The effects of metal vapour in arc welding Anthony B Murphy CSIRO Materials Science and Engineering, PO Box 218, Lindfield NSW 2070, Australia Email: tony.murphy@csiro.au Abstract Metal vapour is formed in arc welding processes by the evaporation of molten metal in the

weld pool, and in the case of gas–metal arc welding, in the wire electrode and droplets. The

presence of metal vapour can have a major influence on the properties of the arc and the size

and shape of the weld pool. Previous experimental and computational work on the production

and transport of metal vapour in welding arcs, in particular those relevant to gas–metal arc

welding and gas–tungsten arc welding, are reviewed. The influence of metal vapour on the

thermodynamic, transport and radiative properties of plasmas is discussed. The effect of metal

vapour on the distributions of temperature, current density and heat flux in arcs is examined

in terms of these thermophysical properties. Different approaches to treating diffusion of

metal vapour in plasmas, and the production of vapour from molten metal, are compared. The

production of welding fume by the nucleation and subsequent condensation of metal vapour is

considered. Recommendations are presented about subjects requiring further investigation,

and the requirements for accurate computational modelling of welding arcs.

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1 Introduction

Arc welding is a very important industrial process that is used to join metals. An arc is struck

between two electrodes, one of which is the workpiece, i.e. the pieces of metal that are being

joined. The high energy flux from the arc melts a region of the workpiece, forming the weld

pool. While there are many arc welding processes, such as flux-core arc welding and manual

metal arc welding, the two most widely used in automated processes are gas–metal arc

welding (GMAW) and gas–tungsten arc welding (GTAW). The great majority of diagnostic

and modelling efforts have concentrated on these two variants, and they will be the focus of

this review. Further, while welding can be performed at pressures well above atmospheric (for

example in underwater environments), the vast majority is undertaken at atmospheric pressure,

and only such cases will be considered.

Figure 1 shows schematic diagrams of the two processes. In the following it will be assumed

that the workpiece is the lower electrode, as is usual in welding. In GMAW, the upper

electrode is a metal wire. The wire, which is continuously fed to maintain an approximately

constant arc length, melts to form droplets that fall through the arc to the weld pool. The

standard polarity for GMAW is electrode positive; i.e. the wire is the anode, and the

workpiece is the cathode. Electrode-negative operation increases the melting rate of the wire,

but it is normally difficult to maintain a stable arc in this case [1]; this problem can be

ameliorated by using a cored wire containing metal oxides.

GMAW techniques can be classified depending on the mode of metal transfer from the wire

to the weld pool. In dip transfer, also known as short-arc transfer, the wire is fed at a rate

faster than it is melted by the arc, so that it eventually bridges the arc gap and reaches the

Figure 1. Schematic diagram illustrating the (a) gas–tungsten arc welding and (b) gas–metal arc welding processes.

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weld pool. The resistive heating of the short circuit heats and ruptures the thin filament of

metal bridging the gap, and the arc is re-established until the cycle is repeated. While the

current is high (200 A to 400 A) when the short circuit is established, the mean current is

typically below 100 A, and the heat transfer is low.

In other modes of transfer, there is always a gap between the wire and weld pool. At lower

currents, large droplets form at the end of the wire, and subsequently detach and fall through

the arc; this is termed globular transfer. As the current increases, there is a transition to spray

transfer, in which smaller droplets are formed and detach more frequently, up to a few

hundred times per second. The transition current depends on the diameter and composition of

the wire and the shielding gas composition, but is typically between 140 A and 280 A [1]. Use

of pulsed currents allows spray-type transfer to be achieved at lower average currents; one-

drop-per-pulse mode is widely used in automated processes. The arc length varies as the

droplet forms and detaches, but is typically less than about 5 mm.

GMAW is also known as metal–inert-gas (MIG) welding or metal–active-gas (MAG) welding,

depending on whether the shielding gas is inert (e.g., argon or helium) or active (containing

oxygen or carbon dioxide).

In GTAW the upper electrode it is made of a refractory material, usually tungsten, that does

not melt. If reinforcement of the weld is required, a metal filler rod is inserted in the arc close

to the workpiece. The tungsten cathode is usually doped with a rare-earth oxide, such as

thoria, to decrease the work function and thereby increase the current density at a given

temperature. The standard polarity for GTAW is electrode negative; i.e. the tungsten electrode

is the cathode and the workpiece is the anode. The usual shielding gases are argon, helium, or

argon–helium mixtures. In some cases, hydrogen may be added, but it is not possible to add

oxygen or carbon dioxide because this will rapidly erode the tungsten cathode. The addition

of helium or hydrogen increases the heat flux density to the workpiece [1,2]. Arc currents

range from around 100 A to 400 A, welding speeds can up to around 10 mm s-1, depending on

the current, and arc lengths are typically 1.5 mm to 4 mm [1]. GTAW is also known as

tungsten–inert-gas (TIG) welding.

Arc temperatures in GTAW are generally around 20 000 K just below the cathode, falling to

about 15 000 K just about the anode, and decreasing rapidly in the radial direction [3,4,5].As

will be discussed in this review, the influence of metal vapour in GMAW arcs generally leads

to much lower temperatures. In both GTAW and GMAW, the high current density at the tip

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of the upper electrode drives a strong downwards convective flow, with velocities reaching

200 m s-1 at 150 A, and more for higher arc currents [5].

It is well known that large amounts of metal vapour are produced in arc welding, particularly

in GMAW. In GTAW the only significant source of vapour is from the weld pool, while in

GMAW, vaporization of the wire electrode and droplets are additional sources. The metal

vapour is important for a number of reasons. It may lead to cooling of the arc through effects

including increased radiative emission, and also changes the electrical conductivity and other

properties of the arc. All of these effects lead to changes in the transfer of energy and current

to the workpiece, and thus the size and shape of the weld pool. Further, metal vapour is the

main precursor in the production of welding fume, which is an important occupational health

problem.

The presence and influence of metal vapour in arcs has been studied over many years, but has

recently become re-established as a focal point of research into arc welding, and thermal

plasmas more generally. A comprehensive understanding of the problem presents many

difficulties. Experimentally, the presence of both metal vapour atoms and ions and those of

the shielding gas makes spectroscopic measurements more difficult, since emission depends

on both the metal vapour concentration and the local temperature. Other diagnostic

approaches, such as laser scattering, also become more complicated in the presence of metal

vapour. Computational modelling of arcs in the presence of metal vapour requires treatment

of vaporization of the metal and the transport of metal vapour species, as well as the effects of

metal vapour on the thermodynamic, transport and radiative properties of the plasma. All of

these provide additional complications, and the choice between the available data and

methods is often difficult.

Metal vapour is an important factor in many other processes that use thermal plasmas. There

is a wide range of applications in which metal vapour is an essential component of the process.

An obvious example is arc lighting; for example high-intensity discharge (HID) lamps use the

emission from mercury, often together with other metals such as sodium, scandium and

indium, to provide the intense emission required in applications such as floodlighting, street

lighting, commercial lighting and video and data projection [6]. Metal vapour is an important

precursor in methods that use plasmas for nanoparticle production [7,8]. Laser ablation

methods for thin film deposition [9] and analytic chemistry [10] typically involve the

generation of plasmas with high metal vapour concentrations. Inductively-coupled plasma

atomic emission spectrometry (ICP-AES) [11,12] and inductively-coupled plasma mass

5

spectrometry (ICP-MS) [12,13] use the generation of metal vapour plasmas for the purposes

of analytic chemistry.

There are other thermal plasma applications in which, like arc welding, the appearance of

metal vapour is incidental to the process, but nonetheless significant. The importance of metal

vapour in the arcs that are formed by erosion of the electrodes in circuit breakers has been

demonstrated experimentally (e.g. [14]). Computational studies have been presented of the

influence of electrode vaporization in high-voltage SF6 [15,16] and low-voltage air circuit

breakers [17] and of the evaporation of metal droplets ejected from the contacts in gas-blast

circuit breakers [18]. In this issue, Yang et al present a computational study of the influence

of erosion of the splitter plates in a low-voltage circuit breaker [19]. Splitter plates are used to

divide the arc into many short arcs, thereby increasing the arc voltage and promoting

extinction. Yang et al show that the presence of metal vapour fundamentally changes the

splitting process. Finally, arc furnaces and arc melting processes for metal production [20],

and in some cases plasma waste treatment facilities [21], also produce plasmas with high

metal vapour concentrations.

In this article, published research on the effects of metal vapour in welding arcs is critically

reviewed. In section 2, measurements of metal vapour concentration and its influence on arc

properties are discussed. Sections 3 and 4 are concerned with computational modelling of the

influence of metal vapour in welding arcs. Section 3 considers methods used in modelling,

including equations, transport properties, treatment of metal vapour diffusion, radiative

emission coefficients, and vaporization rates, while section 4 focuses on predictions of

computational models. The production of welding fume from metal vapour is discussed in

section 5.

The article has two main purposes. The first is to give an overview of the published research

and the methods that have been applied. The second is to identify the optimum approaches,

and, where there are deficiencies in existing approaches, the improvements required in order

to obtain a better understanding of the influence of metal vapour. This second purpose will be

evident throughout the review, and the main findings will be summarized and discussed in

section 6.

2 Measurements of arc properties in the presence of metal vapour

Emission spectroscopy is the most widely used diagnostic method for thermal plasmas. The

technique is particularly simple when (a) the assumption of local thermodynamic equilibrium

(LTE) is valid, (b) there is only one chemical element present, and (c) the plasma is

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axisymmetric. Although other techniques such as laser scattering [22,23] and enthalpy probes

[24,25] have often been used to measure the properties of free-burning arcs, emission

spectroscopy has been by far the most commonly-used method for welding arcs containing

metal vapour. Other methods are certainly feasible and have been used occasionally. For

example, Kühn et al [26] used laser-induced fluorescence to measure the distribution of

tungsten impurities near the cathode in a free-burning arc. Terasaki et al [27] used Thomson

scattering to determine the electron temperature of a GTAW in helium contaminated by metal

vapour.

It is generally accepted that LTE can be assumed in free-burning arcs at atmospheric pressure

[3,4,22,23,28,29,30,31], except in regions close to the electrodes [32,33,34,35] or in the arc

fringes [36,37]. When only one chemical element is present in a plasma in LTE, it is possible

to determine the temperature and the species densities from the emission intensity of a single

line. The intensity of the line can be calibrated against a known source, or techniques such as

the Fowler–Milne [3,38] can be applied. Alternatively, more than one line can be measured,

and the temperature determined from the ratio of the intensities [39]. If a number of lines are

used, this is termed the Boltzmann plot method. An alternative is the Olsen–Richter method

[40,41], which requires lines emitted by species in consecutive ionization states. It should be

noted that in all these methods, deviations from LTE will lead to errors in the temperature and

species densities that are derived.

Emission spectroscopy has the disadvantage that it doesn’t give a local measurement of

emission intensity (since it measures emission integrated along a chord through the plasma).

However, stationary free-burning arcs are generally axisymmetric, and it is then possible to

convert a lateral scan to a radial distribution of emission intensity using an Abel transform

[38].

When metal vapour is present in large enough concentrations to decrease the concentration of

the shielding gas significantly, then the plasma can no longer be assumed to contain one

chemical element for the purposes of emission spectroscopy measurements. The emission

intensity of a line then depends both on temperature and on the mole fraction of the chemical

element. It is necessary in these circumstances to measure the emission from at least two lines

to determine the temperature and species concentration, even under the assumption of LTE. A

further complication is that many metal lines show strong self-absorption; however, lines that

are unaffected by this problem can be chosen [42]. If the width of at least two spectral lines is

measured (for example, using the method proposed by Sola et al [43]), it is possible to

determine electron temperature and density independent of the existence of LTE [42].

7

In real welding situations, the arc moves along the seam between the metals to be joined, and

deviations from axisymmetry may occur. However, in many of the investigations described in

this section, the arc is stationary, so the assumption of axisymmetry can be made. It should be

noted, however, that the concentration of metal vapour in a stationary arc will tend to increase

with time, particularly in the first few tens of seconds after arc initiation, so that the

measurement is not steady-state. A method adopted [42,44,45,46] for the case of a moving arc

is to measure the emission along the line of motion of the arc. In this case the arc is

symmetric in the plane perpendicular to the optical axis. Although the arc will not be

completely axisymmetric, an Abel inversion is nevertheless likely to be acceptably accurate if

the translational velocity of the arc is low. There have been attempts to generalize the Abel

inversion to non-axisymmetric distributions (e.g. [47]) and to use tomographic

reconstructions [48], but these methods have not been applied to the measurement of welding

arcs containing metal vapour.

A simple spectroscopic approach is to use a high-speed camera combined with a narrow-

bandwidth filter centred on metal vapour lines. This allows the shape of the region with

substantial metal vapour concentration to be monitored [49,50].

An application of the spectroscopic measurement of the radiative emission from welding arcs

is to monitor defect formation in welds. Mirapeix et al [51] has used the ratio of Fe I lines as a

means of real-time detection of the formation of defects in GTAW. In related work, Alfaro et

al [52] have used the ratios of Fe I lines and of Mn I lines to monitor defect formation in

GMAW.

In the following subsections, measurements made in low-current wall-stabilized arcs will first

be considered; although these are not welding arcs, relevant results have been obtained. This

is followed by analysis of spectroscopic measurements of GTAW and GMAW arcs. Finally,

laser-scattering measurements of metal vapour in arcs will be considered.

2.1 Spectroscopic measurements of wall-stabilized arcs

There have been a number of studies of the influence of metal vapour in wall-stabilized arcs

that have used emission spectroscopy techniques. The parameters in these experiments are

different from those used in arc welding, since the arc current is lower and the wall-stabilized

configuration also differs substantially from the free-burning arc used in GTAW, GMAW and

related welding processes. Nevertheless, some of the trends observed are relevant to welding

arcs.

8

Bouaziz et al [53] investigated departures from LTE by measuring the time-dependent

emission of argon and copper lines at a position just above a copper anode, after interruption

of argon arcs with currents between 25 and 90 A. Rahal et al [54,55] measured the diffusion

velocities of copper formed by vaporization of the anode in 20 A nitrogen arcs. They found

that copper vapour concentrations were larger away from the axis, except close to the anode.

Andanson and Cheminat [56] measured the concentration of copper vapour and the

temperature near the copper anode in 15 A and 30 A argon arcs. They found that the presence

of copper vapour, at concentrations up to 1% by mole, decreased the temperature close to the

anode by about 2000 K. Cheminat et al [57] investigated demixing effects in argon arcs with

low concentrations of silver vapour formed by vaporization of a silver anode at currents

between 20 A and 50 A. The influence of demixing led to the silver vapour becoming

concentrated in the fringes of the arc. Temperature decreases of up to 2000 K near the anode

were observed for silver concentrations of up to 0.4% by mole.

Adachi et al [58] investigated the influence of iron vapour on an argon wall-stabilized arc by

injecting iron powder through the cathode into the arc plasma. They found that the addition of

iron corresponding to a mole fraction of between 3 and 5% iron vapour led to a decrease in

the arc voltage of from about 110 V to about 90 V for arc currents from 10 A to 60 A, with

the effect larger for larger iron vapour concentrations.

A number of trends relevant to arc welding were highlighted. In particular, there were

decreases in temperature and arc voltage associated with the presence of metal vapour.

Further, demixing led to the metal vapour becoming concentrated in the fringes of the arc.

This is attributable to two demixing effects: diffusion due to mole fraction gradients, in which

the chemical element with the lower ionization energy diffuses preferentially to lower

temperature regions, and demixing due to collisional forces, in which the heavier chemical

element diffuses to lower temperature regions [59].

2.2 Spectroscopic measurements of GTAW arcs

The standard free-burning arc configuration, used in a vast number of studies of arc plasmas,

uses argon shielding gas, a thoriated tungsten cathode and a flat copper anode, in most cases

water-cooled to avoid melting and possible vapour contamination. Aside from the water

cooling, this is the same configuration generally used in GTAW. In a small proportion of the

studies, the anode has not been cooled in an effort to investigate the influence of metal vapour

on the arc properties. These studies are strongly relevant to GTAW.

9

In most of the spectroscopic measurements, temperatures were obtained using a single Ar I

line. As noted above, this relies on the concentration of the metal vapour being small enough

so as not to reduce the mole fraction of argon significantly. This is a reasonable assumption

for most GTAW arcs, since the metal vapour mole fraction is generally less than 1%.

However, in many studies, the metal vapour concentration was not determined, so this was

not confirmed.

Razafinimanana et al [60] measured the temperature distribution in a 90 A argon arc with a

copper cathode. For a pure argon arc, both the absolute intensity of an Ar II line and the

Fowler–Milne method for an Ar I line were used, while when copper vapour was present, the

ratio of the intensities of three Cu I lines was used. It was found that copper vapour arising

from the anode had a significant influence on the plasma temperature distribution, even

though the concentration was less than 0.3% by mole everywhere. The temperature in the

region within 2 mm of the anode was about 2000 K lower when copper vapour was present.

Etemadi and Pfender [61] studied the influence of copper vapour in a 150 A argon arc by

comparing the properties of arc with a flat water-cooled copper anode, a molten copper anode,

and an anode that had previously been molten but subsequently solidified and water cooled.

The latter anode allowed the influence of the change of shape of the anode associated with

melting to be investigated independently of the influence of metal vapour. Temperature

distributions of the arc were obtained by measuring the intensities of an argon line using the

Fowler–Milne method. Thus, it was assumed that copper vapour concentrations were

sufficiently small not to affect the temperature measurements. Temperatures at an axial

position 1 mm above the anode were found to be similar for the molten anode and solidified

anode on axis, but about 2000 K lower for the molten anode at a radius of 5 mm.

Temperatures near the cathode were the same for all anodes. The arc voltage was about 1.5 V

lower for the molten anode than the solidified anode for arc currents between 150 A and

250 A.

Akbar and Etemadi [62] performed temperature measurements of 200 A argon arcs with a

molten copper anode, and compared the results to measurements made with a solid anode.

Measurements were performed using the absolute intensity of an Ar I line, and the ratio of

intensities of two Cu I lines. The arc length was 13 mm. There were some discrepancies in the

results obtained with the two methods, and in any case temperature comparisons were only

possible for the Ar I measurements. The measurements relied on the assumption that copper

vapour concentrations were small enough not to lower the argon mole fraction significantly.

While atomic copper number densities were measured, there was no attempt to determine the

10

total copper number density, which would have been higher because of the strong ionization

of copper atoms. Nevertheless, the atomic copper number densities were measured to be

always below 18 310 m− , so the assumption that the argon mole fraction was not significantly

affected was probably reasonable. It was found that the presence of copper vapour decreased

the temperature 2 mm above the anode, where the atomic copper concentration was highest,

and had no effect on temperatures at distances 6 mm and 10 mm above the anode.

Gonzalez et al [63] performed measurements on a 90 A argon arc with an iron anode. The

temperature was deduced from a Boltzmann diagram obtained using ten Fe I lines, and the

iron concentration from the temperature and the absolute intensity of an Fe I line. The iron

concentration was largest on axis near the anode, reaching 0.075% by mole 1 mm above the

anode and 0.043% 2 mm above the anode. The effect of the vapour was to decrease the

temperature by just over 1000 K, as shown in Figure 2. The figure also shows predictions of a

computational model, which agree well with the measurements for radii below about 3 mm.

At larger radii, the measured temperatures are significantly higher; this is probably due to

departures from LTE due to resonant absorption and reemission of radiation [37,38], as is

supported by laser-scattering measurements of atomic argon temperatures at large radii,

which agree with the theoretical predictions [22,64]. The presence of iron vapour had no

Figure 2. Radial temperature profile at an axial position 1 mm above the anode for a pure argon arc and argon arc with iron vapour present. Both measured and calculated profiles are given. Data are from [63].

0 2 4 6 8 10

4000

6000

8000

10000

12000

Argon, experiment Argon-iron, experiment Argon, theory Argon-iron, theory

Tem

pera

ture

(K

)

Radius (mm)

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effect on the arc voltage.

In contrast to the above measurements, all of which found a decrease in temperature near the

anode due to the influence of copper vapour, Farmer et al [65] found no significant difference

in the temperatures measured for 200 A argon arcs with a water-cooled and a molten stainless

steel anode. The temperature was measured using the Fowler–Milne methods applied to an

Ar I line. The metal vapour concentration was monitored by measuring the intensity of a Cr I

line, and reached 0.025% by mole 0.5 mm above the anode. This is a lower concentration

than measured in the experiments discussed above, which may explain the absence of an

influence of the metal vapour on the temperature.

Tanaka et al [66] measured the influence of the arc current, the shielding gas flow rate and the

flow rate of water cooling a copper anode in an argon arc. The used a CCD array to detect

two-dimensional images of the copper vapour distribution. The mode of attachment of the arc

to the anode changed as the parameters were altered. When the anode was more strongly

heated by the arc, the attachment became constricted; this was attributed to the higher vapour

concentration, which increased the local electrical conductivity.

Apart from Farmer et al [65], all researchers that measured temperature found a decrease in

arc temperature in the region near the anode associated with the presence of metal vapour.

The metal vapour concentrations, when quantified, were small, less than 1%. The arc voltage,

when measured, either decreased slightly or remained constant.

2.3 Spectroscopic measurements of GMAW arcs

Measurements of GMAW arcs are more difficult than those of GTAW arcs. The arc is not

steady because droplets are continually forming at the wire anode, then detaching and falling

through the arc. These droplets also interrupt the line of sight in spectroscopic and laser

scattering measurements. As a consequence, there have been many fewer measurements of

GMAW arcs.

Ton [67] presented measurements of the temperature distribution and composition for plasma-

MIG welding. This is a hybrid process, in which a filler wire is introduced into an arc

between a tungsten electrode and the workpiece. Both the filler wire and tungsten electrode

are connected to power supplies, with a potential difference between the electrode and the

wire, and the wire and the workpiece, with the electrode and wire having the same polarity.

Results were presented for an argon arc with a steel filler wire, and for both positive and

negative electrode and wire polarities. In all cases, the arc consisted of a highly luminous

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inner core and a surrounding plasma of lower luminosity. Temperatures were measured by

comparing the intensities of different spectral lines. The central part of the arc was found to

contain iron, manganese, copper, calcium and argon at temperatures in the range 6000 K to

7000 K, while the outer region shows only argon spectral lines and was at a temperature of

about 13 000 K. The metals detected were all present in the filler wire. Ton calculated that the

electrical conductivity and therefore the current density in the central region were much

smaller than in the outer region.

Lancaster [68] mentioned measurements of iron arcs in air in which the central core contained

vaporized iron, and referred to measurements of an argon-shielded GMAW arc by Smars et al

[69] that found a peak temperature of 8000 K on axis. Lancaster noted a discrepancy between

measurements of arcs with iron and steel wire anodes and those with aluminium wire anodes,

and referred to measurements by Smars and Acinger [70] showing peak temperatures of up to

20 000 K occurring on axis in a 250 A GMAW arc with an aluminium wire anode.

Goecke et al [50] performed spectroscopic measurements of a pulsed GMAW arc in argon

with a copper alloy wire anode. They measured several Cu I and Ar I lines, whose intensity

was calibrated against a tungsten lamp. The ratio of two copper lines was used to determine

the excitation temperature, and the intensity of a copper line to obtain the number density of

copper atoms. Two Saha equations, determining the relationship of the atom and ion densities

for copper and for argon respectively, and Dalton’s law, were used to calculate the densities of

the other species and the heavy-particle temperature. It was assumed that the excitation

temperature was equal to the electron temperature. It was found that at the start of a 2 ms

high-current pulse the arc was essentially composed of argon, with the temperature reaching a

maximum value of about 14 000 K on axis. Towards the end of the pulse, the arc appearance

had changed, with a bright core and a less-luminous outer region, as shown in Figure 3. This

appearance is typical of GMAW arcs. At this time, the copper ion number density was

calculated to be above 23 310 m− on axis, but was still less than half of the argon number atom

density. The atomic copper number density was measured to be below 22 310 m− , so the

copper was strongly ionized. The copper density fell rapidly away from the axis, while the

argon density increased slowly. The heavy-species temperature was calculated to be about

7000 K on axis, well below the 14 000 K measured at the start of the pulse when the copper

density was negligible. In the central region of the arc, it was found that the electron

temperature was about 13 000 K, indicating that the arc was not in LTE in this region.

13

Goecke [71] performed spectroscopic measurements of a pulsed GMAW arc in argon, and

argon with 0.1% nitrogen or oxygen added, with a aluminium–5% magnesium alloy wire

anode. Measurements were perfomed during the high-current (340 A) pulses, at a vertical

position 2 mm above the molten cathode. In a thorough study, Goecke measured Ar I, Al I,

Mg I and Mg II lines, and analysed them using absolute emission, line ratio and Fowler–Milne

methods. Although the results given by each method were not completely consistent, all

indicated that the temperature on axis was 1000 K to 2000 K lower than the maximum

temperature, which was around 12 000 K and which occurred about 1.0 mm to 1.5 mm off

axis.

Zielińska et al [42] measured the temperature distribution in GMAW spray-transfer mode and

globular transfer mode. Results were given for arcs in pure argon and in mixtures of argon

and 5.4% and 20.2% carbon dioxide by mole, with a mild steel anode. In the first two cases,

spray transfer occurred, while globular transfer occurred for the higher CO2 concentration. In

all cases, a bright central region with strong emission from iron species was observed.

Interestingly, the shape of this region for a pure argon arc was conical, rather than cylindrical

for the pulsed-transfer mode arc of Goecke et al shown in Figure 3. The Stark broadening of

an Ar I and an Fe I spectral line was measured; together these measurements allowed the

electron temperature and number density to be determined, independent of any assumption of

LTE. The temperature profiles are shown in Figure 4. For arcs in argon and argon with 5.4%

carbon dioxide by volume, the electron temperature was found to have a local radial

minimum on axis, while for the arc in argon with 20.2% carbon dioxide, the temperature was

maximum on axis. For example, for the pure argon arc, the electron temperature was 8500 K

on axis for axial positions 3 mm and 4.5 mm above the workpiece, and the maximum

Figure 3. High-speed photographs of a pulsed GMAW arc with copper wire anode, after 1.75 ms of a 250 A current pulse. From left to right: with a neutral density filter; with a 510 3 nm± interference filter that passes copper lines; with a 780 3.5 nm± interference filter that passes argon lines. From Goecke S F et al ChopArc. MSG-Lichtbogenschweißen für den Ultraleichtbau ©2005 Fraunhofer IRB Verlag, Stuttgart, Germany [50].

14

temperature of 11 500 K occurred at radii 1.3 mm and 2.3 mm respectively. The electron

density was measured to be higher than predicted under the assumption of LTE for the

electron temperatures measured on the arc axis, indicating a departure from LTE. The

temperature measurements for pure argon, and the processes leading to the conical shape of

the bright central region, are analysed in the paper by Schnick et al. [72] that appears in this

issue.

Four spectroscopic investigations of GMAW are presented in this issue. Valensi et al [46]

present a further investigation of the argon GMAW arc in spray transfer mode. They again

used Stark broadening of an Ar I and an Fe I spectral line to measure electron temperature,

but also measured the excitation temperature with a Boltzmann plot of three Fe I lines. The

good agreement suggested that the arc is in partial LTE (i.e., the electron temperature is equal

to the excitation temperature of the atoms). The ratio of emission coefficients for an Ar I and

an Fe I line was used to measure the metal vapour concentration, which was found to be less

than 1% everywhere. The authors note that this was much lower than predicted in some

modelling studies; this will be discussed further in section 4.2.

Zielinska et al [73] present results indicating that a GMAW arc can be used to determine the

Stark parameters of atomic metal spectral lines, and apply this to the measurement of the

Stark parameters of Mn I and Fe I lines, as well as the temperature dependence of the

broadening of one of these lines. They suggest that because the composition of the wire

electrode is easily altered, the technique can easily be adapted to other metals.

Rouffet et al [44] measured the properties of a GMAW arc operating in one-drop-per-pulse

mode. A steel wire and argon shielding gas were used, and measurements were made in the

Figure 4. Radial dependence of electron temperature for 326 A arcs in argon and two mixtures of argon with carbon dioxide (percentages are by mole). Axial positions are ▲ 3 mm, ■ 4.5 mm, ● 6.0 mm and ♦ 7.5 mm above the workpiece cathode. From [42].

15

high-current phase of the cycle, for which the current was 450 A. A Boltzmann plot of Fe I

lines was used to determine temperature, while the electron density was obtained from the

Stark broadening of an Ar I line. The latter measurement was independent of the assumption

of LTE. The temperature was measured to be about 8000 K in the central region of the arc,

rapidly increasing to about 13 000 K at larger radii. The iron concentration was about 60% by

mole in the central region, falling to at most a few percent in the hotter regions of the arc. The

iron concentration is largest at the start of the high-current pulse, and gradually decreases at

the iron vapour diffuses to larger radii over a period of just under 1 ms during the pulse.

Wilhelm et al [45] investigated GMAW operating in the dip transfer mode. A steel wire, and

carbon dioxide and argon–oxygen shielding gases, were used, and the cold metal transfer

process was adopted, in which the current was controlled so that it was minimum during the

short circuit and rapidly increased after separation of the wire and workpiece. The emission

from Fe I lines, and O I or Ar I lines, depending on the shielding gas, was measured during

the current pulse after the short circuit. The emission from iron was strongly concentrated in

the arc centre, and increased rapidly over the first millisecond of so of the pulse, before

becoming reasonably steady. The oxygen and argon concentration peaked on the arc axis at

the start of the pulse, but the peak subsequently moved radially outwards. Iron vapour mole

concentrations on the arc axis were estimated to be about 25% for argon–oxygen shielding

gas, about 75% for carbon dioxide, with temperatures of around 8000 K in this region. By

analysing the radial dependence of the measured line emission, the arc voltage, and calculated

thermophysical properties of the plasma, it was concluded that the arc was more strongly

constricted when the shielding gas was carbon dioxide.

Despite the wide range of parameters and processes that have been investigated, there are

strong similarities in the results that have been obtained from spectroscopic measurements of

GMAW. The presence of metal vapour in GMAW arcs has a dramatic effect on the arc

appearance, with the arc appearing to contain two separate regions. The emission from the

bright central region is dominated by metal lines, while that from the less luminous outer

region is dominated by emission from the shielding gas.

The general consensus of measurements is that a temperature minimum occurs on axis in

GMAW arcs, accompanied by high concentrations of metal ions. The minimum is more

pronounced for heavy metals such as iron and copper, but has been found to be weaker light

metals such as aluminium and magnesium (in one case [70] it was not observed at all) or

when there is a high carbon dioxide concentration in the shielding gas [42]. The weaker

16

temperature minimum for light metals can be explained by the lower radiative emission from

these metals, and will be discussed further in section 3.4.

There is a large variation in the measured iron concentrations. Goecke et al [50] measured a

concentration of order 30%, and Rouffet et al [44] up to 60%, while Valensi et al [46] found a

very low concentration, less than 1%. Even though different welding conditions were

investigated, such a large difference is surprising, and needs to be resolved by further studies.

2.4 Laser-scattering measurements

Laser-scattering has been applied frequently to measure temperature and other properties of

welding arcs. Methods used include Rayleigh scattering (scattering from atoms and

molecules) [38,74], Thomson scattering (scattering from electrons) [23,75,76], laser-induced

fluorescence [77,78,79], and combinations of these methods [4,22,80]. An advantage of laser

scattering over emission spectroscopy is that it gives a local measurement (at a point defined

by the intersection of the laser beam and the measurement axis). However, as with

spectroscopy, care has to be taken in interpreting the measured signal. In particular, the

application of Thomson scattering to measure electron temperatures has shown to be

unreliable due difficulties in accounting for heating of the electrons by the laser pulse

[23,29,31], and the low number of electrons in a Debye sphere rendering the usual method of

determining temperature from the scattered signal inaccurate [30].

Terasaki et al [27] used Thomson scattering to measure the electron temperature in a helium

GTAW arc, with an arc current of 150 A. Results obtained using a stainless steel anode and a

water-cooled copper anode were compared. In the former case, spectroscopic measurements

revealed the presence of iron and chromium in the arc, with stronger concentrations near the

anode. The appearance of the arc was altered, with a blue luminous region near the anode

associated with the presence of metal vapour. This is shown in Figure 5, together with the

electron temperatures measured by Thomson scattering. When the metal vapour is present,

the electron temperature was much lower, by around 6000 K. This was attributed to the

broader current density distribution, associated with the increased electrical conductivity at

low temperature, and the increased radiative emission. The arc voltage was decreased for the

stainless-steel anode, which confirmed the importance of the first mechanism. While the

precise values of electron temperature may be incorrect as a consequence of the problems

with applying Thomson scattering to thermal plasmas mentioned above, the trends found are

expected to be reliable.

17

Kühn et al [26] used laser-induced fluorescence to measure the distribution of tungsten atoms

and ions evaporated from the cathode in a free-burning arc in argon. The arc currents were

less than 10 A, and therefore not relevant to arc welding. Nevertheless, the results illustrate

the potential of the technique; in particular, two-dimensional distributions of tungsten species

at concentrations below 1 ppm were obtained. Laser-induced fluorescence has also been

applied, for example, to the detection iron atoms and ions in a beam of iron vapour produced

by a hollow-cathode discharge [81], and copper atoms [82] and molybdenum atoms [83] in

low-pressure pseudo-spark discharges. Clearly there is scope to apply this technique to the

measurement of metal vapour densities in welding arcs.

3 Modelling of welding arcs: methods

3.1 Equations

Computational modelling of a welding arc plasma uses a set of coupled partial differential

equations that express the conservation of mass, momentum, energy and charge. Here the

equations are given in a typical form, with the time-dependent term and convective term on

the left-hand side, and the diffusion term and source terms on the right-hand side.

The equation of mass continuity is

Figure 5. Electron temperatures measured by Thomson scattering for a helium GTAW arc with a water-cooled copper cathode (left-hand side) and a stainless steel anode (right-hand side). The results are superimposed on a photograph of the arc plasma. Reproduced with kind permission from Springer Science+Business Media: Terasaki H, Tanaka M and Ushio M 2002 Effects of metal vapor on electron temperature in helium gas tungsten arcs Metall. Mater. Trans. A 33A 1183–8, Figure 8 [27].

18

( ) 0,vt

ρ ρ∂ + ∇ ⋅ =∂ ɶ

(1)

where ρ is the mass density, vɶ

is the flow velocity, and t is time.

The equation of momentum conservation is

( )

( ) ,v

vv P j B gt

ρ ρ τ ρ∂ + ∇ ⋅ = −∇ − ∇ ⋅ + × +∂ ɶ ɶɶ ɶ ɶ ɶ ɶɶ

(2)

where P is the pressure, τɶɶ

is the stress tensor, jɶ

is the current density, Bɶ

is the magnetic

field strength, and gɶ

is the acceleration due to gravity. The terms on the right-hand side

describe respectively the forces due to pressure gradients, viscous stress, the Lorentz or

magnetic pinch force, and gravity.

The equation of energy conservation is

2

5(,

)( )

2B

p p

j kh kvh U h j h

t c ec

ρ ρσ

∂ + ∇ ⋅ = − − ∇ ⋅ ∇ + ⋅∇ ∂

ɶɶ ɶ

(3)

where h is the enthalpy, σ is the electrical conductivity, U is the net radiative emission

coefficient, k is the thermal conductivity, pc is the specific heat at constant pressure, Bk is

Boltzmann’s constant, and e is the electronic charge. The terms on the right-hand side

describe respectively resistive heating, radiative emission, thermal conduction, and energy

transfer arising from the flow of electrons. The enthalpy is the integral of specific heat with

respect to temperature, and the temperature at any position is easily derived from the enthalpy

at that position. As discussed in section 3.4, the net radiative emission coefficient method is

the most widely used approach to radiative transfer; if a different method were used, then the

radiative emission term in (3) would have to be altered.

The equation of current continuity is

( ) 0,σ φ∇ ⋅ ∇ = (4)

where φ is the electric potential. The current density is given by j σ φ= − ∇ɶ

.

19

The magnetic field strength Bɶ

, which appears in (2), also has to be calculated. This can be

done by solving for the magnetic potential Aɶ

:

20 ,A jµ∇ = −

ɶ ɶ

(5)

and using B A= ∇ ×

ɶ ɶ.

Finally, in a welding arc containing a shielding gas and metal vapour, an equation is required

for the conservation of the metal vapour mass. It is usually assumed that the plasma can be

treated as containing two separate components or ‘gases’, the metal vapour and the shielding

gas. This requires that the species derived from the metal vapour (e.g. Fe, Fe+, Fe2+, Fe3+, etc

for iron vapour) are treated as one gas, and those derived from the shielding gas (e.g. Ar, Ar+,

Ar2+, Ar3+, etc for argon) are treated as the other gas. Electrons are divided among the two

gases so that each gas is charge neutral. The equation for conservation of metal vapour mass

is then

( ) MM

M MY

vY J St

ρ ρ∂ + ∇ ⋅ = −∇ ⋅ +∂ ɶ ɶ

(6)

where MY is the sum of the mass fractions of the metal vapour species, MJɶ

is the average

mass flux, relative to the mass-average velocity, of the metal vapour species, and MS is the

metal vapour source term (mass per unit volume and time). The first term on the right-hand

side describes diffusion of the metal vapour, and the second term describes production of

metal vapour due to evaporation of the electrodes, and any loss terms considered, such as

condensation of the metal vapour.

An additional term

· ( )Mp

S Mh h Yk

c

−∇ − ∇

(7)

is added to the right-hand side of the energy conservation equation (3) to account for the

change in enthalpy resulting from mixing of the metal vapour and the shielding gas; Mh and

Sh are respectively the enthalpies of the metal vapour and shielding gas, defined as the

20

sum of the enthalpies of the species making up the respective gases. Note that in previous

papers [59,84] an additional term in MJɶ

was included; however, it has been pointed out that

this term is already implicit in the thermal conductivity [85].

The metal vapour source term MS in (6) should also be added to the right-hand side of the

mass conservation equation (1), and an evaporative cooling term should be included on the

right-hand side of the energy conservation equation (3). This will be discussed further in

section 3.5.

The equations are usually solved using a finite volume method [86], although finite element

approaches are increasingly being applied to modelling of thermal plasmas.

The properties of a thermal plasma depend critically on the thermophysical properties of the

plasma gas, which feature in (1) to (7). These properties can be divided into thermodynamic

properties (density, specific heat, enthalpy), transport coefficients (viscosity, electrical

conductivity, thermal conductivity, diffusion coefficients) and radiative emission coefficients.

The presence of metal vapour affects all of these properties, although the largest changes are

to the electrical conductivity and the radiative emission coefficients. Diffusion coefficients

are required to calculate the mass flux of metal vapour; along with the convective flow, they

determine the distribution of the metal vapour in the arc. Thermodynamic and transport

properties are discussed in section 3.2. Diffusion coefficients will be considered separately in

section 3.3, and radiative properties in section 3.4.

Further, it is necessary to have a method of determining the rate of evaporation of the metal

vapour from the electrodes (the source term in (6)), and possible approaches are considered in

section 3.5.

3.2 Calculation of thermodynamic properties and transport coefficients

The starting point in the calculation of these properties is the determination of the

composition of the plasma. If LTE is assumed, this can be done by solving Saha equations for

ionization reactions and Guldberg–Waage equations for dissociation reactions, or by

minimizing the Gibbs free energy of the plasma [87]. For non-LTE plasmas, the correct

methods are still the subject of research [36].

Thermodynamic properties are relatively easy to calculate once the plasma composition is

known, and require only data for the temperature dependence of the specific heat of each

21

species. Such data is often available in tables (e.g., [88]), or can be calculated from

spectroscopic data. Transport coefficients require, in addition, knowledge of the collision

integrals between all pairs of species present [87,89], and it can be difficult to obtain accurate

values. Collision integrals are averages over a Maxwellian energy distribution of the collision

cross-sections, and are derived from interatomic potentials and other fundamental data.

While reliable transport coefficients have been published for most plasma gases of interest

(e.g., argon , nitrogen and oxygen [90,91], air [92,93], helium [94] and hydrogen [95]) and

many mixtures of such gases [90,92,94,95,96], this is not the case for most metal vapours.

This is partly because they have been of less widespread interest, and partly because of the

lack of accurate collision integral data for the interactions between metal species, and metal

species and other species. The most sophisticated interatomic potentials that have been used

in plasma calculations are for argon–copper mixtures [97] and for silver and silicon dioxide

mixtures [98]. In these papers, the Hulburt–Hirschfelder potential [99,100,101] was used to

calculate the collision integrals for neutral–neutral interactions between the metal species. In

other work, a Morse potential was used for the interactions between copper atoms

[102,103,104]. Experimental data was used to assist in the calculation of ion–neutral and

electron–neutral collision integrals for copper [97], while for silicon and silver, only estimates

and empirical formulas were available for these collision integrals.

Hoffmann et al [105] used the Stockmayer (12,6,3) potential for neutral–neutral interactions,

and the (16,6,4) potential for elastic neutral–ion interactions, in their calculation of the

properties of mixtures of iron, copper, aluminium and calcium with nitrogen, argon and

helium. A weakness in this work was the assumption that the specific heat of the species was

constant at high temperatures, and the use of approximate thermodynamic data for multiply-

ionized species.

In other calculations, approximate interatomic potentials such as the Lennard–Jones (12,6)

potential for interactions between neutral species, empirical formulas [106] for charge

exchange interactions between atoms and ions of the same metal, and the polarization

potential for elastic interactions between neutral species and ions were used. For example,

Cressault et al [107] used these approximations in determining the properties of plasmas in

mixtures of air with iron, silver and copper, as did Dunn and Eagar [108] for mixtures of

argon or helium with iron, aluminium or calcium, Gu et al [109] in calculating properties of

plasmas in mixtures of argon and silicon vapour, Abdelhakim et al [110] for copper–nitrogen

plasmas and Dassanayake and Etemadi [111] for nitrogen–aluminium plasmas.

22

For the purposes of this paper, thermodynamic and transport properties of mixtures of argon

with iron, aluminium, chromium and manganese vapours have been calculated. The

approximations mentioned in the previous paragraph have been used for interactions

involving metal atoms. For the electron–atom interactions, collision integrals were

determined by integrating the momentum transfer cross-section, which was obtained using the

effective radius approximation for low collision energies, and the classical approximations for

high collision energies [112]. For interactions between argon species, the methods of Murphy

and Arundell [90] were used. Further details are given by Yang et al in this issue [19].

Figure 6 shows a comparison of transport coefficients calculated by different authors. Results

are given for mixtures of argon and iron and copper vapours. There is generally good

agreement between the published values of the thermal conductivity and electrical

conductivity for argon–copper mixtures. The main discrepancy is that at temperatures of

above about 13 000 K, the values of Cressault and Gleizes [104] are larger than those of the

other researchers. This is due to a smaller value of the Coulomb cross-section, most likely

Figure 6. Comparison of transport properties of argon–copper and argon–iron plasmas calculated by different authors. Percentages are by mole. (a) Thermal conductivity of argon–copper mixtures; (b) thermal conductivity of an argon–iron mixture; (c) viscosity of an argon–copper mixture; (d) electrical conductivity of argon–copper mixtures. References from which the data were taken are: Murphy (argon–copper) [103], Mostaghimi [102], Cressault [104], Aubreton [97], Murphy (argon–iron) [19], Dunn [108], Hoffmann [105].

0 10000 20000 300000

1

2

3

4

5

6 Murphy 5% Cu Mostaghimi 5% Cu Cressault 5% Cu Murphy 50% Cu Aubreton 50% Cu

The

rmal

con

d. (

W m

-1 K

-1) (a)

0 10000 20000 300000.0

5.0x10-5

1.0x10-4

1.5x10-4

2.0x10-4

2.5x10-4

Murphy 50% Cu Aubreton 50% Cu

Vis

cosi

ty (

kg m

-1 s

-1)

(c)

0 10000 20000 300000

1

2

3

4

5

Murphy 10% Fe Dunn 10% Fe Hoffmann 10% Fe

The

rmal

con

d. (

W m

-1 K

-1)

Temperature (K)

(b)

0 10000 20000 300000

2000

4000

6000

8000

10000

12000

Murphy 5% Cu Mostaghimi 5% Cu Cressault 5% Cu Murphy 75% Cu Aubreton 75% CuE

lect

rical

con

d. (

S m

-1)

Temperature (K)

(d)

23

resulting from the inclusion of both ions and electrons, rather than just electrons, in

calculating the Debye radius. This issue has been discussed in more detail elsewhere [95].

The data for thermal conductivity of the argon–iron mixture differ between 5000 K and

14 000 K. The positions of the peaks at around 7000 K and 14 000 K, corresponding to the

reaction thermal conductivity associated with first ionization reactions of copper and argon

respectively, are slightly offset in the Hoffmann et al [105] calculation. This is probably due

to the approximations made in their thermodynamic data, which could lead to inaccuracies in

the ionization temperatures. The first peak is missing in the results of Dunn and Eagar [108].

The viscosity determined by Aubreton and Elchinger [97] is about 10% larger than that of

Murphy [103] for temperatures around 7000 K. At this temperature, the cross-section for

elastic collisions between atoms and ions is dominant. Murphy used the polarization cross-

section for Cu–Cu+ interactions, while Aubreton and Elchinger use the experimental data of

Witko and Beckmann [113] for the 2gΣ state and a fitting procedure to derive the potential

for the 2 uΣ state, which is likely to be more accurate.

Figure 6 indicates that the differences between the copper transport coefficients of Aubreton

and Elchinger, calculated with the more sophisticated cross-sections for interactions between

copper species, and those calculated using approximate cross-sections, are relatively small. It

is expected that the approximate methods used for most other metal vapours be have a similar

level of accuracy. It is difficult to generalize about the influence that changes in the transport

coefficients have on the predictions of computational models of welding arcs. However, as a

rough guide, based on calculations for different gas mixtures [2], a given change in a transport

coefficient causes a similar relative change in parameters of interest to welding, such as the

heat flux distribution at the weld pool surface. It should not be difficult to develop Hulburt–

Hirschfelder potentials for many other metals, since the parameters of the potential can be

derived from spectroscopic constants; this would improve the accuracy of the transport

coefficients and therefore of the predictions of modelling.

Figure 7 shows the calculated dependence of the specific heat, thermal conductivity, electron

conductivity and viscosity on the concentration of iron vapour in an argon plasma. All these

properties are substantially altered by the addition of 50% iron vapour, and there are small

changes for the addition of 10% iron vapour. However, only the electrical conductivity in the

range 4000 K to 10 000 K is affected by the presence of 1% iron vapour. This is a

consequence of the lower ionization energy of iron atoms.

24

Figure 7. Calculated properties of plasmas in different mixtures of argon and iron vapour. Percentages are by mole.

0 10000 20000 300000

2000

4000

6000

8000

10000

12000

14000

Spe

cific

hea

t (J

kg-1

K-1

)(a)

0 10000 20000 300000.0

5.0x10-5

1.0x10-4

1.5x10-4

2.0x10-4

2.5x10-4

3.0x10-4

Vis

cosi

ty (

kg m

-1 s

-1)

(c)

0 10000 20000 300000

1

2

3

4

5

The

rmal

con

d. (

W m

-1 K

-1)

Temperature (K)

(b)

0 10000 20000 300000

2000

4000

6000

8000

10000

12000

100% Ar 99% Ar, 1% Fe 90% Ar, 10% Fe 50% Ar, 50% Fe 100% Fe

Ele

ctric

al c

ond.

(S

m-1

)

Temperature (K)

(d)

Figure 8. Calculated properties of plasmas in mixtures of 90% argon and 10% metal vapour by mole, for five different metals.

0 10000 20000 300000

2000

4000

6000

8000

10000

12000

14000

Spe

cific

hea

t (J

kg-1

K-1

)

(a)

0 10000 20000 300000.0

5.0x10-5

1.0x10-4

1.5x10-4

2.0x10-4

2.5x10-4

3.0x10-4

Vis

cosi

ty (

kg m

-1 s

-1)

(c)

0 10000 20000 300000

1

2

3

4

5

The

rmal

con

d. (

W m

-1 K

-1)

Temperature (K)

(b)

0 10000 20000 300000

2000

4000

6000

8000

10000

12000

90% Ar, 10% Cu 90% Ar, 10% Al 90% Ar, 10% Fe 90% Ar, 10% Cr 90% Ar, 10% Mn

Ele

ctric

al c

ond.

(S

m-1

)

Temperature (K)

(d)

25

Figure 8 compares the specific heat, thermal conductivity, electrical conductivity and

viscosity of mixtures of argon and different metal vapours. The differences are generally

minor. The most obvious differences are the higher specific heat of aluminium at high

temperatures, and the lower electrical conductivity of copper at temperatures below 10 000 K.

However, it is possible that the electrical conductivity of copper should in fact be larger. The

momentum transfer cross-section for collisions between electrons and copper atoms, which is

important in this temperature range, was taken from the work of Chervy et al [114]. They

used the measured values of Scheibner et al [115] at high energies and the theoretical values

of Trajmar et al [116] at low energies. As discussed by Chervy et al, the height of the lower

energy peak in the momentum transfer cross-section is important in determining the electrical

conductivity. The peak for the case of copper is larger (about 20 2390 10 m−× ) than those

calculated by the approximate methods for the other metals, which range between

20 2120 10 m−× for aluminium and 20 2180 10 m−× for chromium. It is likely, however, that

the ‘momentum transfer cross-section’ values of Scheibner et al that were used by Chervy et

al are in fact total cross-sections (see [97] and [117]) and are therefore too high.

3.3 Treatments of diffusion and calculation of diffusion coefficients

The transport of metal vapour in the arc plasma occurs due to both convection and diffusion.

Convection is described by the second term on the left-hand side of (6), and does not require

any special treatment. Diffusion is however, more complicated to handle.

In the most general treatment of plasmas containing more than one chemical element, mass

conservation equations for individual species (e.g., Ar, Ar+, Fe, Fe+, e–):

( )ii i i

YvY J r

t

ρ ρ∂+ ∇ ⋅ + ∇ ⋅ =

∂ ɶ ɶ (8)

have to be solved everywhere in the plasma. Here iY is the mass fraction of species i, and ir

is the net rate of production of species i due to chemical reactions, vaporization, etc. For a gas

or plasma containing N species, the diffusion mass flux of species i, iJɶ

, is given by

2

1

ln ,N

Tii i i i j ij j i

j

m nm n v m D d DJ T

ρ =≡ = − ∇∑

ɶɶ ɶ (9)

26

where ivɶ

is the diffusion velocity of species i (relative to the mass-average velocity), and

im and in are respectively the mass and the number density of the ith species [89]. The

ordinary diffusion coefficients ijD and thermal diffusion coefficients TiD are in this case

multicomponent diffusion coefficients. Their calculation requires values of the mole fractions

and the masses of all the species present and the collision cross-sections for binary

interactions between each pair of species present. The driving force term jdɶ

is given by

1

ln .N

j j j jj j j j l l

j l

n m n md x x P F n F

P m

ρρ ρ =

= ∇ + − ∇ − −

∑ɶ ɶɶ

(10)

The three terms describe respectively diffusion due to gradients in the mole fraction jx , the

pressure P, and the external forces jFɶ

acting on species j. Because diffusion velocities are

defined with respect to the mass-average velocity, only 1N − need be calculated, and (8) has

to be solved for only 1N − species. In plasmas, the diffusion coefficients have to be modified

to take into account ambipolar diffusion [118,119]. This arises because electrons diffuse more

rapidly than ions because of their lower mass, inducing an electric field that accelerates the

ions and slows the electrons.

Clearly, solving conservation equations (8) for each species, and calculating ordinary

diffusion coefficient for each pair of species and thermal diffusion coefficients for each

species, is computationally expensive. As a consequence, simplified methods are generally

used. There is a range of methods of varying levels of simplicity and accuracy [103,120].

Here I consider those that have been applied to plasmas in metal vapours.

The standard approach is to group together the metal vapour species into one ‘gas’ and the

shielding gas species into another ‘gas’, which means that only a metal vapour mass fraction

conservation equation (6) is required. The main difficulty in applying (6) is to determine MJɶ

.

The optimum approach is the combined diffusion coefficient method, initially developed for

neutral gases [121] and then for plasmas [84,119,122]. If LTE can be assumed, this method is

mathematically equivalent to the full multicomponent diffusion treatment for mixtures of

homonuclear gases that do not react with each other. The requirement of non-reacting

homonuclear gases means that a gas is equivalent to a chemical element. The diffusion mass

flux of the metal vapour can then be written

27

( )2

ln ln ,x PM

E TM G MG G MG MG MG

nJ m m D x D P D E D T

ρ= ∇ ∇ + − ∇+

ɶɶ (11)

where Mm and Gm are respectively the average masses of the heavy species of the metal

vapour and the shielding gas and Gx is the sum of the mole fractions of the species of the

shielding gas; G Mx x∇ = −∇ . The combined ordinary diffusion coefficient xMGD , combined

pressure diffusion coefficient PMGD , combined electric field diffusion coefficient EMGD and

combined temperature diffusion coefficient TMGD describe, respectively, diffusion due to

mole fraction gradients, gradients of the total pressure, externally-applied electric fields and

temperature gradients. They are linear combinations of the multicomponent diffusion

coefficients; expressions are given in Refs [119,122]. The first three depend on only the

ordinary diffusion coefficients, while TMGD depends on both the ordinary and thermal

diffusion coefficients. Values of the combined diffusion coefficients have been given in the

literature for many gas mixtures [90,92,94,95,123].

Values of combined diffusion coefficients of plasmas containing metal vapours have been

published by Murphy [103] and Aubreton and Elchinger [97] for argon–copper mixtures. In

this issue, Cressault and Gleizes [124] present combined ordinary diffusion coefficients for

argon–copper mixtures, and for mixtures of copper, iron and silver with air, as well as

combined electric field diffusion coefficients for air–iron mixtures. Aubreton and Elchinger,

and Cressault and Gleizes, have presented comparisons of combined diffusion coefficients for

mixtures of equal parts copper vapour and argon, and the agreement is good, with

discrepancies of about 10% or less. The differences can be attributed to the different collision

integrals used for elastic collisions between atoms and ions, similar to the case of the

viscosity discussed in section 3.2. The combined diffusion coefficient method has been

extended to two-temperature plasmas by Rat et al [125] and values given for argon–copper

mixtures [97]; note however that some aspects of their methods have been questioned [96].

Figure 9 shows combined ordinary, temperature and electric field diffusion coefficients

calculated for different mixtures of argon and iron vapour. All the combined diffusion

coefficients are strongly dependent on composition and temperature. The combined ordinary

diffusion coefficient is independent of the relative concentrations of the two gases (iron

vapour and argon in this case), except as the concentration affects the degree of ionization of

28

the gases [90]. Iron vapour is more strongly ionized at a given temperature when its mole

fraction is low. The strong Coulomb cross-section dominates at lower temperatures,

decreasing the mean free path and therefore the diffusion coefficient. The combined

temperature and electric field diffusion coefficients depend directly on the relative

concentrations of the two gases, and as is usually the case, they are larger when the two gases

are present in approximately equal concentrations [90].

Combined pressure diffusion coefficients are not shown since pressure diffusion is negligible

in welding arcs due to the small pressure gradients. Cataphoresis (diffusion due to applied

electric fields) is more important for large mass differences between the species, and hence is

expected to be relatively small for mixtures of metal vapour and argon. The combined electric

field diffusion coefficients for the argon–iron mixtures are about an order of magnitude

smaller than those for mixtures of argon and helium or hydrogen [126].This difference is

reflected in the results of arc modelling studies; cataphoresis has been found to have a

0 10000 20000 30000-4x10-5-3x10-5-2x10-5-1x10-5

01x10-52x10-5

(c)

99.9% Ar, 0.1% Fe 99% Ar, 1% Fe 90% Ar, 10% Fe 50% Ar, 50% Fe

Temperature (K)

DE

Fe

Ar (

m2 V

-1 s

-1)

-5x10-4

-4x10-4

-3x10-4

-2x10-4

-1x10-4

0 (b)

DT

Fe

Ar (

kg m

-1 s

-1)

0

2x10-3

4x10-3

6x10-3

8x10-3

Dx F

e A

r (m

2 s-1

) (a)

Figure 9. Combined (a) ordinary, (b) temperature and (c) electric field diffusion coefficients for different mixtures of argon and iron vapour. Percentages are by mole.

29

significant influence on the composition in argon–helium GTAW arcs [126], but Schnick et al

[72] have found its effects on iron vapour diffusion to be negligible in argon GMAW arcs.

As well as the combined diffusion coefficient approach, other simpler approaches have also

been applied to calculate the mass flux term MJɶ

in (6); these have been reviewed and

compared for different scenarios [103]. In most of these cases, the mass flux of metal vapour

is calculated using

,M MG MJ D Yρ= − ∇ɶ

(12)

where MY is the sum of the mass fractions of the metal vapour species, and approximate

expressions are used to determine the diffusion coefficient MGD . Here the focus will be on

their application to the diffusion of metal vapour in welding arcs.

The simplest approximation that has been used is the ‘binary diffusion coefficient

approximation’:

,MG mgD =D (13)

where the mgD is binary diffusion coefficient describing diffusion between metal vapour

atoms and shielding gas atoms (or molecules for molecular gases). This approach neglects the

influence of ionization and of dissociation of molecules, and is therefore only accurate at

temperatures below about 5000 K or less, for which no dissociation or ionization has taken

place [103]. The mass flux MJɶ

was calculated using (12).

A ‘viscosity approximation’, derived using an expression given by Wilke [127] that

interpolates the viscosity of the gases present, has been widely used. The diffusion coefficient

is calculated in terms of the viscosities Mη and Gη of the two gases:

( )( )

( ) ( )1 14 4

12

22 2 2 2 2 2

4 2 1 1,

M G

M M M M G G G

MG

G

m mD

m mρ β η ρ β η

+=

+

(14)

where Iρ is the mass density of the gas I and the Iβ are constants, usually set to 1.385. The

mass flux MJɶ

was calculated using (12). Note that this approximation was called the ‘second

30

viscosity approximation’ in Ref. [103]; the ‘first viscosity approximation’ described there has

not been applied to metal vapour plasmas and is not considered here. For a discussion on the

accuracy of viscosity approximations for gas mixtures, see Cressault et al [128].

Bakken and Gu [129,130,131] developed and applied the ‘quasi-binary diffusion coefficient

approximation’:

2 1 2 1

(1 ) (1 ) / ,p q p q

i i i i i j iji i p i j

MGp

D Z x Z x x x D= = + = = +

= + +

∑ ∑ ∑ ∑ (15)

where species 2, ,i p= … are metal vapour species, and species 1, ,i p q= + … are shielding

gas species, while species 1, which doesn’t appear explicitly in (15), is the electron. In one

paper [131], it was noted that rather than using (12), the mass flux MJɶ

should be determined

on the basis of the mole fraction gradient, and the following expression was derived to take

this into account:

( )ln ,M MG M MG M G M GJ D Y D Y Y k kρ ρ= − ∇ − ∇ɶ

(16)

2 2 1 1

1 , 1 .q q

M G

p p

i i i i i ii i i p i p

Z x x Z x xk k= = = + = +

= + = +

∑ ∑ ∑ ∑ (17)

Finally, some authors have used only the combined ordinary diffusion coefficient in

calculating the mass flux term MJɶ

in (6). In work published to date [18,123,132], the

combined ordinary diffusion coefficient has simply been used directly in (12); i.e.

.xMG MGD D= (18)

A more sophisticated approach would be to use an abbreviated form of (11):

2

2,x xM G

M G MG G M MM Gm mn

J m m D x D xm

ρρ

= ∇ = − ∇ɶ

(19)

where m is the average mass of all species present. These two approaches will be called the

‘combined ordinary diffusion coefficient mass fraction gradient’ and the ‘combined ordinary

31

diffusion coefficient mole fraction gradient’ approaches, respectively.

Figure 10 gives a comparison of the ordinary diffusion coefficients determined using the

combined diffusion coefficient method and the approximate methods. The coefficients are in

agreement for temperatures below 6000 K, at which the main species present are argon and

iron atoms. At higher temperatures, ionization becomes important, and the approximate

methods become less accurate. The influence of ions and electrons, which reduce the

diffusion coefficient because of the high Coulomb cross section, is ignored in the binary

diffusion coefficient approximation. The viscosity approximation, which was developed for

neutral gas mixtures [127], underestimates the diffusion coefficient, while the quasi-binary

approximation leads to an overestimate.

To allow the accuracy of the different approaches to be estimated in situations of interest to

arc welding, the diffusion mass flux has been calculated for temperature and iron vapour

concentration distributions typical of those near the wire anode in GMAW, and near the

workpiece anode in GTAW. The distributions are shown in Figure 11. The temperature near

the anode and the iron vapour concentration are larger for GMAW.

Figure 10. Dependence of the ordinary diffusion coefficient Fe ArD on temperature for a

mixture of 10% iron vapour and 90% argon by mole. Results are given for the combined

ordinary diffusion coefficient Fe ArxD , the binary diffusion coefficient approximation, the

viscosity approximation and the quasi-binary diffusion coefficient approximation.

0 5000 10000 15000 20000 25000 300000.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

Ord

inar

y di

ffusi

on c

oeffi

cien

t (m

2 s-1

)

Temperature (K)

Comb. ordinary diff. coeff't Binary approx. Viscosity approx. Quasi-binary approx.

32

The mass fluxes of iron vapour calculated for the distributions of Figure 11 are shown in

Figure 12. The full combined diffusion coefficient approach is equivalent to a complete

multicomponent diffusion calculation if LTE is assumed, and is therefore the benchmark with

which the other approximations are compared.

At the high temperatures present near the GMAW wire, Figure 12(a) shows that the binary

diffusion coefficient approximation greatly overestimates the mass flux of iron vapour. The

other approximations all underestimate the mass flux, with the combined ordinary diffusion

coefficient using the mole fraction gradient the most accurate. The mass fraction and mole

fractions of metal vapour are almost identical, so the difference between the two combined

ordinary diffusion coefficient calculations is due to the ratio of masses 2

M Gm m m appearing

in (19).

The temperatures and metal vapour concentrations are lower for the GTAW workpiece anode.

Figure 12(b) shows that most of the approximate methods are within a factor of two of that

calculated with benchmark combined diffusion coefficient method. However, the influence of

the negative mole fraction gradient close to the anode cannot be taken into account for those

Figure 11. Dependence of temperature and iron vapour mole fraction x and mass fraction Y on distance from the anode in an argon–iron plasma, used to represent typical metal vapour diffusion paths from (a) a GMAW wire anode and (b) a GTAW workpiece

0.0

0.2

0.4

0.6

0.8

0.00

0.02

0.04

0.06

0.08

0.10

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

2000

4000

6000

8000

10000

12000

(b)

Y

Tem

pera

ture

(K

)

Distance from anode (mm)

x

T

0.0 0.5 1.0 1.5 2.0 2.50

2000

4000

6000

8000

10000

12000

14000

16000

T

xT

empe

ratu

re (

K)

Y

(a)

Mas

s &

mol

e fr

actio

ns M

ass

& m

ole

frac

tions

33

methods for which the mass fraction gradient is used to calculate the diffusion mass flux. The

mass flux calculated with the combined ordinary diffusion coefficient using the mole fraction

gradient is negative in this region, while the influence of the temperature gradient term in (11)

ensures that the mass flux calculated using the full combined diffusion coefficient method is

positive in this region.

It can be concluded from these examples that accurate treatment of diffusion requires the use

of the full combined diffusion coefficient method. However, it should be note that convection

is often the dominant method of metal vapour transport in certain regions of the arc, for

example in the centre of the arc below the wire anode in GMAW. Thus, use of an

approximate diffusion treatment may give acceptable results in these regions.

0 1 2 3 4-0.005

0.000

0.005

0.010

0.015

0.020(b)

Comb. diff. coeff't - full treatment Comb. ord. diff. coeff't, mole frac. Comb. ord. diff. coeff't, mass frac. Binary approx. Viscosity approx. Quasi-binary approx.

Mas

s flu

x (k

g m

-2 s

-1)

Distance from anode (mm)

0.0 0.5 1.0 1.5 2.0 2.50.00

0.05

0.10

0.15

0.20

0.25

0.30

Mas

s flu

x (k

g m

-2 s

-1) (a)

Figure 12. Mass flux of iron vapour versus distance for the composition and temperature profiles shown in Figure 11 (a) and (b) respectively. Results are given for the full combined diffusion coefficient approach with the mass flux calculated using (11); the combined ordinary diffusion coefficient only with the mass flux calculated using (19); the combined ordinary diffusion coefficient only, the binary diffusion coefficient approximation and the viscosity approximation with the mass flux calculated using (12); and the quasi-binary diffusion coefficient approximation with the mass flux calculated using (16).

34

3.4 Radiative emission coefficients

It is well known that plasmas in metallic elements radiate more strongly than those in the

usual shielding gases such as argon, helium, nitrogen and hydrogen. The standard method of

treating radiation from thermal plasmas such as welding arcs is the net emission coefficient

method [133]. The method has the particular advantage that radiative cooling of the arc can

be described by the temperature-dependence of single quantity, the net radiative emission

coefficient U. Other methods of treating radiative transfer in thermal plasmas have been

discussed elsewhere, e.g. [134]. The method of partial characteristics has particular

advantages in modelling of arcs such as in circuit breakers, where quantifying the absorption

as well as the emission of radiation is important. Calculations of the required functions for

mixtures of sulphur hexafluoride and copper vapour have been presented by Raynal et al

[135]. However, for gas mixtures relevant to welding arcs, net emission coefficient data

appear far more frequently in the literature.

Calculation of the net radiative emission coefficient is a difficult task, particularly for metal

vapours, for which a very large number of emission lines must be considered. There is

significant variation among the data presented in the literature.

The calculations assume that the plasma is homogeneous, isothermal and in LTE. First, the

plasma composition is calculated as a function of temperature, pressure and the concentration

of different chemical elements. The total net emission coefficient is then the sum of the

contributions due to all the lines and the continuum. The latter requires contributions of

bremsstrahlung, radiative recombination and radiative attachment to be considered. In some

calculations, molecular bands are taken into account. Emission coefficients can be calculated

for an optically-thin plasma, in which case self-absorption of line radiation can be ignored.

However, in reality, an atmospheric-pressure plasma cannot be considered as optically-thin

for all wavelengths and spectral lines, so net emission coefficients have to be calculated

taking into account self-absorption, which requires calculation of the line shape. Detailed

descriptions of the methods used have been given elsewhere [133,136,137].

The net emission coefficients are quoted for a given plasma radius, and in thermal plasma

modelling, this radius is chosen to be the approximate radius of the strongly-radiating high-

temperature region of the arc, which is about 1 mm for a welding arc.

Cram [138] used a simplified statistical method to obtain the contributions of line radiation to

the net emission coefficient, and presented results for plasmas in mixtures of argon and iron

vapour. The method has the advantage that only a statistical sample of atomic data is required,

35

but it is expected to be less accurate than more sophisticated calculations. All other

calculations have used standard approaches, taking into account continuum emission and the

emission from a large number of lines, although there are of course some variations in data

sources, the numbers of lines considered, the methods used to calculate line shapes, and in

other approximations.

Gleizes et al [139] presented net emission coefficients for mixtures of copper vapour and

argon, nitrogen and sulphur hexafluoride, and mixtures of iron vapour and argon. Essoltani et

al presented data for mixtures of iron vapour and argon in an initial paper [140], and

subsequently for mixtures of iron vapour, argon and hydrogen [141] and mixtures of iron,

silicon and aluminium vapour with argon [142]. Menart and Malik [143] presented results for

iron vapour–argon mixtures. Cressault et al [144] recently published data for mixtures of air

with iron, copper and silver vapours. In this issue, Aubrecht et al [145] give net emission

coefficients for thermal plasmas in air and copper vapour or tungsten vapour.

Figure 13 shows the net radiative emission coefficients for mixtures of 1% by mole of

different metal vapours in an argon plasma. It can be seen that the presence of just 1% of

metal vapour greatly increases the radiative emission at all temperatures. The emission is

strongest from iron vapour. Emission for lighter metals such as aluminium and silicon is

much weaker, owing to the many fewer lines. It was noted in section 2.3 that the observed

temperature decrease on axis due to the presence of metal vapour in GMAW was much

smaller for aluminium than for iron vapour. This is likely to be a consequence of the weaker

radiative emission from the lighter metal.

Essoltani et al [142] did not present data for copper, so the argon–copper data were taken

from Gleizes et al [139]. To allow a better comparison between different metals, argon–iron

data from Gleizes et al are also shown in Figure 13. It can be seen that the emission from the

argon–copper mixture is weaker than that from argon–iron mixture calculated by both groups

of authors. The iron emission coefficients of Gleizes et al are lower than those of Essoltani et

al, suggesting that the methods of Essoltani et al would give higher emission coefficients for

the argon–copper mixture than those of Gleizes et al, so it is likely that emission from copper

is stronger than from aluminium.

Cressault et al [144] found that emission from iron vapour was stronger than that from copper

vapour, which was stronger than that from silver vapour. This was true for the pure metal

vapours, or when they were mixed with air. The calculations of Aubrecht et al [145] for

36

mixtures with air indicate that emission from copper vapour is stronger than that from

tungsten vapour for temperatures above about 12 500 K, and weaker for lower temperatures.

Figure 14 shows the influence of the absorption length on the net emission coefficient of iron

vapour. In common with all the metal vapours discussed above, the absorption is very strong

in the first 1 mm, but beyond this radius, there is little further absorption. As noted above, the

usual choice of the absorption radius for net emission coefficients used in welding arcs is

1 mm, but choice of a larger radius would make only a small difference to the calculations.

Figure 15 gives a comparison of net emission coefficients for an iron vapour plasma

calculated by different researchers. The data of Cram [138] were calculated by an

approximate statistical method, and are significantly higher than the other data (although

Cram’s data for argon, presented in the same paper, are in good agreement with most other

values for this gas). The results of Menart and Malik [143] and Cressault et al [144] are in

reasonable agreement, while those of Aubrecht [146] show a similar temperature dependence

but are a little lower. The data of Essoltani et al [142] agree with those of Menart and Malik

and Cressault et al at temperatures up to about 11 000 K, but are significantly lower at higher

5000 10000 15000 20000 25000 30000100

101

102

103

104

105

106

107

108

109

1010

Net

em

issi

on c

oeffi

cien

t (W

m-3

sr-

1 )

Temperature (K)

1% Fe, 99% Ar (Essoltani) 1% Al, 99% Ar (Essoltani) 1% Si, 99% Ar (Essoltani) 1% Cu, 99% Ar (Gleizes) 1% Fe, 99% Ar (Gleizes) 100% Ar (Essoltani)

Figure 13. Comparison of the net emission coefficients for mixtures of argon with 1% by mole of iron, copper, aluminium and silicon vapours, and pure argon. The plasma radius is 1 mm. Data are from Essoltani et al [142] and Gleizes et al [139].

37

temperatures. The data of Aubrecht are unpublished, but were calculated using methods

similar to those employed in their other work [145,147,148].

In computational modelling, radiative emission coefficients for a wide range of metal vapour

concentrations are required. Data for all such concentrations is generally not available, so a

method of interpolation is required. Cressault et al have shown that a simple linear

interpolation based on the mole fraction of the metal vapour gives acceptable results [128].

In this issue, Schnick et al [72] present an analysis of the influence of the net radiative

emission coefficients chosen for modelling of a GMAW arc. The concentration of iron vapour

is between 50 and 100% by mass on the arc axis, resulting in a temperature minimum for all

sets of net emission coefficients analysed. The on-axis temperature in a 250 A arc depended

strongly on the choice of net emission coefficients. For the data of Aubrecht with 1 mm

absorption radius, the temperature 1.5 mm above the workpiece was about 9000 K, and for

the equivalent data of Menart and Malik, the temperature was about 7000 K. For emission

coefficients calculated by Aubrecht, Menart and Malik, and Cram for zero absorption, the on-

Figure 14. Comparison of net emission coefficients for 100% iron vapour, for different plasma radii. Data are from Essoltani et al [142].

5000 10000 15000 20000 25000 30000104

105

106

107

108

109

1010

1011

1012

Net

em

issi

on c

oeffi

cien

t (W

m-3

sr-

1 )

Temperature (K)

R = 0 mm R = 1 mm R = 15 mm

38

axis temperature decreased to about 4000 K. Clearly, accurate values of net emission

coefficients are important in modelling arcs in the presence of metal vapour.

Iwao et al [149] examine the influence of self-absorption of radiation in GTAW arcs in this

issue. The absorption of radiation incident from the top and two sides of each computational

cell was calculated using the absorption coefficient for the argon–iron vapour mixture. The

absorption of radiation led to significant changes, including the heating of the arc in the

regions of high metal vapour concentration and a broader arc temperature profile. However, it

should be noted that the approach used neglected the wavelength-dependence of absorption,

and is therefore only approximate and may give misleading results.

3.5 Calculation of the production rate of metal vapour

Accurate determination of the rate of evaporation of metal vapour from the electrode regions,

and other metal surfaces such as the droplets in the case of GMAW, is vital in assessing the

effects of the metal vapour on the arc. A number of different approaches have been used, and

these are discussed in the following subsections.

Figure 15. Comparison of net emission coefficients for 100% iron vapour for a plasma radius of 1 mm. Data are from Cram [138], Essoltani et al [142], Menart and Malik [143], Cressault et al [144] and Aubrecht [146].

5000 10000 15000 20000 25000 30000104

105

106

107

108

109

1010

1011

1012

1013

Net

em

issi

on c

oeffi

cien

t (W

m-3

sr-

1 )

Temperature (K)

Cram Essoltani et al Menart and Malik Cressault et al Aubrecht

39

3.5.1 Uniform concentration.

The simplest approximation is the assumption that the metal vapour concentration is uniform

through the plasma region. Since vapour concentration will increase with time, and the

calculation is steady state, there is no real connection between the vapour concentration and

the vaporization rate. The approach, which has been used by Tashiro et al [150], is therefore

only useful in providing a rough estimate of the influence of metal vapour.

3.5.2 Fixed vaporization rate.

The next simplest approximation is to assume a fixed rate of vaporization from a particular

region of the electrode. This approach has been used by Schnick et al [72,151] in modelling

of GMAW. The vaporization rate was given as a percentage of the wire feed rate, and the

chosen rates were justified by reference to experimental data. The vaporization rate is

included as the source term MS in (6) (after dividing by the width of the control volume

adjacent to the surface to give the correct dimensions). The same source term should also be

included in the mass continuity equation (1). The approach is not self-consistent, and it

requires somewhat arbitrary choices of the regions of the electrode from which the vapour

emanates. Nevertheless, if the vaporization rate is supported by experimental evidence, it

should give reasonable results.

3.5.3 Energy flux approaches.

An approach that is widely used for ablative vapour production is to determine the mass flux

of metal vapour as the ratio of the heat flux incq incident on the metal surface and the

enthalpy required to vaporize the metal totH :

vap inc totJ q H= (20)

As in the fixed vaporization rate method, this approach gives the source term MS in (6). The

approach neglects the cooling of the metal by conduction, and is therefore only appropriate

when there is a very large energy flux that leads to rapid vaporization. For this reason, it is not

used in modelling of arc welding, but rather in modelling of circuit breakers [15,16,18] and

polymer ablation [152,153]. Typically it is assumed no molten region is present, with the

material being ablated directly from the solid state, so totH will include both the latent heats

of melting and vaporization.

40

Improvements to this method have been developed in the context of erosion of vacuum arc

cathodes [154] and plasma ablation of polymers [155,156]. These approaches have not been

used in the calculation of metal vapour concentrations in welding arcs, but it is possible that

the methods could be adapted to improve the methods described in the next section.

3.5.4 Vapour pressure methods.

Probably the most widely-used method of determining the evaporation rate of metal vapour is

to calculate the vapour pressure vapP of metal vapour at the interface between the plasma and

liquid metal using the Clausius–Clapeyron equation:

vapvap atm

1 1exp

l b

HP P

R T T

− = −

(21)

where atmP is atmospheric pressure, vapH is the molar heat of evaporation, lT is the

temperature of the liquid metal, bT is the boiling temperature of the metal at atmospheric

pressure, and R is the ideal gas constant.

Two approaches have been used to incorporate this vapour pressure in the calculations. The

most widely used [63,157,158,159,160,161,162] is to provide a boundary condition for the

mass fraction of metal vapour at the interface, which is given by

( )vap

vap atm vap

MM

M G

P MY

P M P P M=

+ − (22)

where MM and GM are respectively the molar masses of the metal and the plasma gas.

The other approach is to use the Hertz–Knudsen–Langmuir equation to calculate the mass

flux associated with the vapour pressure, and to use this as the source term MS in (6) (after

dividing by the width of the control volume adjacent to the surface to give the correct

dimensions). In its simplest form, it is written

1 2

Mvap vap2 B l

mJ P

k Tπ

=

(23)

41

where Mm is the mass of the vapour atoms, This approach has been used by Haidar [163].

More complicated formulations, such as

1 12 2

1 2vap

vap ,2

Me c

B l

Pm PJ

k T Tσ σ

π∞

∞

= −

(24)

take into account the pressure P∞ and temperature T∞ at a distance far from the surface, and

an evaporation coefficient eσ and condensation coefficient cσ that may be less than one

[164]. However, such formulations have not been applied to welding arcs. One consideration

is that cσ is reduced by flow away from the surface [165]; this flow is particularly strong

near the wire electrode in GMAW arcs. Furthermore, it has been argued [166] that if the

evaporation rate is reduced below that given by (23), then the evaporative cooling of the

droplets forming on the wire electrode will be reduced. This could increase the temperature of

the droplet to above the boiling point, leading to explosive evaporation that would

compensate for the reduction.

As noted in section 3.5.3, it may be possible to develop better approaches from the methods

used to treat ablation of polymers; these methods calculated vapour fluxes taking account of

the sheath region adjacent to the solid. In an approach differing from others in the literature,

Gu et al [131,167] treated the transport of the silicon vapour from the weld pool as a Stefan

problem, with the diffusion of the vapour through a stagnant inert gas layer taken into account.

Another possible approach, applicable for cases in which the liquid metal temperature is close

to the boiling point, is to calculate the vaporization rate by equating vap vap MJ H M to the net

heat flux to the surface of the liquid metal [168].

Haidar [163] emphasized the importance of also including a source term MS in the mass

conservation equation. This is an important point, since it allows the influence of the vapour

production on the flow in the plasma to taken into account. Further, an equivalent enthalpy

source term is required in the energy equation.

The approach based on a mass fraction boundary condition (22) does not allow these effects

to be incorporated, and is therefore likely to underestimate the velocities in the direction away

from the vapour source, and the enthalpy supplied by the vapour. This will be important for

large vapour fluxes, such as occur in GMAW, as will be discussed further in section 4.2. In

42

the case of GTAW, where the vaporization rates are smaller, the effects will be weaker, and

the boundary condition approach is likely to be reasonably accurate.

Use of the Clausius–Clapeyron equation is in principle an improvement on the fixed

vaporization rate approach, in that it allows a self-consistent calculation of the metal vapour

concentration, including its dependence on position, at the interface between the plasma and

molten metal. However, since the vapour pressure depends very strongly on temperature, an

accurate determination of the molten metal surface temperature is required, and this is not a

simple matter.

In the literature, different degrees of sophistication are used in the treatment of the anode in

GTAW, ranging from estimates [157,158,159], through self-consistent calculations that

neglect electrode melting [160], to self-consistent calculations that include flow in the molten

region of the electrode [161].

The direction of flow of liquid metal in the anode strongly influences the shape of the weld

pool, and can lead to a shallow weld pool with a relatively large surface area, or a deep weld

pool with a smaller surface area. This is determined by factors including the surface tension

of the molten metal and in particular its temperature dependence, and the current density at

the weld pool surface [5]. Therefore a sophisticated model of weld pool flow is a prerequisite

for an accurate calculation of the surface temperature, and thus the evaporation rate, of the

metal.

Finally, while most models of GTAW assume that the weld pool surface is flat, in fact the

surface is in general curved due to the influence of the arc pressure and the surface tension of

the molten metal. This can also influence the flow in the weld pool and the location and

properties of the arc–anode attachment region [169]. Tracking of the deformed surface can be

performed using the volume-of-fluid method [170] or methods that calculate the equilibrium

surface profile taking into account the different forces [171,172]. Both these approaches have

been implemented to determine the weld pool surface profile in GTAW [173,174], but usually

only for models whose computational domain does not include the arc, and not when metal

vapour production has been considered.

Latent heat of vaporization should of course be taken into account in calculating the anode

surface temperature. The latent heat of fusion will also affect the boundary between the solid

and molten region of the anode, and needs to be considered; the standard approach is that of

Voller and Prakash [175]

43

In the case of GMAW, most metal vapour emanates from the wire anode and the droplets. As

for GTAW, a self-consistent calculation for the anode is necessary, taking into account the

heat fluxes between the metal and plasma, the latent heat of vaporization, and the latent heat

of fusion at the boundary between the molten and solid regions. A complete calculation would

require tracking of the change in shape of the anode as droplets form and detach, and the

motion of droplets through the arc. Some success has been achieved in such calculations

using the volume-of-fluid method [176,177,178,179,180], although in none of these cases has

the influence of metal vapour been considered. Haidar [163] did use anode shapes determined

using the volume-of-fluid method as a starting point for his metal vapour calculations, but the

calculation was not self-consistent.

4 Modelling of welding arcs: results

Computational modelling of welding arcs is performed using the coupled partial differential

equations (1) to (7) describing the conservation of mass, momentum, energy and charge.

Appropriate internal boundary conditions are required to treat the interfaces between the

electrodes and the plasma. There have been a number of recent reviews of computational

modelling of thermal plasmas [5,84,134,181], all of which give a good overview of the

techniques involved.

The great majority of computational models of welding arcs have considered GTAW, despite

GMAW being a more widely-used process. The reason is the same as that noted in section 2

in the context of experiments; GTAW is much simpler to treat. In contrast to GMAW, the arc

can be assumed to be steady in time, there are no droplets to consider, and the cathode can be

treated as a thermionic emitter.

Modelling in which the influence of metal vapour has been considered has also concentrated

on GTAW; it is only recently that the influence of metal vapour in GMAW has been seriously

addressed computationally. This is despite the observation that far more vapour is produced in

GMAW.

4.1 Modelling of GTAW arcs

Gu et al [109,129,167] modelled the influence of silicon vapour evaporating from the anode

on the properties of an argon arc. Radiative emission properties were determined using

Cram’s statistical method [138]. In early work, it was assumed that the silicon vapour was

evenly distributed through the plasma, which led to a decrease in temperature through

increased radiative emission [109]. The model was subsequently improved to include a

44

species conservation equation for silicon vapour, initially with an estimated anode surface

temperature [167], and subsequently with the anode temperature calculated self-consistently,

taking in to account flow in the molten metal [129,130]. The quasi-binary diffusion

coefficient method was used to treat diffusion. The rate of evaporation of silicon vapour from

the molten anode was determined assuming that mass diffusion through a stagnant inert gas

layer adjacent to the anode was the rate-limiting step. The anode was included in the

computational domain, and flow of the molten metal was included.

Results were given for a 200 A, 10 mm long arc [129,167]; these parameters are relevant to

arc welding. When the molten silicon temperature was calculated self-consistently [129], the

silicon evaporation rate was about 3.5 mg s–1, and the silicon mass fraction reached 8% on

axis near the anode, decreasing rapidly to less than 0.2% at a distance of less than 1 mm from

the anode. The presence of silicon vapour increased the electrical conductivity in the off-axis

regions close to the anode, decreasing the current density and heat flux density to the anode.

This had the effect of decreasing the surface temperature of the molten anode, and also led to

a decrease in the arc voltage.

Preliminary results were also given for a 600 A 183 mm long arc, relevant to mineral

processing applications [129,130]. In this case, the strong radiative emission associated with

the higher silicon concentration cooled the arc sufficiently for the decrease in electrical

conductivity due to the lower temperature to dominate the increase due to the presence of

metal vapour, leading to an increase in the arc voltage. This result is illustrated in Figure 16.

It shows that even very low silicon concentrations, less than 0.01% by mass, decrease the

voltage due to increased electrical conductivity. Radiative effects are only significant for

concentrations above about 0.1%. The decrease in voltage due to the increased electrical

conductivity caused by the presence of metal vapour dominates for silicon vapour

concentrations up to 5% by mass, above which the radiative cooling leads to an increased

voltage.

Menart and Lin [157] and Zhao et al. [158] modelled GTAW argon arcs with copper vapour

evaporating from the anode. The anode region was not treated self-consistently; rather a

surface temperature was assumed, and from this the vapour pressure of copper vapour was

determined (see section 3.5.4). Zhao et al. used the binary diffusion coefficient approximation,

which, as noted in section 3.3, is only accurate at temperatures for which both copper and

argon are not ionized, and overestimates diffusion velocities, while Menart and Lin used the

somewhat more accurate viscosity approximation, also discussed in section 3.3. Copper

45

vapour mass fractions of about 0.1% were reached close to the anode, which had the effect of

decreasing the temperature in this region.

Gonzalez et al [160] investigated the influence of iron vapour in a GTAW arc with an iron

anode. The anode surface temperature was calculated self-consistently, but flow in the liquid

weld pool was not included. The binary diffusion coefficient approximation was used, so

metal vapour diffusion velocities and therefore concentrations will be overestimated.

Gonzalez et al. predicted iron vapour mole concentrations to reach 7% and 60% respectively

on axis adjacent to the anode for 200 A and 300 A argon arcs, falling to about 1% and 5%

respectively 2 mm above the anode. The metal vapour led to a significant cooling of the arc

due to increased radiative emission. This led to a decrease in the heat flux to the anode, and as

a consequence the depth of the anode region at temperatures above the melting temperature of

iron was decreased.

Gonzalez et al [63] used a similar approach to model a 90 A argon GTAW arc with an iron

anode. The predicted vapour mass concentration in this case reached only 0.7% 1 mm above

the anode, falling to less than 0.2% 3 mm above the anode. As was discussed in section 2.2

Figure 16. Calculated arc column voltage for a 600 A, 183 mm long arc in argon, for different uniform concentrations of silicon. Results taking into account the influence of silicon on only the electrical conductivity, on only the radiative emission coefficient, and on both parameters, are shown. Data are from [129,130].

10-5 10-4 10-3 10-2 10-160

70

80

90

100

Arc

vol

tage

(V

)

Silicon mass fraction

Radiation only Electrical conductivity only Both effects

46

and shown in Figure 2, the predicted temperatures agree well with spectroscopic

measurements for radii less then about 3 mm, with discrepancies at larger radii likely being

due to experimental errors. The presence of metal vapour was found to decrease the

temperature by 1500 K.

Lago et al [159] modelled the influence of copper, iron and aluminium vapours in a GTAW

arc. They also did not model flow in the liquid weld pool, and used the vapour pressure of

iron at 1000 K as a boundary condition at the anode surface. The diffusion of iron vapour was

treated using the viscosity approximation. A 200 A argon arc with no metal vapour was

compared to an arc with metal vapour for the same input electrical power. The iron vapour

concentration was very high, over 40% by mole, adjacent to the anode, falling rapidly to less

than 1% about 1 mm above the anode. The presence of iron vapour increased the voltage by

1.5 V, due to cooling of the arc by increased radiative losses, so the current was decreased

commensurately. While the total heat flux to the anode was decreased by the presence of

metal vapour, the heat flux density on axis was almost twice as large. This was explained in

terms of the temperature and concentration dependence of the electrical conductivity. On axis,

the electrical conductivity was increased by the presence of metal vapour. At large radii,

however, the influence of the lower temperature overrode the increase in electrical

conductivity at a given temperature due to the presence of metal vapour.

Tashiro et al. [150] investigated the influence of iron vapour on a helium TIG arc. In a

strongly simplified calculation, they assumed a uniform iron vapour concentration throughout

the arc. They predicted a lower arc temperature due to radiative losses and changes in the

electrical conductivity, and a lower heat flux density to the anode, for iron vapour mole

concentrations from 5% to 30%.

Yamamoto et al. [161] calculated the influence of iron vapour on helium and argon TIG

welding arcs. The main advance in this work was that flow in the molten weld pool was

included in the model, which allowed a more realistic surface temperature to be determined,

and thus a better estimate of the vapour pressure at the surface of the weld pool. The viscosity

approximation was used to treat diffusion of the metal vapour. It was found that metal vapour

concentrations in a 150 A arc were much larger for a helium arc than an argon arc, as shown

in Figure 17. Results are given for a time 20 s after arc initiation; it was found that the vapour

concentration increased rapidly with time for the first 5 s, and then more slowly, approaching

a steady state [182]. The results illustrate the importance of weld pool temperature in

determining the metal vapour concentration; the temperature is about 500 K greater for

helium, but this leads to an increase of the maximum iron vapour mole concentration from

47

0.2% to 7.0%. This reinforces the need for accurate determination of the weld pool

temperature, as was pointed out in section 3.5.4.

The effect of iron vapour on the current density and heat flux density at the anode workpiece

surface for the conditions of Figure 17 was discussed in detail by Murphy et al [169]. While

the iron vapour concentration in the argon arc was too low to affect the plasma properties, the

heat flux density and current density on axis were approximately halved in the helium arc.

This was mainly due to the increased electrical conductivity at lower temperatures, which

meant that more current could flow through the cooler regions at large radii, leading to a less-

peaked current density profile near the anode. This in turn influenced the heat flux density.

The presence of metal vapour was also found to decrease the helium arc temperature near the

anode. This was attributed to increased radiative emission, and also the decreased ohmic

heating due to the lower current density. The arc voltage was found to decrease from 19.9 V

for a pure helium arc to 18.5 V when metal vapour was taken into account.

In subsequent work, Yamamoto et al [182] and in this issue, Tanaka et al [183] investigated

the influence of the direction of flow in the weld pool on the vapour concentration in the arc.

Workpieces of low- and high-sulphur stainless steel were compared. In the former, the surface

tension decreases as temperature increases, whereas in the latter, surface tension increases

Figure 17. Temperature distribution (on the right-hand side of each plot) and iron vapour mole fraction distribution and velocity vectors (on the left-hand side of each plot) in the arc and electrodes for 150 A GTAW arcs in argon and helium. Results are given for a 304 stainless steel anode after 20 s of operation. The temperature interval is 2000 K in the arc, 200 K in the tungsten cathode, and 250 K in the anode. The maximum values of the iron vapour mole fraction are given, as is the arc voltage in each case. © Maney Publishing [161].

48

with temperature. The Marangoni effect then leads to flow in the weld pool that is radially

outwards, and axially upwards in the centre, for low-sulphur stainless steel, and radially

inwards, and axially downwards in the centre, for high-sulphur stainless steel. The weld pool

is deeper and radially narrower, and has a higher maximum temperature, in the case of high-

sulphur stainless steel. This leads to a higher vapour concentration above the centre of the

weld pool, but with a more rapid radial decrease, as shown in Figure 18. This result is a

compelling illustration of the importance of an accurate treatment of the weld pool, as was

discussed in section 3.5.4.

A further illustration of the importance of accurate calculation of weld pool temperature is

given by the calculation of the time dependence of iron vapour concentrations in helium and

argon arcs for a low-sulphur stainless-steel anode [183]. As the weld pool surface temperature

increases after the arc is struck, the metal vapour concentration is found to increase

accordingly. For the argon arc, the maximum iron vapour mole concentration increases from

zero to 0.25% as the weld pool temperature increases from 1800 K to 2200 K, and for the

helium arc the iron vapour concentration increases from 4% to 7% as the temperature

increases from 2550 K to 2700 K. The main determining factor of the iron vapour

concentration is the weld pool temperature, and clearly relatively small difference in

temperature can lead to very large differences in concentration. Incidentally, the calculated

helium concentrations are in good agreement with those measured by Terasaki et al [27], and

shown in Figure 5.

Figure 18. Radial distribution of the iron vapour mole fraction immediately above the workpiece anode for a 150 A helium arc, 20 s after ignition. Results are given for low-sulphur and high-sulphur stainless steel workpieces. Reproduced with permission from John Wiley and Sons [182].

49

Yamamoto et al [184] have also investigated the production of vapours of different metals

(iron, chromium and manganese) from a stainless-steel workpiece. The different metal

vapours were treated separately; i.e., there was no attempt to model their influence on each

other. The composition of the stainless steel was 80.5% Fe, 18% Cr and 1.5% Mn by weight.

Despite this, it was calculated that the vapours of all three metals had similar concentrations,

with manganese the highest, because of its lower boiling point and consequent higher vapour

pressure at the weld pool surface temperature.

Iwao et al [149] presented a study of pulsed GTAW in a paper in the current issue. Pulsing is

used to control heat transfer and to allow increased welding speed. Their results demonstrated

the importance of the convective flow from the cathode in determining the distribution of the

metal vapour in the arc. The convective flow velocity is higher during the peak current

periods, which causes the region with a given iron vapour concentration to shrink towards the

anode. Iwao et al also included a model that tracks absorption of radiation throughout the

plasma, as discussed in section 3.4.

In summary, metal vapour concentrations for argon GTAW conditions are usually calculated

to be relatively small, at most of the order of 1%, in accordance with experimental results.

The main exceptions are the work of Lago et al [159] and Gonzalez et al [160] for iron

anodes, in which much higher concentrations were predicted. Low levels of metal vapour lead

to an increase in electrical conductivity in the cooler off-axis regions near the anode,

decreasing the current density and therefore the heat flux density near the centre of the anode.

Higher concentrations of metal vapour lead to radiative losses. In both cases, the temperature

of the arc tends to be decreased.

For a helium arc, the metal vapour concentration is calculated to be much larger than an argon

arc carrying the same current, because the weld pool temperature is higher.

The effect of metal vapour on the arc voltage depends on the concentration. As noted above in

the discussion of the work of Gu et al [167], there are two conflicting effects, which can be

understood from the dependence of electrical conductivity on metal vapour concentration and

temperature (see Figure 7(d)). For low concentrations of metal vapour, the increased electrical

conductivity due to the presence of metal vapour at low temperatures dominates and the

voltage decreases. At high concentrations, the increased radiative emission cools the arc, and

the fall in electrical conductivity as temperature decreases dominates, so that the arc voltage

increases.

50

4.2 Modelling of GMAW arcs

Very little modelling work has considered the influence of metal vapour on GMAW arcs.

This is despite strong experimental evidence (described in section 2.3) that metal vapour has a

large effect on the arc properties.

Etemadi et al [185] performed a study in which the evaporation of copper from the upper

electrode of a free-burning arc was investigated. The polarity of the arc was the same as in

GTAW, so the upper electrode was the cathode. Nevertheless, the presence of the metal

vapour source at the top of the arc means that there are strong similarities to GMAW. A metal

vapour production rate of 1 mg s-1 from the tip region of the cathode was assumed. The binary

diffusion coefficient was used, which will lead to a large overestimate of the diffusion

velocity at the high temperatures present near the cathode (see Figure 10). Nevertheless,

convective flow dominates in this region, so the copper vapour distribution should still be

reasonably reliable. A more serious problem is that radiation from the copper vapour was

neglected, since argon radiative emission coefficients were used. Further, it appears that the

influence of the metal vapour source was not taken into account in the mass continuity

equation. It was predicted that the electrical conductivity is increased by the presence of high

concentrations of copper (ranging from mass fractions of 0.8 at the cathode to 0.15 at the

anode on axis), which led to greater arc constriction and therefore increased temperatures in

the arc core and decreased temperatures in the fringes. The use of argon radiative emission

coefficients means that the additional radiative cooling due to the presence of copper, which

will be substantial, was neglected. This, together with the neglect of the metal vapour mass

source term in the mass continuity equation, means that the results will be unreliable.

Schnick et al. [151] presented results of calculations of the influence of iron vapour in a

GMAW arc. A fixed vaporization rate of the wire anode was assumed, with the metal vapour

source term included in the metal vapour and mass continuity equations. The combined

diffusion coefficient method was used, allowing accurate calculation of the transport of the

iron vapour by diffusion. A strong concentration of iron vapour near the axis of the arc

occurred due to the rapid downward convective flow. Demixing effects led to a concentration

of metal vapour in the arc fringes, with a minimum in the intermediate region. The most

dramatic result was the prediction of a temperature minimum on the arc axis. All these

features are shown in Figure 19. The temperature minimum was accompanied by a minimum

in the current density on axis. By performing calculations assuming an influx of cold argon at

the same rate as the metal vapour influx, and of argon with either the electrical conductivity

51

or the radiative emission coefficient of the argon–iron mixture, it was shown that it was the

intense radiative emission of the iron vapour that caused the temperature minimum.

In this issue, Schnick et al [72] present an investigation of the influence of different

vaporization rates and different net radiative emission coefficient datasets on their results. The

same methods were used as in their previous paper [151]. As noted in section 3.4, calculated

radiative emission coefficients for iron vary by factors of up to about 100. While these have a

large influence on the predicted temperatures on axis, in all cases a central temperature

minimum is observed for a vaporization rate of 1% of the wire metal feed rate. Only when the

vaporization rate was decreased to an unrealistically low 0.1% did the central temperature

minimum disappear. Schnick et al also compared the predictions of their model to both the

high-speed images and the temperatures measured by Zielińska et al [42]. They found that it

was possible to obtain good agreement if relatively high vaporization rates were used. In

particular, the conical shape of the luminous central region could be reproduced. Interestingly,

for high vaporization rates, a flow reversal occur on the arc axis, with the direction of flow

being upwards from the workpiece as a consequence of the strong cooling of the central

regions of the arc.

Haidar [163] recently performed calculations of the influence of iron vapour in GMAW arcs.

He used data for the wire anode shape and surface temperature obtained from a model of

GMAW in pure argon [176]. The metal vapour evaporation rate was calculated using the

Figure 19. Distribution of metal vapour concentration and temperature, and flow vectors, for a 250 A arc in argon assuming iron vapour is produced at the wire anode at a rate of 0.015 g s-1, corresponding to 1% of the wire metal feed rate. The dimensions are 15 mm horizontally by 10 mm vertically. From [151].

52

Hertz–Knudsen–Langmuir equation (23). The influence of the metal vapour source was also

taken into account in the mass and energy conservation equations. Diffusion of metal vapour

was neglected, so the distribution was determined only by convective flow. Further, the

influence of iron vapour on the radiative emission was neglected, and difficulties in obtaining

convergence means that the transport and thermodynamic properties for mixtures of more

than 25% iron vapour are represented by the properties for 25% iron vapour. Temperature

distributions neglecting and including the metal vapour source were compared. For the latter

case, a temperature minimum on axis was predicted. Temperature distributions obtained for a

pure argon plasma, but including a source of cold argon from the wire anode, were found to

be similar to those obtained for argon–iron vapour plasma. It was found that it was the influx

of cold gas, whether metal vapour or argon, that dominated this cooling, and it was concluded

that this is the most important effect.

While the neglect of the influence of metal vapour on the radiative emission is obviously a

serious shortcoming in Haidar’s model, his work has the advantages of taking into account

more realistic wire anode shapes and of calculating evaporation rates directly. The results

confirm the conclusion of Schnick et al [72,151] that metal vapour can significantly decrease

the temperature in the central region of the arc in GMAW. However, Haidar’s conclusion that

the influx of cold argon is important does not agree with the results of Schnick et al [72,151],

who found the cooling effect of the cold gas influx to be small compared to that of the strong

radiative emission from iron vapour. It should be noted that the cold gas flux used by Haidar

for most of his calculations, 0.07 g s-1, is about five times larger than that used by Schnick et

al. The corresponding iron vapour mass fraction is also larger, reaching 100% in some

regions of the arc. However, Haidar did present results for a cold argon flux of 0.0175 g s-1,

which is similar to that used by Schnick et al. In this case, Haidar found there is still an on-

axis minimum in the radial temperature distribution, although the minimum is not as deep; the

temperature on axis is at most around 2000 K lower than the maximum temperature.

There are at least two factors that may account for the discrepancy. First, the neglect of

diffusion in Haidar’s model will lead to an overestimate of the cooling. Second, the

distribution of the metal vapour source is different in the two models, with that of Schnick et

al being only an estimate. This may lead to errors in the description of the flow in the arc,

which could be significant.

Some evidence of the importance of the flow distribution was provided by an experiment on a

GTAW arc in argon with a current of 500 A, in which the effect of an additional argon flow

through a 0.8 mm diameter hole in the cathode was measured spectroscopically [186]. The

53

additional argon flow (0.014 g s-1) led to a cooling of central region of the arc. The

temperature, which was above 20 000 K without the additional flow, fell to below 15 000 K at

radii below 0.5 mm. Further, large deviations from LTE were observed in this region, as a

consequence of the rapid influx of cold gas.

The relative effects of the direct cooling effect of a flux of metal vapour from the anode, and

of radiation, can be compared for the conditions of Schnick et al [151]. For the vaporization

rate of 0.015 g s-1, the power required to vaporize the iron is 93 W, and the additional power

require to heat iron from the boiling point of 3023 K to a temperature of 15 000 K

(approximately the maximum present in the 250 A arc) is 410 W. This can be compared to the

calculated radiative emission of 2030 W from the arc. Clearly for these conditions, radiative

emission dominates the cooling effect of the influx of vapour. For higher vaporization rates,

the latter effect will become more important, although quantification is difficult, since higher

metal vapour concentrations will increase the radiative emission coefficient for a given

temperature, while the arc temperatures will be lower, which will decrease both the power

required to heat the metal vapour and the radiative emission.

It can be concluded that modelling of the influence of metal vapour in GMAW demonstrates,

in accordance with the available experimental evidence, that metal vapour emanating from the

wire anode has a very large influence on the arc properties, in particular leading to a radial

minimum of temperature and current density on the arc axis. This strong decrease in

temperature and current density will inevitably have a major influence on the heat transport to

the workpiece, and therefore must be taken into account in models of arc welding.

5 Welding fume

The term welding fume is used to describe the small particles and clusters of particles that are

formed during arc welding. The particles, typically of submicron dimensions, are small

enough to remain airborne. They can therefore be inhaled, and are a significant occupational

health problem. Fume is formed in much larger amounts in GMAW than in GTAW.

Welding fume arises from nucleation and subsequent growth of particles from the metal

vapour in the arc plasma. The metal vapour can emanate from the weld pool, from the

droplets (both before and after detachment from the wire electrode) in GMAW, and from

spatter. Spatter refers to tiny droplets of molten metal detached from the molten regions of the

electrode.

54

It has also been proposed that fume is partly composed of small spatter droplets [187,188].

However, while there is a correlation between spatter and fume formation rates as welding

parameters change, and while there are measurements that indicate that spatter is responsible

for between 6% and 35% of fume [189], it is unlikely that that spatter makes a significant

direct contribution. Although some of the spatter droplets are small enough to remain airborne

and therefore to be inhaled (less than 20 µm), measurements have indicated that their

concentration is many orders of magnitude lower than the submicron fume particles [190].

It has been suggested that rapid oxidation of spatter particles forms fume [187,191]. This

hypothesis was based on the detection of spatter droplets that were porous and apparently

oxidized, and the observation that better inert-gas shielding of the arc reduced the amount of

fume. However, Jenkins and Eagar [192] performed experiments and calculations that

indicated that only spatter droplets larger than 2 mm could oxidize and form significant

amounts of fume, and that such large droplets do not form a substantial proportion of the

spatter. They concluded that the observed correlation between spatter and fume formation

rates was due to their being determined by the same welding process variables.

It therefore seems likely that a large proportion of fume is formed from metal vapour. The

metal vapour will be in the form of atoms or ions in the high-temperature central regions of

the arc. Much of this vapour will condense on the workpiece and will therefore not contribute

to fume production [166]; Deam et al estimate that between 16% and 80% of the metal

vapour will be condensed in GMAW, depending on the wire electrode feed rate [188]. The

remaining metal vapour will be transported by convection and diffusion to the cooler edge

regions of the arc. Since the saturation vapour pressure decreases rapidly with temperature,

the metal vapour can become supersaturated and nucleate to form metal nanoparticles.

Alternatively, in the presence of oxygen, metal oxide molecules can form in the gas phase,

and then nucleate to form metal oxide nanoparticles. The nanoparticles then grow by

condensation, and by collisions to form larger particles or chains of particles. Generally

oxidation occurs at some stage of the process, so that fume is usually composed of metal

oxide.

Typically the fume particles are below 500 nm in aerodynamic diameter, which gives them a

high probability of deposition in parts of the lungs where rapid clearance mechanisms are not

effective. The chemical composition depends on the alloys being welded; for stainless steel,

oxides of iron, chromium, manganese and nickel are major components. While all

components of fume have been shown to negative health consequences, chromium

(particularly hexavalent chromium) and nickel are of particular concern [193].

55

There is an extensive literature on the health effects of fume, including many epidemiological

and animal studies; these are reviewed in Refs [193] and [194]. There are also extensive

studies on means of reducing exposure, including altering the welding process parameters,

shielding gas composition, ventilation, design and composition of electrodes, etc (e.g.

[187,194,195]).

Efforts to calculate fume production rates from welding have generally been rudimentary, and

have largely involved engineering estimates of droplet temperatures and evaporation rates

(e.g., [188,189,196]). Haidar [176] developed a self-consistent two-dimensional

computational model of droplet formation in GMAW, which allowed the droplet shape and

temperature to be predicted, and thus the evaporation rate to be estimated with some

confidence.

Tashiro et al [197] have made a significant step in predictive modelling of fume formation in

work presented in this issue. They use two-dimensional computational models of GMAW and

GTAW to determine self-consistently the weld pool temperature, and in GMAW, the droplet

temperature. This allows the vapour concentration in the arc to be determined. They then use

a two-dimensional sub-model that tracks nucleation of nanoparticles from the vapour,

subsequent condensation of vapour onto the particles, and collisions of particles. A feature is

that the treatment allows differentiation between coalescence (to form a larger particle) and

agglomeration (to form a chain of separate particles) of colliding particles. The approach

allows prediction of the size and shape of fume particles formed at different regions of the arc.

The predictions are compared with measured fume particles and show reasonable agreement.

There are of course many improvements that could be made in future work. For example,

oxidation reactions are not included in the model, and the method of differentiating between

coalescence and agglomeration, based on whether the temperature is above or below the

melting temperature, can be improved upon by considering solid state diffusion effects [198].

Nevertheless, the work of Tashiro et al [197] is a major step towards a more complete

understanding of fume formation from metal vapour.

6 Discussion and conclusions

The production of metal vapour is clearly an important phenomenon in arc welding. Since

successful welding relies on the melting of the metal workpiece, it is inevitable that at least

some metal vapour will be produced. The amount will depend on the temperature and surface

area of the weld pool in both GTAW and GMAW, and also of the wire electrode and droplets

56

in GMAW. Metal vapour production can be reduced by reducing the arc current and altering

other parameters in order to reduce the temperature of the molten metal regions, but doing so

will also tend to reduce the effectiveness of welding.

Measurements and calculations indicate that the effects of metal vapour are larger in GMAW

than in GTAW. There are two reasons for this. First, the tip of the wire electrode and the

droplets are at a higher temperature than the weld pool, and the exponential dependence of

vapour pressure on temperature leads to a greater metal vapour concentration. Second, the

strong convective flow from the wire electrode means that metal vapour is highly

concentrated in the central regions of the arc. In contrast, flow near the weld pool is directly

mainly radially outwards, so the metal vapour originating from the weld pool tends to become

concentrated away from the central regions.

As a consequence of the different concentrations and distribution of metal vapour in GMAW

and GTAW, the relative importance of the physical mechanisms by which metal vapour

influences the arc properties is altered. As discussed in section 3, even low concentrations of

metal vapour have a large effect on two thermophysical properties: the net radiative emission

coefficient and the electrical conductivity. The influence on electrical conductivity is most

important at low temperatures; in particular just 1% of metal vapour means that the plasma

will conduct at temperatures as low as 4000 K, rather than 7000 K for an argon plasma. This

means that the main influence of the metal vapour produced in GTAW, which tends to be

present in the lower temperature regions near the anode, is to extend the conducting region to

higher radii. This has the effect of decreasing the current density, and therefore the heat flux

density, near the centre of the anode.

Metal vapour increases the radiative emission coefficient across the full range of temperatures

present in arcs, and the increase is approximately proportional to the metal vapour

concentration. Thus the main influence of the metal vapour in GMAW is to increase the

radiative emission from the central region of the arc, thereby cooling this region. This leads to

the characteristic appearance of GMAW arcs, shown in Figure 3, in which a bright central

region dominated by metal vapour radiation is surrounded by the argon region, which may

even be at a higher temperature than the central region.

The presence of metal vapour generally leads to a decrease in the arc temperature, since both

the increase in electrical conductivity, and the increase in radiative emission, have this effect.

The influence on the arc voltage, as discussed in section 4.1, is less clear. The increased

electrical conductivity tends to decrease the voltage, but the temperature decrease associated

57

with strong radiative emission has the opposite effect (since conductivity increases with

temperature). As illustrated in Figure 16, the voltage tends to decrease for low metal vapour

concentrations and increase for high concentrations.

While the most important effects of metal vapour in welding arcs are reasonably well

understood, there are still many areas of uncertainty that warrant detailed investigation.

Experimentally, there is a wide scope for further studies, particularly of GMAW arcs. The

question of the concentration of metal vapour is unresolved; Valensi et al [46] measured

concentrations below 1%, in contrast to the much higher concentrations found by Goecke et

al [50] and Rouffet et al [44], and predicted in modelling [72,151,163,185]. The influence of

shielding gas composition on metal vapour concentration also requires thorough investigation.

Measurements indicate that arc voltage initially decreases when carbon dioxide is added to

argon, but subsequently increases as the carbon dioxide concentration increases. This may be

related to changes in the metal vapour concentration, although formation of an insulating

layer on the electrode surface has also been suggested as a mechanism [46,49].

The existence of LTE in the central region dominated by metal vapour is unclear, with some

evidence available that the rapid flow of vapour into this region leads to deviations from LTE.

Further studies using techniques that do not rely on the existence of LTE, such as laser

scattering, or spectroscopic methods based on line broadening, are required.

There is a wide range of GMAW and GTAW processes (dc, ac, pulsed, short-arc, different

polarities, etc), and only recently have efforts been made to develop an understanding of the

role of metal vapour in many of these modes. There is also a wide variation in wire

composition, with different steel alloys, different metals, and wires cored with oxides and

other materials all being used. There has only been very limited investigations of the

influence of wire composition. For example, the influence of vapours of light metals in

GMAW is unclear, with one study [70] finding that no temperature minimum occurs if an

aluminium wire anode is used.

There is also the question of when metal vapour begins to have an important influence on arc

properties. One study of GTAW arcs failed to find a measureable influence [65], and a careful

examination of the influence of arc current and other parameters on the metal vapour

distribution and arc temperature would be valuable.

58

While there have been many modelling investigations devoted to the influence of metal

vapour in welding arcs, there have been no definitive studies published. An ideal model

would require accurate calculation of the metal vapour source term, of the diffusion of the

metal vapour in the plasma, and of the effect of the metal vapour on the plasma

thermophysical properties. All of these issues have been discussed in detail in this review.

Here the main points are summarized.

Determining the metal vapour source term is clearly critical in calculating the amount of

vapour in the arc. The two requirements are an accurate determination of the surface

temperature of the molten metal regions, and of the vaporization rate for a given temperature.

The temperature itself is a function of the vaporization rate through the influence of

evaporative cooling (both directly, and in the case of GMAW, through the energy transported

the weld pool by droplets). As has been discussed in section 3.5.4, determining the molten

metal temperature requires a self-consistent model of the arc and electrode regions that takes

into account fluid flow in the weld pool, and in the case of GMAW, the shape of the droplets.

The usual methods to determine the vapour production rate have been based on a boundary

condition derived from the vapour pressure of the molten metal at the metal–plasma interface,

or a direct calculation using the Hertz–Langmuir–Knudsen equation. The latter method has

the advantage that it also allows the source terms required by the mass and energy

conservation equations to be determined. As shown by Haidar [163] this is important for the

high vaporization rates occurring in GMAW, although it will be less significant for GTAW. It

was noted in section 3.5.4 that the Hertz–Langmuir–Knudsen equation is only an

approximation, and a more detailed understanding of the boundary region is required to

develop a better model.

Diffusion of metal vapour is best treated using the combined diffusion coefficient method,

which is equivalent to a full multicomponent treatment under the assumption of LTE. As

shown in section 3.3, other methods are inaccurate, and thus give only approximate results.

This can be partially justified when convection is the dominant transport mechanism, as in the

central region of the arc in GMAW. Nevertheless, the combined diffusion coefficient is only

slightly more difficult to implement that the approximate methods, so there is little reason not

to use it.

Values of the thermodynamic and transport properties given in the literature are generally

very consistent, as discussed in section 3.2. There is some scope for improving the accuracy

of transport coefficients by use of more accurate intermolecular potentials, but this is not a

major source of inaccuracy in computational models. More significant are the discrepancies

59

between net radiative emission coefficients given in the literature, which can be more than an

order of magnitude (see Figure 15). Schnick et al [72] have shown that the different values

have a strong influence on the calculated temperature in a GMAW arc; the effects will be

weaker in a GTAW arc since radiation is less important. Iwao et al [149] have shown that

self-absorption of radiation can be important by using a simplified method, and a study using

more sophisticated approaches, for example the method of partial characteristics, would be

worthwhile.

A final question is that of removal of metal vapour from the arc plasma. The vapour may be

transported to the fringe regions, it may nucleate and condense to form solid particles

(welding fume), or it may be recondensed on the electrodes. Investigations of fume formation

indicate that a large fraction of the metal is deposited on the electrodes (e.g., [166,188]). The

problem of how to best deal with these effects in a computational model is not fully resolved.

Haidar [163] assumed that all metal vapour in GMAW that reached the region immediately

above the workpiece was condensed; such an approach is useful, but would require

refinement if a molten weld pool was considered. The work of Tashiro et al [197] on

modelling of fume formation suggests an approach for calculating the removal of vapour by

nucleation and subsequent condensation on solid particles.

In summary, the production, transport and removal of metal vapour in welding arcs are

subjects that have attracted strong research attention. In the past, this has largely been

focussed on GTAW, but advances in experimental, theoretical and computational techniques

have allowed the more challenging case of GMAW to be tackled recently. There are many

issues to be resolved, some of major importance such as the concentration of metal vapour in

GMAW arcs. Since the presence of metal vapour affects the transport of current and energy to

the weld pool, it has an influence, sometimes a very large influence, on the weld pool depth

and shape. For this reason it is of great practical importance.

This review has highlighted the main findings of previous research, the shortcomings of the

techniques that have been used, and the areas that require further effort. It is hoped it will

stimulate continuing research into the subject.

60

Acknowledgements

I thank Dr Jawad Haidar and Dr John Lowke of CSIRO, Dr Michael Schnick of Technical

University Dresden and Professor Manabu Tanaka of Osaka University for many useful

discussions. I am grateful to Dr Vladimir Aubrecht of Brno University of Technology for

permission to use his unpublished radiation data for mixtures of argon and iron vapour.

61

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List of figure captions Figure 1. Schematic diagram illustrating the (a) gas–tungsten arc welding and (b) gas–metal arc welding processes. Figure 2. Radial temperature profile at an axial position 1 mm above the anode for a pure argon arc and argon arc with iron vapour present. Both measured and calculated profiles are given. Data are from [63]. Figure 3. High-speed photographs of a pulsed GMAW arc with copper wire anode, after 1.75 ms of a 250 A current pulse. From left to right: with a neutral density filter; with a 510 3 nm± interference filter that passes copper lines; with a 780 3.5 nm± interference filter that passes argon lines. From Goecke S F et al ChopArc. MSG-Lichtbogenschweißen für den Ultraleichtbau ©2005 Fraunhofer IRB Verlag, Stuttgart, Germany [50]. Figure 4. Radial dependence of electron temperature for 326 A arcs in argon and two mixtures of argon with carbon dioxide (percentages are by mole). Axial positions are ▲ 3 mm, ■ 4.5 mm, ● 6.0 mm and ♦ 7.5 mm above the workpiece cathode. From [42]. Figure 5. Electron temperatures measured by Thomson scattering for a helium GTAW arc with a water-cooled copper cathode (left-hand side) and a stainless steel anode (right-hand side). The results are superimposed on a photograph of the arc plasma. Reproduced with kind permission from Springer Science+Business Media: Terasaki H, Tanaka M and Ushio M 2002 Effects of metal vapor on electron temperature in helium gas tungsten arcs Metall. Mater. Trans. A 33A 1183–8, Figure 8 [27]. Figure 6. Comparison of transport properties of argon–copper and argon–iron plasmas calculated by different authors. Percentages are by mole. (a) Thermal conductivity of argon–copper mixtures; (b) thermal conductivity of an argon–iron mixture; (c) viscosity of an argon–copper mixture; (d) electrical conductivity of argon–copper mixtures. References from which the data were taken are: Murphy (argon–copper) [103], Mostaghimi [102], Cressault [104], Aubreton [97], Murphy (argon–iron) [19], Dunn [108], Hoffmann [105]. Figure 7. Calculated properties of plasmas in different mixtures of argon and iron vapour. Percentages are by mole. Figure 8. Calculated properties of plasmas in mixtures of 90% argon and 10% metal vapour by mole, for five different metals. Figure 9. Combined (a) ordinary, (b) temperature and (c) electric field diffusion coefficients for different mixtures of argon and iron vapour. Percentages are by mole. Figure 10. Dependence of the ordinary diffusion coefficient Fe ArD on temperature for a

mixture of 10% iron vapour and 90% argon by mole. Results are given for the combined

ordinary diffusion coefficient Fe ArxD , the binary diffusion coefficient approximation, the

viscosity approximation and the quasi-binary diffusion coefficient approximation. Figure 11. Dependence of temperature and iron vapour mole fraction x and mass fraction Y on distance from the anode in an argon–iron plasma, used to represent typical metal vapour diffusion paths from (a) a GMAW wire anode and (b) a GTAW workpiece

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Figure 12. Mass flux of iron vapour versus distance for the composition and temperature profiles shown in Figure 11 (a) and (b) respectively. Results are given for the full combined diffusion coefficient approach with the mass flux calculated using (11); the combined ordinary diffusion coefficient only with the mass flux calculated using (19); the combined ordinary diffusion coefficient only, the binary diffusion coefficient approximation and the viscosity approximation with the mass flux calculated using (12); and the quasi-binary diffusion coefficient approximation with the mass flux calculated using (16). Figure 13. Comparison of the net emission coefficients for mixtures of argon with 1% by mole of iron, copper, aluminium and silicon vapours, and pure argon. The plasma radius is 1 mm. Data are from Essoltani et al [142] and Gleizes et al [139]. Figure 14. Comparison of net emission coefficients for 100% iron vapour, for different plasma radii. Data are from Essoltani et al [142]. Figure 15. Comparison of net emission coefficients for 100% iron vapour for a plasma radius of 1 mm. Data are from Cram [138], Essoltani et al [142], Menart and Malik [143], Cressault et al [144] and Aubrecht [146]. Figure 16. Calculated arc column voltage for a 600 A, 183 mm long arc in argon, for different uniform concentrations of silicon. Results taking into account the influence of silicon on only the electrical conductivity, on only the radiative emission coefficient, and on both parameters, are shown. Data are from [129,130]. Figure 17. Temperature distribution (on the right-hand side of each plot) and iron vapour mole fraction distribution and velocity vectors (on the left-hand side of each plot) in the arc and electrodes for 150 A GTAW arcs in argon and helium. Results are given for a 304 stainless steel anode after 20 s of operation. The temperature interval is 2000 K in the arc, 200 K in the tungsten cathode, and 250 K in the anode. The maximum values of the iron vapour mole fraction are given, as is the arc voltage in each case. © Maney Publishing [161]. Figure 18. Radial distribution of the iron vapour mole fraction immediately above the workpiece anode for a 150 A helium arc, 20 s after ignition. Results are given for low-sulphur and high-sulphur stainless steel workpieces. Reproduced with permission from John Wiley and Sons [182]. Figure 19. Distribution of metal vapour concentration and temperature, and flow vectors, for a 250 A arc in argon assuming iron vapour is produced at the wire anode at a rate of 0.015 g s-1, corresponding to 1% of the wire metal feed rate. The dimensions are 15 mm horizontally by 10 mm vertically. From [151].