effects of surface active elements on weld pool fluid flow...

Effects of Surface Active Elements on Weld Pool Fluid Flowand Weld Penetration in Gas Metal Arc Welding

Y. WANG and H.L. TSAI

This article presents a mathematical model simulating the effects of surface tension (Marangoni effect)on weld pool fluid flow and weld penetration in spot gas metal arc welding (GMAW). Filler dropletsdriven by gravity, electromagnetic force, and plasma arc drag force, carrying mass, thermal energy,and momentum, periodically impinge onto the weld pool. Complicated fluid flow in the weld poolis influenced by the droplet impinging momentum, electromagnetic force, and natural convection dueto temperature and concentration gradients, and by surface tension, which is a function of bothtemperature and concentration of a surface active element (sulfur in the present study). Although thedroplet impinging momentum creates a complex fluid flow near the weld pool surface, the momentumis damped out by an “up-and-down” fluid motion. A numerical study has shown that, depending uponthe droplet’s sulfur content, which is different from that in the base metal, an inward or outwardsurface flow of the weld pool may be created, leading to deep or shallow weld penetration. In otherwords, it is primarily the Marangoni effect that contributes to weld penetration in spot GMAW.

I. INTRODUCTION falling droplets and weld pool and the Marangoni effectswere not considered. Choo et al.[19] built a water-alcoholIN gas tungsten arc welding (GTAW), the importantphysical model to study the Marangoni interaction whenforces that could affect the weld pool convection and weldalcohol droplets fall onto the water pool. Based on experi-penetration include buoyancy force, electromagnetic force,mental observations, they concluded that Marangoni flowplasma arc pressure, and surface tension force (Marangonimight be responsible for fluid flow in the weld pool.flow).[1,2,3] However, it has been reported that surface tensionRecently, Wang and Tsai[20] presented a mathematical modelforce dominates the flow behavior in the weld pool andto study the droplet-impinging process and the weld pooldetermines the shape and penetration of the solidified welddynamics in GMAW. The objective of this article is to extendbead.[4–9] Because surface tension force is a function of boththe model by Wang and Tsai[20] to study the effects of surfacetemperature and some trace elements[10,11,12] (surface activeactive elements on weld pool fluid flow, weld penetration,elements) contained in the molten metal, it is possible toand the shape of the solidified weld bead in GMAW.increase or decrease weld penetration by adding some sur-

In this article, a transient two-dimensional model based onface active elements (e.g., S, O, Se, and Te for stainlessthe volume-of-fluid (VOF) technique[21] and the continuumsteels) to the weld pool during the welding process. Surfaceformulation[22] is used to simulate fluid flow, heat transfer,active elements can be added to the weld pool throughand species concentration when droplets periodicallyshielding gas, coating flux on the surface of the joint priorimpinge onto the weld pool. The VOF technique is used toto welding, or doped filler metal.[13] So far, however, allhandle the transient, deformed shape of the weld pool sur-mathematical models studying the surface tension effects onface, while the continuum model handles fusion, solidifica-weld penetration are limited to GTAW.[14,15,16]

tion, and fluid flow in the regions of liquid, solid, and mushVery few experimental or theoretical studies on the weldzones. With its easily available thermophysical properties,pool fluid flow in GMAW have been reported. Tsao andsulfur is selected as the surface-active element in this study.Wu[2] presented a two-dimensional, stationary weld poolThe weld pool shape, fluid flow, temperature, and sulfurconvection model by assuming the weld pool surface toconcentration distributions in the weld pool are calculatedbe flat. Using boundary-fitted coordinates, Kim and Na[17]

as a function of time.presented a three-dimensional quasi-steady heat and fluidflow analysis for the moving heat source of the GMAWprocess with free surface. Ushio and Wu[18] used a boundary-

II. MATHEMATICAL MODELfitted non-orthogonal coordinate system to handle the largelydeformed gas metal arc (GMA) weld pool surface and pre- A. Governing Equationsdicted the area and configuration of the weld reinforcement.

Figure 1 shows the schematic sketch of a stationary axi-In their study, however, although the size and profile of thesymmetric GMAW welding system. It assumes that sphericalweld pool were predicted, the dynamic interaction betweendroplets at a certain height fall onto the base metal. Thedroplets, driven by gravity, electromagnetic force, andplasma arc drag force, and carrying mass, thermal energy,Y. WANG, formerly Graduate Student, Department of Mechanical and

Aerospace Engineering and Engineering Mechanics, University of and momentum, periodically impinge onto the base metal.Missouri-Rolla, Rolla, MO 65409, is Engineer, Watlow Heater Technology The droplets and the base metal may have different sulfurCenter, Fenton, MO 63026. H.L. TSAI, Professor of Mechanical Engi- concentrations. A molten weld pool is gradually formed atneering, is with the Department of Mechanical and Aerospace Engineering

the surface of the base metal by the deposited droplets andand Engineering Mechanics, University of Missouri-Rolla.Manuscript submitted September 11, 2000. the arc energy. The mathematical formulation given in this

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 32B, JUNE 2001—501

Energy

t(rh) 1 ¹ ? (rVh) 5 ¹ ? 1k

cs¹h2

[4]

1 ¹ ? 1kcs

¹(hs 2 h)2 2 ¹ ? (r (V 2 Vs)(h1 2 h))

Species

t(r f a) 1 ¹ ? (rVf a) 5 ¹ ? (rD¹f a)

[5]1 ¹ ? (rD¹( f a

1 2 f a)) 2 ¹ ? (r (V 2 Vs)( f a1 2 f a))

The last term in the right of Eq. [2] and the second termfrom the last on the right of Eq. [3] represent the contribu-tions from electromagnetic force and will be discussed next.The last term on the right of Eq. [3] is the plasma drag forceacting only on the droplet, which will be discussed later.Note that the assumptions used to derive the aforementioned

Fig. 1—Schematic sketch of a stationary GMAW system and dimensions equations and the physical meanings for each term appearingof the weld workpiece. in the equations were discussed previously[22,23] and will not

be repeated here. In spot GMAW, because the arc heat fluxis fairly concentrated and the weld cooling rate is very fast,as compared to those in a typical casting solidification proc-section is valid for both the base metal and the liquid droplet. ess,[24,25] the mushy zone is expected to be small. Hence,The initial temperature and sulfur concentration of the drop- the solid-phase velocity is assumed to be 0. In Eqs. [1]let are assumed to be constant and uniform. Once a droplet through [5], the continuum density, specific heat, thermalreaches the weld pool surface, the droplet is immediately conductivity, mass diffusivity, solid mass fraction, liquidconsidered to be part of the base metal; at that point, the mass fraction, velocity, enthalpy, and mass fraction of consti-mixing of momentum, energy, and species begins. tute a are defined as follows:Based on the continuum formulation by Chiang and

Tsai[22] and Diao and Tsai,[23] the conservation of mass, r 5 gsrs 1 glrl; c 5 fscs 1 flcl; k 5 gsks 1 glklmomentum, energy, and species for the welding system canbe expressed as follows. D 5 fsDs 1 flDl; fs 5

gsrs

r; fl 5

glrl

r[6]

ContinuityV 5 fsVs 1 flVl; h 5 hs fs 1 hl fl; f a 5 fs f a

s 1 fl f al

If the phase-specific heat is assumed constant, the phase

t(r) 1 ¹ ? (rV ) 5 0 [1] enthalpy for the solid and the liquid can be expressed as

hs 5 csT; hl 5 clT 1 (cs 2 cl)Ts 1 H [7]Momentum where H is the latent heat of fusion or solidification for

the alloy.The assumption of the permeability function in the mushy

t(ru) 1 ¹ ? (rVu) 5 rg 1 ¹ ? 1ml

rrl

¹u2 2pr zone requires consideration of the growth morphology spe-

cific to the alloy under study. In the present study, the perme-ability function analogous to fluid flow in porous media is

2ml

Krrl

(u 2 us) 2Cr2

K1/2rl.u 2 us.(u 2 us) [2] assumed by employing the Carman–Kozeny equation:[26,27]

K 5g3

l

cl(1 2 gl)2 ; cl 5180d 2 [8]

2 ¹ ? (r fs flVr ur) 1 ¹ ? 1mlu¹1rrl22 1 J 3 B.r

where d is proportional to the dendrite dimension, which isassumed to be a constant and is approximately 1022 cm.

t(rv) 1 ¹ ? (rVv) 5 ¹ ? 1ml

rrl

¹v2 2pz The inertial coefficient C can be calculated from[26]

C 5 0.13g23/2l [9]

2ml

Krrl

(v 2 vs) 2Cr 2

K1/2rl.v 2 vs.(v 2 vs)

[3] B. Tracking of Free Surface2 ¹ ? (r fs flVrvr) 1 ¹ ? 1mlv¹1r

rl22 The algorithm of VOF is used to track the moving free

surfaces.[21] The fluid configuration is defined by a VOF1 rgbT (T 2 T0) 1 J 3 B.z 1 Fdrag function F(x, y, t), which tracks the location of free surface.

502—VOLUME 32B, JUNE 2001 METALLURGICAL AND MATERIALS TRANSACTIONS B

This function represents the VOF per-unit volume and satis- heat flux is absorbed by the weld pool. The heat loss dueto convection, radiation, and melt evaporation can befies the following conservation equation:expressed by

dFdt

5Ft

1 (V ? ¹)F 5 0 [10] qconv 5 hc(T 2 T`) [17]

qradi 5 s«(T 4 2 T 4`) [18]When averaged over the cells of a computing mesh, the

average value of F in a cell is equal to the fractional volumeqevap 5 WHv [19]of a cell occupied by the fluid. Hence, a unit value of F

corresponds to a cell full of fluid, whereas a 0 value indicates where Hv is the latent heat for the liquid-vapor phase change,that the cell contains no fluid. Accordingly, cells with F and W is the evaporation mass rate. For a metal such asvalues between 0 and 1 are partially filled with fluid and steel, W can be written as[29]

are identified as surface cells.log (W ) 5 Av 1 log Patm 2 0.5 log T [20]

C. Boundary Conditions log Patm 5 6.121 218836

T[21]

The boundary conditions corresponding to Eqs. [1]through [10] are given as follows. 2. Bottom surface

1. Top free surface2k

Tz

5 qconv [22]For cells that contain a free surface, that is, cells thatcontain fluid but that have one or more empty neighbors,the following pressure condition must be satisfied:[21] u 5 0; v 5 0 [23]

p 5 pv 1 gk [11] f a

z5 0 [24]

where p is the pressure of the fluid, pv is the vapor pressureor any other applied external pressure acting onto the free

3. Symmetrical axissurface, g is the surface tension, and k is the free surfacecurvature, which is given by[21]

Tr

5 0 [25]

k 5 2F¹ ? 1 n.n.2G5

1.n. F1 n

.n.? ¹2.n. 2 (¹ ? n)G [12]

u 5 0;vr

5 0 [26]where n is an outward vector normal to the local free surface(Figure 1), which is the gradient of VOF function f a

r5 0 [27]

n 5 ¹F [13]4. Side surface

Because the welding current used in the present study isbelow 200 A, the effect of arc pressure is neglected[28] and

2kTr

5 qconv [28]pv is assumed to be the atmospheric pressure.The Marangoni shear force, a function of temperature and

u 5 0; v 5 0 [29]concentration, is given byf a

r5 0 [30]ts 5 ml

(V ? s)n

5gT

Ts

1gf a

f a

s[14]

where s is a tangential vector to the local free surface. TheD. Electromagnetic Forcetop surface receives arc heat flux and dissipates heat into

the surroundings through convection, radiation, and metal In order to solve Eqs. [2] and [3], the terms caused byvaporization via the following equation: the electromagnetic force should be calculated first. Assum-

ing that the electric field is quasi-steady state and that thek

Tz

5h (1 2 hd)Iuw

2ps 2q

exp 12r 2

2s 2q22 qconv 2 qradi 2 qevap electrical conductivity is constant, the scalar electric poten-

tial f satisfies the following Maxwell equation:[9]

[15]¹2f 5

1r

r 1rfr2 1

2fz2 5 0 [31]

f a

z5 0 [16]

Note that, although the weld pool fluid flow is transient,the electric current is an input welding condition, which iswhere I is the welding current, h is the arc heat efficiency,assumed to be unaffected by the weld pool dynamics andhd is the ratio of droplet thermal energy to the total arcis time independent. The required boundary conditions forenergy, uw is the arc voltage, and sq is arc heat flux distribu-the solution of Eq. [31] aretion parameter. Note that in Eq. [15], the arc heat flux is

assumed to be a Gaussian distribution and impacts perpen-dicularly to the weld pool. Also, the irregular weld pool 2se

fz

5I

2ps 2c

exp 12r 2

2s 2c2; at top surface [32]

surface is assumed to have little effect on the way that arc


F. Surface Tensionfz

5 0; at z 5 0 [33]Due to the availability of experimental data, a binary Fe-

S system is selected for the present study. The surface tensionfr

5 0; at r 5 0 [34] for a pseudobinary Fe-S system as a function of temperatureT and the sulfur concentration f a is given by[10]

f 5 0; at r 5 Rb [35]g 5 1.943 2 4.3 3 1024(T 2 1723) 2 RT 3 1.3

[44]where se is the electrical conductivity. Note that Eq. [32]implies that electric current impacts the weld pool surface 3 1028 ln 11 1 0.00318f a exp 11.66 3 108

RT 22perpendicularly. This assumption is consistent with that ofthe arc heat flux in Eq. [15]. After the distribution of electri-

where R is the gas constant. The surface tension is plotted incal potential is solved, the distributions of current densityFigure 2(a) as a function of temperature for several differentin the r and z directions can be calculated viasulfur concentrations. A dotted line tracing the maximumsurface tension (g /T 5 0) for different sulfur concentra-

Jr 5 2sefr

[36] tions is also shown. For a given sulfur concentration, thesurface tension increases as the temperature increases, thenreaches a maximum value and decreases thereafter.Jz 5 2se

fz

[37]The contours of both g /T and g /f a are plotted in

Figures 2(b) and (c) as a function of temperature and sulfurThe self-induced azimuthal magnetic field is derived fromconcentrations. It is seen that g /f a is always negative,Ampere’s law via[9]

while g /T changes its sign from positive, for lower temper-atures, to negative, for higher temperatures, when the sulfur

Bu 5m0

r er

0Jzr dr [38] concentration is above 0 ppm.

where m0 is the magnetic permeability. Finally, the two com-III. NUMERICAL CONSIDERATIONSponents of the electromagnetic force that appeared in Eqs.

[2] and [3] are, respectively, calculated via The aforementioned coupled equations of continuity (Eq.[1]), momentum (Eqs. [2] and [3]), energy (Eq. [4]), speciesJ 3 B.r 5 2JzBu [39](Eq. [5]), VOF (Eq. [10]), electromagnetic force (Eq. [31]),

J 3 B.z 5 JrBu [40] and all boundary and auxiliary conditions were solved by acontrol-volume-based finite difference procedure using theSIMPLEC algorithm. A detailed discussion regarding theE. Plasma Drag Forcenumerical procedure and the check of numerical conver-

In Eq. [3], the liquid droplet is subject to plasma drag gence and accuracy was given previously.[20]

force Fdrag during the falling process. The plasma drag force Since the governing equations are valid for the entireis obtained by the drag theory for a gaseous fluid[30] using region, including liquid, solid, and mushy zone, there is nothe following equation: need to track the geometrical shape and the extent of each

region. A fixed-grid system was used in the numerical calcu-lation, consisting of 202 3 102 points for the total computa-Fdrag 5 Cds

12

rgv2g1pD2

d

4 2 [41]tional domain 60 3 30 mm. Due to the axisymmetry of thedomain, only half of the grid points (102 3 102) were usedwhere Cds , rg , vg , and Dd are the drag coefficient, the arcin the calculation. Finer spacing was used in the weld poolplasma density, the arc plasma velocity, and the dropletdomain. Note that the selected grid system represents adiameter, respectively. It is assumed that the central arccompromise between numerical accuracy and computationalplasma velocity has the same distribution as that in GTAW[31]

time. Calculations were executed on HP*-9000/C200 work-at low welding currents and that it can be approximated bythe following formula: *HP is a trademark of Hewlett-Packard Company, Colorado Springs, Co.

stations and the total CPU time was about 4 hours.vg

vg max5

274 1z2 Hb

Hw2

2

11 2z 2 Hb

Hw2 [42]

IV. RESULTS AND DISCUSSIONwhere vg max is the maximum velocity, which is assumed tobe 50.0 m/s,[32] Hw is the initial height of the droplets, which Both the base metal and the droplets are assumed to beis the distance between the electrode tip and the base metal, 304 stainless steel and their thermophysical properties areand Hb is the thickness of the base metal. summarized in Table I. It is assumed that the sulfur concen-

The drag coefficient depends on the Reynolds number tration in base metal is 100 ppm. Based on Figure 2 and onand is given by[30]

our previous experience in GTAW,[16] two representativesulfur concentrations for the droplet were selected, 300 ppm

Cds 524Re

16

!1 1 Re

1 0.4 for 0 , Re , 200,000 [43] (Case I) and 150 ppm (Case II).In the present study, the following welding conditions are

assumed:[33,34,35] welding current 155 A; welding voltage 12where Re 5 rgvgDd /mg and mg is the plasma gas viscosity.Here, the values of rg and mg are employed at an aver- V; arc thermal efficiency 80 pct; ratio of droplet energy to

the total arc energy 30 pct; droplet diameter 1.20 mm; theage arc temperature of 8000 K.[32]


Table I. Thermophysical Properties of 304 Stainless Steel and Welding Conditions

Nomenclature Symbol Value (Unit)

Constant in Eq. [20] Av 2.52Specific heat of solid phase cs 700 (J kg21 K21)Specific heat of liquid phase cl 780 (J kg21 K21)Mass diffusion coefficient of solid phase Ds >0Mass diffusion coefficient of liquid phase Dl 3 3 1025 (cm2 s21)Thermal conductivity of solid phase ks 22 (W m21 K21)Thermal conductivity of liquid phase kl 22 (W m21 K21)Density of solid phase rs 7200 (kg m23)Density of liquid phase rl 6900 (kg m23)Solutal expansion coefficient bs 20.2Thermal expansion coefficient bT 4.95 3 1025 (K21)Radiation emissivity « 0.4Dynamic viscosity ml 0.006 (kg m21 s21)Latent heat of fusion H 2.47 3 105 (J kg21)Magnetic permeability m0 1.26 3 1026 (H m21)Solidus temperature Ts 1670 (K)Liquidus temperature Tl 1725 (K)Reference temperature T0 2400 (K)Ambient temperature T` 293 (K)Convective heat-transfer coefficient hc 80 (W m22 K21)Applied external pressure Pv 1.013 3 105 (N m22)Latent heat of vaporization Hv 7.34 3 106 (J kg21)Gas constant R 8314.3 (J kg21 mole21)Radius of base metal Rb 15.0 (mm)Stefan–Boltzmann constant s 5.67 3 1028 (W m22 K24)Electrical conductivity se 7.14 3 105 (V21 m21)Arc heat flux distribution parameter sq 3.75 3 1023 (m)Arc current distribution parameter sc 3.75 3 1023 (m)Welding voltage uw 12 (V)Welding current I 155 (A)Arc thermal efficiency h 80 pctRatio of droplet energy to total arc energy hd 30 pctDrop height Hw 12.0 (mm)Thickness of base metal Hb 6.0 (mm)Initial base metal sulfur concentration f a 100 (ppm)Initial droplet sulfur concentration (Case I) f a 300 (ppm)Initial droplet sulfur concentration (Case II) f a 150 (ppm)Droplet diameter Dd 1.2 (mm)Drop frequency Fd 27 (Hz)Droplet initial temperature Td 2400 (K)Plasma gas density rg 0.06 (kg m23)Plasma gas viscosity mg 0.00025 (kg m21 s21)

frequency of droplet generation 27 Hz; the droplets’ initial force; this is similar to the case in GTAW.[3] Gravity isimportant in GMAW because a free surface is involved. Intemperature 2400 K; and the arc length 12 mm (between

the droplet and the base metal). The welding conditions used GTAW, the weld pool surface can be considered to be flatwhen the arc current is below 200 A.[28] However, in GMAW,in the present study are also listed in Table I. The selected

droplet size corresponds to the globular metal transfer mode when the free surface is impacted by droplets, the droplets’kinetic energy is converted to the kinetic energy and potentialin GMAW. The fluid flow in the weld pool is subject to the

interaction among several forces, including droplet imping- energy of the weld pool fluid, leading to a wavy weld pool.Gravity (hydrostatic force) tends to drive the fluid froming force, electromagnetic force, buoyancy force due to tem-

perature and sulfur concentration gradients, gravity, and a higher location to a lower location. Droplet impingingmomentum is considered to play an important role insurface tension.

In order to facilitate the following discussion, some of determining the fluid flow in the weld pool. At the instantwhen the droplet impacts the weld pool surface, the dropletthe characteristics of the forces present in this study are

briefly discussed below. Electromagnetic force produces a tends to push its surrounding fluid away and sink to thebottom of the weld pool. The phenomena are similar to thoseflow radically inward and downward near the center of the

weld pool.[36] Buoyancy force results from the difference in of a rock falling into a pond. Surface tension force, a functionof temperature and sulfur concentration, is expected to betemperature and concentration in the weld pool. Because

the weld pool is small and the “hot” fluid is at the top of very important, as found in GTAW.Four representative moments during one “cycle” of thethe pool, the buoyancy force due to temperature gradients

is expected to be small, as compared to the electromagnetic droplet impinging process were selected for discussion of


Fig. 2—Surface tension and its gradients as a function of temperature and sulfur concentration for the pseudobinary Fe-S system. Intersections betw eenthe dotted line and each curve indicate the maximum surface tension for different sulfur concentrations.

the weld pool dynamics and fluid flow. Note, for all velocity As shown in Figures 3 and 4, at t 5 3.571 s, there is a“crater” in the center of the weld pool, caused by the previousplots, only half of the grid nodes were used to increase the

readability of the flow pattern in the weld pool. impinging droplet. At the tip of the crater, the fluid sur-rounding it tends to flow inward to close up the crater (Figure5(a)). The inward fluids collide with each other to produce

A. Case 1: Droplets Containing Higher Sulfur, S 5 an upward flow in the top central area at t 5 3.575 s (Figure300 ppm 5(b)) and t 5 3.584 s (Figure 5(c)). The sequence involving

crater formation, close-up, and, finally, disappearance is anFigures 3 through 5 show both a typical sequence of adroplet impinging onto the weld pool and the temperature, interesting one to observe.

Note that, in Figure 5, velocities of the droplet above thesulfur concentration, and velocity distributions in the weldpool. In order to observe better the weld pool dynamics, the weld pool are not plotted because they are much higher[20]

than those in the weld pool. The flow pattern, shown inselected time lapses between two subfigures are not equal.Because the arc heat flux is assumed to be a Gaussian distri- Figure 5, results from the interaction among those forces

previously mentioned. Near the weld pool center with abution and high thermal energy is carried by the droplets,higher temperatures exist near the center of the weld pool radius of about 1.0 mm, the temperature of the weld pool

surface is 2300 to 2400 K (Figure 3), while the sulfur concen-surface (Figure 3). It is clearly seen that the hot dropletcarries high thermal energy and sinks to the bottom of the tration is 250 to 300 ppm (Figure 4). According to Figure

2, both the surface tension temperature gradients (g /T )weld pool where the thermal energy is dissipated. Similarly,Figure 4 shows the mixing and the variation of sulfur concen- and the surface tension concentration gradients (g /f a) are

negative near the center of the weld pool. Because both thetration in the weld pool. Because the droplets contain 300ppm of sulfur, while the base metal has 100 ppm, the weld temperature and the sulfur concentration at the weld pool

surface decrease outward, the surface tension force in thispool sulfur concentration must be in between 300 and 100ppm. The shape of the weld pool can best be shown by central area is radically outward (i.e., positive), as shown in

Eq. [14]. However, away from the center of the weld pool,Figure 4. The fluid flow pattern in the weld pool, as shownin Figure 5, is generally downward along the center of the the surface temperature is below 2100 K and the sulfur

concentration is below 210 ppm, which leads to positiveweld pool and then upward along the liquid-solid interface,creating a counterclockwise vortex (viewed from the left surface tension temperature gradients (Figure 2(b)).

Although the surface tension concentration gradients are stillside of the figure). The maximum flow velocity in the weldpool is approximately 0.08 m/s. Note that the Reynolds negative (Figure 2(c)), the sum of the contributions due to

g /T and g /f a, as given in Eq. [14], leads to a negativenumber, based on the size of the weld pool and the maximumflow velocity, is approximately 100, which indicates that the Marangoni shear force (i.e., inward). Note, the outward sur-

face tension force described here exists only in a smallfluid flow in the weld pool is laminar.


Fig. 3—(a) through (d ) A typical sequence of droplet impinging onto the weld pool and temperature distributions: droplets S 5 300 ppm, and base metalS 5 100 ppm.

Fig. 4—(a) through (d ) The weld pool sulfur concentration distributions corresponding to Fig. 3.


Fig. 5—(a) through (d ) The weld pool velocity distributions corresponding to Fig. 3.

portion of the surface around the center of the weld pool, that in Case I. Also, the sulfur tends to spread over a widerbut shallower region, as compared to Case I. The phenomenawhile the inward force prevails over most of the weld pool

surface. The falling droplet creates a downward fluid flow shown in both Figures 6 and 7 can be explained with thehelp of Figure 8. It is seen that the area near the weld poolnear the weld pool center. In addition, the electromagnetic

force produces an inward and downward flow. Due to the center has a sulfur concentration of 140 to 150 ppm, whichmeans that the transitional temperature is about 2040 K,interaction among the aforementioned forces, the resulting

surface-tension-driven (Marangoni) flow is radically inward according to Figure 2. However, the surface temperaturenear the weld pool center is 2300 to 2400 K and decreases(Figure 5).

The inward flow brings the higher temperature surface outward to the edge of the weld pool. As a result, the maxi-mum surface tension occurs in the middle of the weld poolfluid downward to the bottom of the weld pool, leading to

a deeper penetration. The existence of a “hole” in the weld surface, which pulls surface fluid from both the center andthe edge toward the middle of the weld pool (Figure 8).pool (Figure 3(b)), predicted by the present model, is remark-

able. It provides an explanation for possible weld defects, Hence, there is a downward flow in the middle of the weldpool surface. There are two visible vortexes: clockwise nearsuch as gas porosity or inclusion, commonly observed in a

solidified weld bead.[28] The formation and closing up of the weld pool center and counterclockwise near the edge ofthe weld pool (Figure 8(b), viewed from the right side).the crater might entrap plasma gas or other “impurities” in

the weld pool. Hence, if shielding gas is not properly applied The flow pattern is influenced mainly by the interaction oftwo forces: electromagnetic force and the droplet impingingduring a welding process, it is possible that some inclusion

or gas porosity can exist in the weld. momentum. The electromagnetic force is inward and down-ward, which may weaken the outward flow by means ofsurface tension near the weld pool center. As shown in Figure

B. Case II: Droplets Containing Lower Sulfur, S 5 8(d), when the droplet impinges onto the weld pool, the fluid150 ppm near the weld pool center is either pushed away from the

center or pushed downward. Hence, the vortex created byFigures 6 through 8 show a typical sequence of a dropletimpinging onto the weld pool and the distributions of temper- the surface tension near the weld pool center is temporarily

destroyed. However, the surface tension quickly repairs theature, sulfur concentration, and velocity in the weld pool.As shown in Figure 6, the shape of the isotherm curves near flow pattern and resumes an inward flow near the center of

the weld pool (Figure 8(b)). The momentum carried by thethe weld pool center is quite complex and is different from


Fig. 6—(a) through (d ) A typical sequence of droplet impinging onto the weld pool and temperature distributions: droplets S 5 150 ppm, and base metalS 5 100 ppm.

Fig. 7—(a) through (d ) The weld pool sulfur concentration distributions corresponding to Fig. 6.


Fig. 8—(a) through (d ) The weld pool velocity distributions corresponding to Fig. 6.

Fig. 9—Final shape of the weld pool and sulfur concentration distribution when the droplet sulfur concentration is (a) S 5 300 ppm and (b) S 5 150 ppm.

droplet rebounds, resulting in a strong upper flow at the center but wider than that in Case I. However, the deepest part ofthe weld pool still occurs at the center, due primarily to theof the weld pool (Figure 8(c)). The fluid near the center of

the weld pool flows downward due to both the electromagnetic thermal energy carried by the droplets. Because the flowpattern is complex, the shape of the weld pool is moreforce and the falling momentum of the droplet.

As the surface fluid flows outward near the center of the complex than that in Case I.weld pool, the thermal energy from the arc flux is spread

C. Final Weld Bead Shape after Solidificationoutward. In addition, the thermal energy carried by the drop-lets does not effectively carry down to the weld pool, as After the last droplet is released, the arc power is turned

off at t 5 4.00 s. Figure 9 shows the sulfur concentrationcompared to Case I. As a result, the weld pool is shallow


Fig. 10—Final weld pool shape and sulfur concentration distribution when (a) surface tension force is neglected and (b) both surface tension force andelectromagnetic force are neglected.

Fig. 11—A sequence of figures showing the impinging process of the last droplet, weld pool dynamics, solidification process, and temperature distri butionsin the weld pool.

distribution and the shape of the weld bead after full solidifi- Case II, except in regions near the bottom and the edge ofthe weld pool and along the heat-affected zone. This is causedcation in Cases I and II. As shown, the weld bead has a

deeper penetration but is a little narrower in Case I than in by the more limited mixing of fluid in these regions. Thepredicted uniform sulfur distribution is consistent with theCase II. Note that the degree of the convexedness in the weld

bead surface is determined by the magnitude of the surface published experimental observation for cases in which twodissimilar metals are welded together or in which the compo-tension. The final sulfur concentration distribution in the

weld bead appears to be fairly uniform for both Case I and sitions of electrodes are different from the base metal.[37]


Fig. 12—The weld pool sulfur concentration distributions corresponding to Fig. 11.

D. If Surface Tension and Electromagnetic Force are not contribute significantly to the weld penetration. Thelimited penetration shown in Figure 10 implies that theNeglectedsinking of droplets, discussed earlier, is caused by the flowIn order to study the effect of surface tension on thedriven by surface tension but not by the impinging momen-shape of the weld bead, the surface tension is omitted in thetum. In fact, the droplet momentum is damped out by anmodeling by assuming the value of surface tension in Eq.up-and-down fluid motion in the weld pool, especially for[14] to be 0. Figure 10(a) shows the final weld pool shapethe spot GMAW considered in the present study.and sulfur distribution when the surface tension force is

neglected. Note that the flat surface of the weld bead is dueto the assumption of zero surface tension force. As shown, E. Weld Pool Solidification Processthe weld pool penetration is very limited, as compared toCases I and II. It appears that the droplet impinging momen- Figures 11, 12, and 13 show the temperature, sulfur con-

centration, and velocity distribution in the weld pool, respec-tum tends to help the droplet spread out (splash phenome-non), which leads to a wider but shallower weld pool, as tively, as a function of time both after the final droplet

impinges onto the weld pool and until the weld pool iscompared to Cases I and II. Figure 10(a) further indicatesthat surface tension plays a very critical role in determining completely solidified (arc power is turned off at t 5 4.00

s). It is noted that the time lapses between the two subfiguresthe weld penetration. Figure 10(b) shows the final weld poolshape and sulfur distribution when the electromagnetic force are not the same. The thermal energy of the weld pool

dissipates into the base metal through conduction and intois nullified in Eqs. [2] and [3]; they also show the surfacetension. As shown, the weld pool is wider and shallower the surroundings through convection and radiation. The high

thermal energy shown by the “dark spot” carried by thethan in any cases previously discussed.By comparing Figures 10(b) and (a), it can be concluded droplet completely dissipates into the surrounding fluid

within 0.076 s at t 5 4.064 s. It is seen that the final locationthat electromagnetic force, which is inward to the center ofthe weld pool and downward, has some effects on weld pool that solidifies is in the center of the weld and near the surface

of the weld bead. It takes about 1.462 s for the weld poolpenetration and weld shape; these effects, however, are notas significant as those of the surface tension. By comparing to completely solidify after the last droplet touches the weld

pool surface. As shown in Figure 12, the high sulfur con-Figures 9 and 10, it is clearly seen that surface tension canpromote weld pool mixing and, as a result, the uniformity tained in the last droplet (S 5 300 ppm) is quickly dispersed

and mixed with the weld pool fluid. After the last dropletof sulfur in the weld. The important conclusion drawn fromFigure 10 is that the droplet impingement momentum does touches the weld pool, within about 0.318 s (at t 5 4.306


Fig. 13—The weld pool velocity distributions and sizes corresponding to Fig. 11.

s), the sulfur distribution in the weld pool is fairly uniform, for a spot GMAW process. The effects of surface tension,which is a function of sulfur concentration and temperature,except at the bottom of the weld. However, the sulfur dissipa-

tion rate in the weld pool is not as fast as that of the heat. on weld pool fluid flow, mixing, and weld penetration havebeen systematically investigated. The distributions of tem-This is understandable because the heat diffusion coefficient

is, in general, higher than the mass diffusion coefficient. perature, velocity, and sulfur concentration were calculatedas a function of time until the welding power supply wasHowever, the sulfur concentration becomes uniform much

earlier than the complete solidification of the weld pool. removed and the weld pool was completely solidified. Fromthe present study, the following conclusions can be made:Due to small velocities, poor mixing, and rapid solidification,

the liquid at the bottom of the weld pool is solidified andbecomes a sulfur-rich region. Also, poor mixing occurs at 1. As in GTAW, surface tension is the major driving force

contributing to the weld pool fluid flow, mixing, andthe edge of the weld bead. The fluid in the weld pool isbounced up and down to absorb the droplet momentum while weld penetration in GMAW.

2. A higher sulfur concentration in droplets produces anthe mixing of sulfur and the solidification processes proceed.Spatter phenomenon is commonly observed in GMAW, inward flow at the surface of the weld pool, which carries

arc energy downward and leads to deep weld penetrationespecially at high welding currents. In the present study,some “particles” above the weld pool were detected in the and good weld mixing. On the contrary, when droplets

contain lower sulfur, an outward surface flow is created,modeling, which can be caused by numerical errors and/or actual spatter. A detailed discussion on possible spatter which leads to a shallow weld pool.

3. A fairly uniform distribution of sulfur in the solidifiedphenomenon found in the modeling is given in the previousarticle[20] and will not be repeated here. weld bead is predicted for both high and low droplet

sulfur concentrations, except in the regions near the cen-tral bottom, at the edge of the weld pool, and along the

V. CONCLUSIONS heat-affected zone, in which the mixing of fluid is limited.4. The impinging momentum carried by the droplets tendsA numerical simulation of the fluid flow, heat transfer,

and species distribution in the weld pool has been conducted to be absorbed and damped out by the wavy fluid in the


weld pool and contributes less, as compared to surface Greek Symbolstension force, to the weld penetration in spot GMAW. bs solutal expansion coefficient

bT thermal expansion coefficientbu self-induced azimuthal magnetic field

ACKNOWLEDGMENT g surface tensiong /f a surface tension concentration gradientsThis work was supported by the United States Armyg /T surface tension temperature gradientsResearch Office under Grant No. DAAH04-95-1-0136,« radiation emissivitywhich is gratefully acknowledged.k free surface curvatureml dynamic viscositym0 magnetic permeabilityNOMENCLATUREh arc efficiency

Av constant, in Eq. [20] hd ratio of droplet energy to the total arc energyB magnetic induction vector f electric potentialBu self-induced azimuthal magnetic field s Stefan–Boltzmann constantc specific heat se electrical conductivitycl permeability coefficient, defined in Eq. [8] sc arc current distribution parameterC coefficient, defined in Eq. [9] sq arc heat flux distribution parameterCds drag coefficient for a sphere r densityd dendrite arm spacing ts Marangoni shear forceD diameterf mass fraction Subscriptsf a species concentration b base metalF volume of fluid function d dropletFdrag plasma drag force on droplets g arc plasma gasg volume fraction or gravitational acceleration l liquid phaseh enthalpy r relative to solid velocityhc convective heat-transfer coefficient between s solid phase

metal and its surroundingsH latent heat of fusionHw droplet drop heightHb thickness of the base metal

REFERENCESHv latent heat of vaporizationI welding current

1. J. Szekely: Recent Trends in Welding Science and Technology, TWR’89,J current density vectorASM INTERNATIONAL, Materials Park, OH, 1990, pp. 3-10.Jr radial current density 2. K.C. Tsao and C.S. Wu: Welding J., 1988, Mar., pp. 70s-75s.

Jz axial current density 3. P.G. Jonsson, R.C. Westhoff, and J. Szekely: J. Appl. Phys., 1993,k thermal conductivity vol. 74, pp. 5997-6006.

4. C.R. Heiple, P. Burgardt, and J.R. Roper: Modeling of CastingK permeability, defined in Eq. [8]and Welding Process II, TMS-AIME, Warrendale, PA, 1984, pp.n normal vector to the local free surface193-205.p pressure 5. C.R. Heiple, J.R. Roper, R.T. Stagner, and R.J. Aden: Welding J.,

pv vapor pressure or any other applied external 1983, Mar., pp. 72s-77s.pressure 6. G.M. Oreper, T.W. Eagar, and J. Szekely: Welding J., 1983, Nov., pp.

307s-312s.qconv heat loss by convection7. T. Zacharia, S.A. David, J.M. Vitek, and T. DebRoy: Recent Trends inqevap heat loss by evaporation

Welding Science and Technology, TWR’89, ASM INTERNATIONAL,qradi heat loss by radiation Materials Park, OH, 1990, pp. 25-30.r-z cylindrical coordinate system 8. S. Kou and Y.H. Wang: Welding J., 1986, Mar., pp. 63s-70s.R gas constant 9. R.T.C. Choo, J. Szekely, and S.A. David: Metall. Trans. B, 1992, vol.

23B, pp. 371-84.Rb radius of the base metal10. P. Sahoo, T. DebRoy, and M.J. McNallan: Metall. Trans. B, 1988, vol.Re Reynolds number

19B, pp. 483-91.s tangential vector to the local surface 11. K.S. Yeum, R. Speiser, and D.R. Poirier: Metall. Trans. B, 1989, vol.t time 20B, pp. 693-703.T temperature 12. T.A. Utigard and J.M. Toguri: Metall. Trans. B, 1987, vol. 18B, pp.

695-702.T0 reference temperature for natural convection13. C.R. Heiple and P. Burgardt: Welding J., 1985, June, pp. 159s-162s.Tl liquidus temperature14. P. Burgardt and R.D. Campbell: Key Eng. Mater., 1992, vols. 69–70,Ts solidus temperature pp. 379-416.

T` ambient temperature 15. T. Zacharia, S.A. David, J.M. Vitek, and T. DebRoy: Welding J., 1989,u velocity in r direction Dec., pp. 510s-519s.

16. Y. Wang, S. Qi, and H.L. Tsai: University of Missouri-Rolla, Rolla,uw arc voltageMO, Metall. Trans. B, 2001, vol. 32B, pp. 145-61.v velocity in z direction

17. J.W. Kim and S.J. Na: Trans. ASME, J. Eng. Industry, 1994, vol. 116,vg plasma gas velocity pp. 78-85.V velocity vector 18. M. Ushio and C.S. Wu: Metall. Mater. Trans. B, 1997, vol. 28B, pp.

509-16.W melt evaporation rate


28. M.L. Lin and T.W. Eagar: Welding J., 1985, June, pp. 163s-169s.19. R.T.C. Choo, K. Mukai, and J.M. Toguri: Welding J., 1992, Apr., pp.139s-146s. 29. T. Zacharia, S.A. David, and J.M. Vitek: Metall. Trans. B, 1991, vol.

22B, pp. 233-41.20. Y. Wang and H.L. Tsai: Int. J. Heat Mass Transfer, 2001, vol. 44, pp.2067-80. 30. H. Schlichting: Boundary-Layer Theory, 6th ed., McGraw-Hill, New

York, NY, 1968, ch. I.21. D.B. Kothe, R.C. Mjolsness, and M.D. Torrey: Report No. LA-12007-MS, Los Alamos National Laboratory, Los Alamos, NM, 1991. 31. S.Y. Lee and S.J. Na: Welding J., 1996, Sept., pp. 269s-279s.

32. Y.S. Kim and T.W. Eagar: Welding J., 1993, June, pp. 269s-278s.22. K.C. Chiang and H.L. Tsai: Int. J. Heat Mass Transfer, 1992, vol. 35,pp. 1763-70. 33. J.N. DuPont and A.R. Marder: Welding J., 1995, Dec., pp. 406s-416s.

34. S. Liu and T.A. Siewert: Welding J., 1989, Feb., pp. 52s-58s.23. Q.Z. Diao and H.L. Tsai: Metall. Trans. A, 1993, vol. 24A, pp. 963-73.24. M.C. Flemings: Solidification Processing, McGraw-Hill, Inc., New 35. J.H. Waszink and L.H.J. Graat: Welding J., 1983, Apr., pp. 108s-

116s.York, NY, 1974, pp. 252-58.25. K. Kubo and R.D. Pehlke: Metall. Trans. B, 1985, vol. 16B, pp. 359-66. 36. R.T.C. Choo, J. Szekely, and R.C. Westhoff : Metall. Trans. B, 1992,

vol. 23B, pp. 357-69.26. P.C. Carman: Trans. Inst. Chem. Eng., 1937, vol. 15, pp. 150-66.27. G.S. Beavers and E.M. Sparrow: J. Appl. Mech., 1969, vol. 36, pp. 37. W.A. Baeslack III, J.C. Lippold, and W.F. Savage: Welding J., 1979,

June, pp. 168s-176s.711-14.


effects of surface active elements on weld pool fluid flow...

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