAW, where the highest temperature in the arc is found at a location close to the cathode, the highest temperature in the gas-metal arc is found at a location close to the anode.

values of the electric potential, including the voltage drop in the electrode, at 150 and 250 A, are - 11.70 and - 15.03 V, respectively. However, the voltage drop in the electrode, calculated using the earlier-mentioned assumptions, is min- imal (0.04-0.07 V) compared to the total calculated volt- age drop. Therefore, the voltage drop in the arc column is given as - 11.66 V at 150 A and - 14.96 V at 250 A.

V. DISCUSSION

In Figs. 7(a) and 7(b) the mass flow (pw) vector plots for two cases representing 150 and 250 A welding currents are shown. The gas is entrained along the anode side and is accelerated toward the workpiece (cathode). Here it impinges and is directed toward the fringes of the system. This is also typically seen in modeling of mass flow for GTAW.” For the same two welding currents the mo- mentum flow (pi?) vectors are depicted in Figs. 8(a) and 8(b), respectively. These plots illustrate how the gas is accelerated in the direction of the workpicce partly by the momentum forces.

A mathematical representation has been developed to describe the electromagnetic force field, the temperature field, and the velocity fields in GMAW arc systems. This appears to be the first time that this problem has been addressed explicitly in this manner. While GMAW arcs do bear a similarity to the much more extensively studied GTAW arcs, there are substantial differences, because of the reverse polarity and the essential absence of a cathode spot in the GMAW systems.

The contours for the electric potential (EP) at 150 and 250 A welding currents are illustrated in Figs. 9(a) and 9 (b) . Here it can be seen that the voltage gradient is higher near the anode than in the arc column. Also, the maximum

Computed results were generated for a somewhat ide- alized system, where the anode was considered to consist of a cylindrical body, thus electrode taper and melting phe- nomena were not considered in the first instance. Further- more, assumptions were made to represent the anode fall and the cathode fall regions, without a detailed consider-

6005 J. Appl. Phys., Vol. 74, No. 10, 15 November 1993 Jt)nsson, Westhoff, and Szekely 6005

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ation of the non-LTE effects that are almost certain to prevail there.

The computed results for the temperature were found to be in excellent agreement with experimental measure ments, which augurs well for the broader, more detailed application of this approach. It should be remarked that as seen in Fig. 5(c) at the higher-current levels, close to the anode surface the theoretical predictions tend to give higher temperatures than measured in practice. This be- havior is consistent with the postulate that at the higher- current levels the rather more frequent metal droplets will have a more pronounced cooling effect.

Having established a framework representing the transport phenomena in the plasma column, which agrees well with measurements, we may now consider the logical extension of this modeling effort in the following direc- tions.

(i) We may now treat the weld pool region in GMAW systems in a similar quantitative manner as has been done for GTAW systems, where models of the arc have been coupled with models of the weld po01.“~“~-~~ Up to the present time this was not possible, because the surface boundary conditions at the weld pool were not available.

(ii) We can now predict the plasma drag and the JX B forces and their effect on tapering, droplet, formation and also droplet detachment and acceleration.

(iii) We can calculate the current density and the ther- mal flux distribution at the anode surface and address the actual melting, taper, and droplet formation phenomena on a fundamental basis.

ACKNOWLEDGMENT

The authors wish to thank the Materials Reliability Division at the National Institute of Standards and Tech- nology (NIST) in Boulder, Colorado for financial support of this study.

‘S. Ramakrishnan and B. Noun, J. Phys. D 13, 1845 (1980). ‘C. J. Allum, J. Phys. D 14, 1041 (1981). ‘K. C. Hsu, K. Etemadi, and E. Pfender, J. Appl. Phys. 54,1293 (1983).

4K. C Hsu and E. Pfender, J. Appl. Phys. 54, 4359 (1983). 5P. Kovitya and J. J. Lowke, J. Phys. D 18, 53 (1985). 6P. Kovitya and L. E. Cram, Weld. J. 12, 34 (1986). ‘J. McKelliget and J. Szekely, Met. Trans. A 17, 1139 (1986). “G. N. Haddad and A. I. D. Farmer, J. Phys. D 17, 1189 (1984). ‘R. C. Westhoff, S.M. thesis, Dept. of Materials Science and Engineer-

ing, MIT, Cambridge, MA, 1989. lo R. C. Westhoff, D.Sc. thesis, Dept. of Materials Science and Engineer-

ing, MIT, Cambridge, MA, 1989. “R. T. C. Choo, J. Szekely, and R. C. Westhotf, Met. Trans. B 23, 357

(1992). “H. A. Diiulescu and E. Pfender, J. Appl. Phys. 51, 3149 (1980). i3C. Delalondre and 0. Simonin, J. Phys. (Paris) Colloq. 51, C5-199

(1990). 14P. Zhu, J. J. Lowke, and R. Morrow, J. Phys. D 25, 1221 (1992). “A. E. Guile, Proc. IEEE 118, 1131 (1971). 16A. E. Guile, Proc. IEEE 131, 450 (1984). “T. Zacharia, A. H. Eraslan, and D. K. Aidun, Weld. J. 68, 18s (1988). “K. C. Tsao and C. S. Wu, Weld. J. 68, 70s (1988). i9K. C. Hsu and E. Pfender, J. Appl. Phys. 54, 3818 (1983). 20A. E. Guile, in The Physics of Welding, edited by J. F. Lancaster (Per-

gamon, Oxford, 1986), p. 120. *‘J. F. Lancaster, in The Physics of E’eyelding edited by J. F. Lancaster

(Pergamon, Oxford, 1986), p. 146. uW. Fmkelnburg and S. M. Segal, Phys. Rev. 83, 582 (1951). 23G. J. Dunn, S.M. thesis, Dept. of Materials Science and Engineering,

MIT, Cambridge, MA, 1984. r4G. J. Dunn and T. W. Eagar, Met. Trans. A 17, 1865 (1986). “B. E. Launder, W. C. Reynolds, W. Rodi, J. Mathieu, and D. Jeandel,

Turbulence Models and their Applications (Editions Eyrolles, Paris, 1984), Vol. 2.

z6W. M. Pun and D. B. Spaldiig, Rep. No. HTS/76/2, Heat Transfer Section, Dept. of Mechanical Engineering, Imperial College, London, 1916.

“C. F. Liu, Ph.D. thesis, Dept. of Mechanical Engineering, University of Minnesota, Minneapolis, MN, 1977.

=R. S. Devoto, Phys. Fluids 16, 616 (1973). 29D. L. Evans and R. S. Tankin, Phys. Fluids 10, 1137 (1967). 3oY. S. Touloukian, The Elements, Thermophysical Properties of High

Temperature Solid Materials (MacMillan, New York, 1967). 3’E. A. Sm&rs and K. Acinger, International Institute of Welding, Rep.

No. 212-162-68, 1968. ‘*L. A. King and J. A. Howes, Physics of the WeZding Arc (The Institute

of Welding, London, 1962), p. 180. 33R T. C. Choo, D.Sc. thesis, Dept. of Materials Science and Engineer-

ing, MIT, Cambridge, MA, 1991. 34R. T. C. Choo, J. Szekely, and S. A. David, Met. Trans. B 23, 371

(1992). “R. T. C. Choo and J. Szekely, Weld. J. (to be published).

6006 J. Appl. Phys., Vol. 74, No. 10, 15 November 1993 Jansson, Westhoff, and Szekely 6006

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