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H. Guo
Department of Mechanical and Aerospace
Engineering,
Missouri University of Science and Technology,
1870 Miner Circle,
Rolla, MO 65409
J. Hu
Department of Mechanical Engineering,
University of Bridgeport,
Bridgeport, CT 06604
e-mail: jjhu@bridgeport.edu
H. L. Tsai
Department of Mechanical and Aerospace
Engineering,
Missouri University of Science and Technology,
1870 Miner Circle,
Rolla, MO 65409
Three-Dimensional Modeling of
Gas Metal Arc Welding of
Aluminum Alloys
A three-dimensional mathematical model and numerical techniques were developed for
simulating a moving gas metal arc welding process. The model is used to calculate the
transient distributions of temperature and velocity in the weld pool and the dynamic
shape of the weld pool for aluminum alloy 6005-T4. Corresponding experiments were
conducted and in good agreement with modeling predictions. The existence of a com-
monly observed cold-weld at the beginning of the weld, ripples at the surface of the weld
bead, and crater at the end of the weld were all predicted. The measured microhardness
around the weld bead was consistent with the predicted peak temperature and other
metallurgical characterizations in the heat-affected zone. 关DOI: 10.1115/1.4001479兴
Keywords: gas metal arc welding, aluminum, ripples, weld
1 Introduction
Gas metal arc welding 共GMAW兲is one of the most popular
welding methods in the industry. It is an arc welding process,
which uses a metal wire as a combined electrode and filler metal
in a plasma arc and inert shielding gas. GMAW has some advan-
tages over other welding methods, such as high productivity, bet-
ter penetration, no need for flux, little spatter, and ability to weld
in all positions. In the auto-industry, due to the demands for a
lower environmental impact through improved fuel efficiency,
weight reduction, and load capacity, aluminum is being more
widely used. A typical weld bead in GMAW of aluminum alloys,
as shown in Fig. 1, can be divided into three zones. At the begin-
ning of the weld, the base metal is heated up from room tempera-
ture, electrode material starts to drop onto the welding coupon,
and the weld bead begins to form. In this zone, the welding pro-
cess is not in a quasisteady state and a cold-weld is formed. The
weld pool temperature, fluid flow, and weld bead shape vary con-
stantly. At the middle of the weld, the welding process is at a
quasisteady state. When the welding comes to an end, the arc is
terminated and there is neither energy nor material transfer into
the weld pool. The molten pool solidifies and forms a crater-
shaped weld end. It can be clearly seen in Fig. 1 that ripples are
formed at the surface of the weld bead. In this paper, the modeling
of the normal weld in the middle of the welding process will be
reported and the other two zones are covered in other papers.
To get a better understanding of the GMAW process of alumi-
num alloys, both experimental and theoretical studies should be
carried out. Many experimental investigations have been con-
ducted on the GMAW process 关1– 8兴. GMAW is a very compli-
cated process involving many coupled parameters such as welding
current, voltage, welding speed, electrode feed speed, base metal
chemical composition, electrode material, electrode size, and
shielding gas. In addition, because welding is a transient process
at high temperatures, it is hard to use experimental methods alone
to understand the transport phenomena involved. Mathematical
modeling provides a convenient way to obtain insightful informa-
tion.
Many theoretical models have been proposed on the simulation
of a gas metal arc welding process. Ushio and Wu 关9兴proposed a
model to calculate the three-dimensional heat and fluid flow in a
moving gas metal arc weld pool. A boundary-fitted nonorthogonal
coordinate system was adopted and it was found that the size and
profile of the weld pool are strongly influenced by the volume of
the molten wire, impact of droplets, and heat content of the drop-
lets. Park and Rhee 关10兴reported that the kinetic energy of the
transferring droplets produces a depression on the weld pool sur-
face. According to the computational investigations by Davies et
al. 关11兴, the impinging droplet momentum dominates the flow
pattern and overrides any surface tension effects at a relatively
high current. While a flat weld pool surface is assumed in the 3D
GMAW model of Jaidi and Dutta 关12兴, the surface deformation
caused by the droplet impingement and weld pool dynamics is
calculated by Wang and Tsai 关13兴, Hu and Tsai 关14兴, and Hu et al.
关15兴. All those research efforts were only focused on the GMAW
of steels. There is hardly any three-dimensional mathematical
modeling on the GMAW of aluminum alloys. However, the weld-
ing behavior of aluminum alloys differs significantly from steel
with physical properties 关16兴, such as high thermal conductivity,
lower melting point, high coefficient of thermal expansion, high
solidification shrinkage, oxide formation at the surface, etc.
The objectives of this project are to conduct numerical simula-
tion and experimental validation on the GMAW of aluminum al-
loys. The three-dimensional fluid flow and heat transfer were cal-
culated when droplets carrying mass, momentum, and thermal
energy impinged onto the weld pool. The transient deformed weld
pool surface was handled by the volume of fluid 共VOF兲technique
关17兴, and the fusion and solidification in the liquid region, the
mushy zone, and the solid region were handled by the continuum
formulation 关18兴. Bead-on-plate experiments were performed, and
the welded samples were characterized to determine the micro-
hardness in the weld bead.
2 Mathematical Model
A sketch of a moving GMAW for a bead-on-plate welding is
shown in Fig. 2. The base metal is aluminum alloy 6005-T4. The
three-dimensional x-y-zcoordinate system is fixed to the base
metal. The arc is moving in the positive xdirection, and droplets
impinge onto the base metal in the negative zdirection while
moving at the same velocity along the xdirection as the arc. Since
Contributed by the Manufacturing Engineering Division of ASME for publication
in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received
June 24, 2009; final manuscript received March 11, 2010; published online April 21,
2010. Assoc. Editor: Wei Li.
Journal of Manufacturing Science and Engineering APRIL 2010, Vol. 132 / 021011-1
Copyright © 2010 by ASME
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the welding process is symmetrical with respect to the x-zplane,
only half of the domain in the ydirection is included in the cal-
culation.
2.1 Governing Equations. The differential equations govern-
ing the conservation of mass, momentum, and energy based on
continuum formulation given by Diao and Tsai 关18兴were modified
and employed in the study, and they are given as follows.
共1兲Continuity,
t+ⵜ·共
V
៝
兲=0 共1兲
where tis the time,
is the density, and V
is the velocity
vector.
共2兲Momentum,
t共
u兲+ⵜ·共
V
៝
u兲=ⵜ·
冉
l
l
ⵜu
冊
−
p
x−
l
K
l
共u−us兲
−C
2
K1/2
l
兩u−us兩共u−us兲
−ⵜ·共
fsflV
៝
rur兲+J
៝
⫻B
៝
兩x共2兲
t共
v兲+ⵜ·共
V
៝
v兲=ⵜ·
冉
l
l
ⵜv
冊
−
p
y−
l
K
l
共v−vs兲
−C
2
K1/2
l
兩v−vs兩共v−vs兲
−ⵜ·共
fsflV
៝
rvr兲+J
៝
⫻B
៝
兩y共3兲
t共
w兲+ⵜ·共
V
៝
w兲=ⵜ·
冉
l
l
ⵜw
冊
−
p
z−
l
K
l
共w−ws兲
−C
2
K1/2
l
兩w−ws兩共w−ws兲
−ⵜ·共
fsflV
៝
rwr兲+
g+
g共

T共T
−T0兲+

s共fl
␣
−fl,0
␣
兲兲 +J
៝
⫻B
៝
兩z+Fdrag
共4兲
where u,v, and ware the velocities in the x,y, and z
directions, respectively, and V
៝
r=V
៝
l−V
៝
sis the relative ve-
locity vector between the liquid phase and the solid phase.
The subscripts sand lrefer to the solid and liquid phases,
respectively; pis the pressure;
is the dynamic viscosity; f
is the mass fraction; Kis the permeability, a measure of the
ease with which fluids pass through the porous mushy
zone; Cis the inertial coefficient;

Tis the thermal expan-
sion coefficient; gis the gravitational acceleration; Tis the
temperature; B
៝
is the magnetic induction vector; J
៝
is the
current density vector; and the subscript 0 represents the
initial condition.
共3兲Energy,
t共
h兲+ⵜ·共
V
៝
h兲=ⵜ·
冉
k
cs
ⵜh
冊
+ⵜ·
冉
k
cs
ⵜ共hs−h兲
冊
−ⵜ·共
共V
៝
−V
៝
s兲共hl−h兲兲 共5兲
where his the enthalpy, kis the thermal conductivity, and c
is the specific heat.
The detailed descriptions of the terms in Eqs. 共1兲–共5兲can be
found in Ref. 关18兴, and will not be repeated here. The solid/liquid
phase-change is handled by the continuum formulation 关18兴. The
third, fourth, and fifth terms in the right-hand side of Eqs. 共2兲–共4兲
vanish at the solid region because of u=us=v=vs=w=ws=0 and
fl=0 for the solid. In the liquid region, since Kgoes to infinity, all
these terms also vanish 关18兴. Those terms are only effective for the
mushy zone where 0⬍fl⬍1 and 0 ⬍fs⬍1. Therefore, the liquid
region, mushy zone, and solid region can be handled by the same
equations. During the fusion and solidification process, latent heat
is absorbed or released in the mushy zone. By the use of enthalpy
in Eq. 共5兲, conduction in the solid region, conduction and convec-
Fig. 1 A typical weld bead of GMAW of aluminum alloys
Fig. 2 Experimental setup and simulation domain of a GMAW system
021011-2 / Vol. 132, APRIL 2010 Transactions of the ASME
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tion in the liquid region and mushy zone, the absorption, and
release of latent heat are all handled in the same equation.
2.2 Tracking of Free Surfaces. The fluid configuration is
defined by a volume of fluid function 关17兴F共x,y,z,t兲, which rep-
resents the volume of liquid metal per unit volume and satisfies
the following conservation equation:
dF
dt =
F
t+共V
៝
·ⵜ兲F=0 共6兲
When averaged over the cells of a computing mesh, the average
value of Fin a cell is equal to the fractional volume of the cell
occupied by fluid. A unit value of Fcorresponds to a cell full of
fluid, whereas a zero value indicates a cell with no fluid. Cells
with Fvalues between 0 and 1 are partially filled with fluid and
identified as surface cells. Gradients of Fdetermine the mean
local surface normal, and, together with Fvalues, allow the con-
struction of an approximate interface.
2.3 Boundary Conditions. The boundary conditions for the
previous equations 共Eqs. 共1兲–共5兲兲 are given below.
2.3.1 Normal to the Local Free Surface. For cells containing a
free surface, that is, cells that contain fluid but have one or more
empty neighbors, the following pressure conditions must be satis-
fied 关14兴:
p=pv+
␥
共7兲
where pis the pressure at the free surface in a directional normal
to the local free surface and pvis the plasma arc pressure, which
is assumed to have a radial distribution in the following form 关13兴:
pv=Pmax exp
冉
−r2
2
p
2
冊
共8兲
where Pmax is the maximum arc pressure at the arc center, which
is calculated from welding current 关13兴,ris the distance from the
arc center, and
pis the arc pressure distribution parameter 关13兴.
in Eq. 共7兲is the free surface curvature given by
=−
冋
ⵜ·
冉
n
៝
兩n
៝
兩
冊
册
=1
兩n
៝
兩
冋
冉
n
៝
兩n
៝
兩·ⵜ
冊
兩n
៝
兩−共ⵜ·n
៝
兲
册
共9兲
where n
៝
is the normal vector to the local surface, which is the
gradient of VOF function
n
៝
=ⵜF共10兲
2.3.2 Tangential to the Local Free Surface. The Marangoni
shear stress at the free surface in a direction tangential to the local
free surface is given by
s
ជ
=
l
共V
៝
·s
៝
兲
n
៝
=
␥
T
T
s
៝
共11兲
where s
៝
is the local surface tangential vector. Since there are no
surface tension coefficient data available for 6005-T4, the prop-
erty of pure aluminum was used instead. For pure aluminum, sur-
face tension coefficient
␥
is a function of temperature 关19兴.
␥
= 868 − 0.152共T−Tl兲共12兲
where Tis the temperature and Tlis the melting temperature of
aluminum.
2.3.3 Top Surface. At the arc center, in addition to droplet
impingement, arc heat flux is also impacting on the base metal.
Since the arc heat flux is relatively concentrated, it is assumed that
the heat flux is perpendicular to the base metal 共i.e., neglecting the
inclination of current and heat flux兲. Therefore the temperature
boundary conditions at the top surface of the base metal are
k
T
z=
共1−
d兲Iuw
2
q
2exp
冉
−r2
2
q
2
冊
−qconv −qradi −qevap 共13兲
where Iis the welding current,
is the arc thermal efficiency,
d
is the ratio of droplet thermal energy to the total arc energy, uwis
the arc voltage, and
qis the arc heat flux distribution parameter
关13兴. The heat loss due to convection, radiation, and evaporation
can be written as
qconv =hc共T−T⬁兲,qradi =
共T4−T⬁
4兲,qevap =WHv共14兲
where hcis the convective heat transfer coefficient 关13兴,T⬁is the
room temperature, which is 293 K in this case,
is Stephan–
Boltzmann constant, is the surface radiation emissivity, Hvis the
latent heat for the liquid-vapor phase-change, and Wis the melt
mass evaporation rate 关20兴.
2.3.4 Symmetrical y =0 Plane.
T
y=0,
u
y=0, v=0,
w
y=0,
f
␣
y=0 共15兲
2.3.5 Other Surfaces.
−k
T
n
៝
=qconv,u=0, v=0, w=0 共16兲
2.4 Electromagnetic Force. In Eqs. 共2兲–共4兲, there are three
terms caused by the electromagnetic force. In order to solve these
three terms, J
៝
⫻B
៝
should be calculated first before the calculation
of velocity. Assuming the electric field is a quasi-steady-state and
the electrical conductivity is constant, the scalar electric potential
satisfies the following Maxwell equation 关13兴in the local r-z
coordinate system:
ⵜ2
=1
r
r
冉
r
r
冊
+
2
z2=0 共17兲
The required boundary conditions for the solution of Eq. 共17兲
are
−
e
z=I
2
c
2⫻exp
冉
−r2
2
c
2
冊
at the top free surface
共18兲
z=0 at z=0 共19兲
r=0 at r=0 共20兲
=0 at r=10
c共21兲
where
eis the electrical conductivity and
cis the arc current
distribution parameter 关13兴. The current density in the rand z
directions can be calculated via
Jr=−
e
r,Jz=−
e
z共22兲
The self-induced azimuthal magnetic field is derived from Am-
pere’s law 关13兴
B0=
0
r
冕
0
r
Jzrdr 共23兲
where
0is the magnetic permeability in free space. Finally, the
three components of electromagnetic force in Eqs. 共2兲–共4兲are
calculated via the following equations 关13兴:
Journal of Manufacturing Science and Engineering APRIL 2010, Vol. 132 / 021011-3
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J
៝
⫻B
៝
兩x=−B
Jz
x−xa
r,J
៝
⫻B
៝
兩y=−B
Jz
y
r,J
៝
⫻B
៝
兩z=B
Jr
共24兲
2.5 Numerical Considerations. The governing equations
were solved iteratively at each time step using the finite volume
method 关21兴. At each time step, the continuity and momentum
equations were solved iteratively with a two-step projection
method involving the time discretization of the momentum equa-
tions to get the velocity and pressure distributions 关15兴. Then the
energy equation was solved explicitly to obtain the enthalpy and
temperature field. The species equation was solved in a similar
way. This process was repeated for each iteration step. Iteration
within a time step was terminated when the solutions of velocity,
pressure, temperature, and species distributions converged. Then
the VOF function equation was solved to obtain the new free
surface and liquid pool domain. The temperature-dependent ma-
terial properties were updated. The time step was then advanced
and the above procedure was repeated until the desired time was
reached.
Since the governing equations are valid for the entire computa-
tional domain including the liquid phase, the solid phase, and the
mushy zone, there is no need to track the shape and extent of each
phase. Therefore, a fixed grid system was used in the calculation
with refined grid cells in the weld pool zone to improve accuracy.
Due to the symmetry of the x-zplane of the domain, a grid system
of 408⫻66⫻56 points was used for the half computational do-
main to save computational time. The finer grids concentrating on
and around the weld pool move with the weld pool as the welding
proceeds. Time-step length varied during the calculation to ensure
the convergence and save computational time. The average time
step is around 2⫻10−5 s. Extensive tests using different grid
sizes and time-step sizes have been conducted to assure consistent
results. The final grid and time-step sizes used in the present study
can be considered as the compromised values between computa-
tional time and accuracy.
The computation was performed on the Dell Precision 650®
workstations with 3.2 GHz Pentium®4 processors. It took about
71 h of CPU time to simulate 1.4 s of real-time welding.
3 Experiments
The experimental setup is shown in Fig. 2. Bead-on-plate welds
were made on aluminum alloy 6005-T4 plates 203.2⫻38.1
⫻5mm
3in dimension, which were extruded by Hydro Raufoss
Automotive. Alloying elements in 6005-T4 are 0.6– 0.9 wt % Si,
0.4–0.6 wt % Mg, ⬍0.35 wt % Fe, ⬍0.1 wt % Cu, ⬍0.1 wt %
Mn, ⬍0.1 wt % Cr, ⬍0.1 wt % Zn, and ⬍0.1 wt % Ti 关22兴. Ev-
ery weld coupon was chemically cleaned and degreased. The elec-
trode material was 4043 produced by Alcoa and the major alloy-
ing element is 5.2 wt % of silicon. The diameter of the electrode
wire was 1.6 mm in all experiments. The welding machine was a
Lincoln PowerWave 455®programmable waveform controlled
welding machine made by Lincoln Electric, Cleveland, OH. The
weld torch was fixed onto a small cart on a rail. Argon was used as
the protecting gas, the flow rate of which was 40 cubic feet per
hour 共7.87 cm3/s兲. To provide an adequate protection of the weld
pool, a welding gun leading angle of 15 deg was used in the
experiments. The weld bead was made under constant current
mode of the welding machine with direct current electrode posi-
tive 共DCEP兲connection at the center of the plate along the x
direction, as shown in Fig. 2. All welds started from 30 mm to the
left end of the weld coupon. Before welding, the upper surface of
the plate was brushed with a stainless steel brush to remove the
oxide layer. Three major parameters could be adjusted during the
process: welding current, wire feed speed, and arc/cart travel
speed. Arc voltage was automatically set by the welding machine
once the other parameters were fixed.
The experiments were closely monitored during the process and
the welding parameters were recorded to be input into the math-
ematical model. This was achieved by connecting the port on the
PowerWave455®front panel to the serial port of a computer and
using WaveDesigner®software from Lincoln Electric. The weld-
ing parameters, such as arc current, voltage, and welding time,
were stored in the computer and used as input in the mathematical
model.
Welded samples were sectioned, grinded, polished, and then
etched for metallurgical characterizations. Sectioning was per-
formed along cross-sectional and longitudinal directions of the
weld coupon on a Leco CM-15®cut-off machine. The sample
grinding and polishing were performed on a Leco Spectrum
System2000®grinder/polisher. The polished samples were then
etched by Tucker’s reagent and Keller’s reagent 关23兴for macros-
copy and microscopy analyses, respectively. Macroscopy analysis
was performed under stereoscopes and optical microscopes. An
image acquisition system including a digital camera and a com-
puter was used to capture and store the images. The weld penetra-
tion, width, and reinforcement were measured. Knoop hardness
measurements were performed on the cross sections of weld
samples using a load of 100 g.
4 Results and Discussion
The formation of the weld bead for a GMAW of 6005-T4 alu-
minum alloy was calculated. The fluid flow pattern, temperature
distribution, and the weld bead shape were obtained. The welding
current is 183 A, voltage is 23.5 V, wire feed speed is 69.8 mm/s,
and welding speed is 14.8 mm/s. Table 1 lists the other welding
conditions and simulation parameters. The simulation parameters
are based on the welding conditions and the results from our pre-
vious studies on droplet generation and transfer 关14,15,24–26兴.
Simulation is started when the welding arc is ignited at x=0, 30
mm to the left edge of the plate. To simulate a realistic welding
process where the weld torch has a 15 deg lead angle and to
account for the moving speed of the welding arc, the droplet also
has a horizontal velocity in the arc moving direction in addition to
the vertical velocity.
Figure 3 shows a partial three-dimensional view of the simu-
lated quasisteady welding process. It is observed that a cold-weld
at the beginning, a crater at the end, and ripples are formed on the
weld bead by the impinging droplets. The temperature, fluid flow,
and formation of ripples will be discussed in Secs. 4.1–4.3.
4.1 Side View of the Welding Process. Figures 4–6 show the
side views of the welding process showing the weld pool, tem-
perature field, and velocity distribution, respectively. At t
=2.8200 s, before a new droplet’s impingement onto the weld
pool, both the previously deposited material and the base metal
are melted by the welding arc. The lowest height of the depressed
weld pool surface is not right under the arc center, but behind it.
For example, at t=2.8200 s, the deepest surface point is nearly 2
mm behind the arc center. The deepest penetration occurs slightly
behind the lowest weld pool surface point, and also around 2 mm
behind the arc center. These phenomena are the results of fluid
flow pattern and heat transfer in the weld pool. The fluid in the
weld pool flows away from the arc center in two directions: one in
the welding direction and the other one in the opposite direction.
The fluid flows downward, and, when reaching the bottom of the
weld pool at the weld center, part of the fluid flows to the left, then
upwards along the solid-liquid boundary and the rest flows up-
ward to the right. It takes some time for the heat to transfer into
the base metal and melt the solid material. Hence, the base metal
continues to melt even after the arc center has passed by, causing
the deepest penetration to occur behind the weld arc center. The
isotherms in Fig. 5 clearly show the heat propagation in the base
metal, where the deepest point of isotherm of 880 K is to the left
of 927 K. Since the solid-liquid boundary is deeper into the base
metal where penetration is deeper and the fluid flowing to the left
021011-4 / Vol. 132, APRIL 2010 Transactions of the ASME
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follows the solid-liquid interface, the molten metal continues to
flow downward and leftward until it reaches the deepest penetra-
tion position where it begins to flow upward and leftward. There-
fore, the lowest weld pool surface point is located behind the weld
arc center and near the deepest penetration position. The velocity
of fluid decreases as it flows uphill, and when reaching the tail
edge of the weld pool, the fluid solidifies and forms the top sur-
face of the weld bead. A weld pool with a crater-shaped surface is
thus formed due to this flow pattern.
The fluid flow pattern is primarily caused by the combined
effect of three factors: first, arc pressure, which depresses the free
surface; second, surface tension, which drives the fluid flow out-
wards in this case, according to Eq. 共12兲, the surface tension co-
efficient decreases as the temperature increases, leading to the
outward surface tension force from the high temperature arc cen-
ter; and third, droplet impingement, which drives the flow down-
ward and outward from the arc center. These three factors main-
tain the outward flow and keep the weld pool surface profile.
Compared with the weld pool formed in the GMAW of steels 关15兴,
the thickness of the molten metal layer in the aluminum weld pool
is thinner because of the faster solidification, and there is no vor-
tex developed in the weld pool.
4.2 Front View of the Welding Process. Figures 7–9 illus-
trate the front view of the cross-sectional weld bead and weld
pool, temperature field, and velocity distribution at the arc center,
respectively. When the droplet impinges onto the weld pool at t
=2.8240 s, the top droplet fluid near the axis of symmetry keeps
flowing downward, while at the same time the bottom droplet
fluid away from the axis of symmetry begins to spread out into the
Table 1 Thermophysical properties and welding conditions used in the model
Property Symbol Value 共unit兲
Specific heat of solid phase cs900a共J/kg K兲
Specific heat of liquid phase cl900a共J/kg K兲
Thermal conductivity of solid phase ks167b共W/mK兲
Thermal conductivity of liquid phase kl167b共W/mK兲
Density of solid phase
s2700b共kg/m3兲
Density of liquid phase
l2300b共kg/m3兲
Coefficient of thermal expansion

T2.34⫻10−5 b共/K兲
Radiation emissivity 0.4
Dynamic viscosity
l0.0012a共kg/ms兲
Heat of fusion H3.97⫻105a共J/kg兲
Heat of vaporization Hv1.08⫻107a共J/kg兲
Solidus temperature Ts880b共K兲
Liquidus temperature Tl927b共K兲
Ambient temperature T⬁293 共K兲
Convective heat transfer coefficient hc80 共W/m2s兲
Electrical conductivity
e2.5⫻107b共⍀−1 m−1兲
Welding voltage uw23.5 共V兲
Welding current I183 共A兲
Arc heat flux distribution parameter
q2.50⫻10−3 共m兲
Arc current distribution parameter
c2.50⫻10−3 共m兲
Welding speed Va14.8 共mm s−1兲
Arc thermal efficiency
60%
Welding speed Va14.8 共mm s−1兲
Arc thermal efficiency
60%
Ratio of droplet thermal energy to total arc energy
d20%
Thickness of base metal Hb5.0 共mm兲
Width of base metal Wb38.1 共mm兲
Length of base metal Lb203.2 共mm兲
Initial base metal temperature Tb293 共K兲
Initial base metal sulfur concentration fb
␣
100 共ppm兲
Electrode wire diameter dw1.60 共mm兲
Electrode wire feed speed Vw69.8 共cm/s兲
Droplet diameter Dd1.0 共mm兲
Droplet generation frequency Fd268 共Hz兲
Droplet impinging velocity Vd50 cm/s
Initial droplet temperature Td1050 共K兲
Initial droplet sulfur concentration fd
␣
300 共ppm兲
Maximum plasma arc pressure Pmax 200 共Pa兲
Plasma arc pressure distribution parameter
p5.0⫻10−3 共m兲
aProperty of pure aluminum 关19兴.
bProperty of 6005 关22兴.
Fig. 3 Partial three-dimensional view of the simulated weld at
t=1.8800 s
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molten pool in the ⫾Ydirections. When the downward fluid
reaches the weld pool bottom, it spreads into the molten pool
along the solid-liquid boundary. The fluid near the impinging
droplet flows outwards under the influences of the three aforemen-
tioned factors. Further away from the weld pool center, the up-
ward and outward fluid flows become weaker. Near the weld pool
edge, the horizontal velocity of the fluid in the Ydirection de-
creases. In the same region, the fluid begins to flow downward
under the influence of gravity.
At t=2.8540 s, the droplet has mixed with the weld pool com-
pletely. The liquid flows downward and outward under the influ-
ence of the three factors mentioned above and thus spreads the
melted metal to both sides of the weld. Therefore, the weld pool is
depressed to form a crater-shaped surface at the center. At t
=2.8175 s, a new droplet impinges into the weld pool and the
process is repeated for another cycle. Compared with the GMAW
of steels 关15兴, the liquid metal is thin, and no vortex is formed on
the cross section either.
4.3 The Formation of Ripples. As shown in Figs. 3 and 4,
ripples formed in the solidified weld bead are very common in the
gas metal arc welding process. To determine the formation of
weld bead and weld quality, it is very helpful to investigate the
Fig. 4 Side view showing the weld bead shape and weld pool
at different times; the region with the darkest color is the weld
pool and the second darkest region is the weld bead
Fig. 5 The corresponding temperature field of Fig. 4
Fig. 6 The corresponding velocity distributions of Fig. 4
Fig. 7 Front view showing the weld bead shape and weld pool
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mechanism of ripple formation. The previous studies of the for-
mation of ripples in the GMAW of steels 关15兴found that the
waves were formed and propagated toward the rear end of the
weld pool. The height level of the fluid upon solidification varied
between the “peak” and “valley” of the waves. Thus, ripples were
formed in the fully solidified weld bead. Although this mechanism
is valid for the GMAW of steels, for gas metal arc welding of
aluminum alloys, the weld pool size is much smaller and the
thickness of liquid metal is much thinner compared with steels.
Therefore, there is no condition for molten metal waves to form
and propagate in the weld pool. It is found that the ripple forma-
tion is the result of droplet impingement onto the weld pool. The
process will be discussed in detail in this section.
The top surface of the weld bead is formed when the fluid
solidifies at solidus at the rear end of the weld pool. Since, in the
GMAW process, the mushy zone between solidus temperature and
liquidus temperature has nearly no flow 关15兴, the height of the
liquidus line of 927 K at the tail edge of weld pool is almost the
same as the height of the solidified metal next to the weld pool tail
edge. The liquidus line can be as high as the ripple peaks.
As shown in Figs. 4–6, at t=2.8200 s, at the tail of the weld
pool, the liquidus line is at z=7.1248 mm, which is at the valley
of the last ripple. At t=2.8240 s, a new droplet just impinges onto
the weld pool. The droplet momentum provides the driving force
for the fluid to flow uphill to the rear end of the weld pool. Be-
cause of the inertia of the fluid, the left end liquidus line does not
rise immediately, which is still at z=7.1248 mm. At t= 2.8305 s,
a new droplet falls into the weld pool, providing a new drive force
pushing liquid up at the tail edge of the weld pool. The liquidus
line at the tail edge begins to rise as a result of the last droplet
impingement, increasing to z=7.2720 mm. At t= 2.8320 s, the
droplet mixes with the weld pool. The tail edge liquidus line con-
tinues to rise as a result of the impingement of the previous drop-
lets, the height of which is z=7.27998 mm. The process continues
and the subsequent droplets supply a continuous driving force to
push the weld pool fluid uphill. The tail edge liquidus line keeps
rising until at t=2.8440 s, it reaches its peak height of z
=7.3943 mm. The peak of a new ripple is thus formed. With the
increase in fluid level, the gravity force increases gradually. When
the fluid level reaches its peak, the gravity force is sufficient to
force the fluid to flow downward. Thus, the fluid level begins to
fall, leading to the decrease in the tail edge liquidus line. At t
=2.8540 s, a new ripple is completely formed, the peak of which
is at z=7.3943 mm. The fluid level decreases to z= 7.1248 mm,
beginning to form a new ripple valley.
From the formation process of a ripple, it is observed that a
single droplet does not provide sufficient momentum to drive the
fluid flowing upward toward the rear of the weld pool against the
hydrostatic force to form a ripple. A series of droplets is needed
for the ripple formation. Since there are 154 droplets falling into
the weld pool per second in this simulation, from t=2.8240 s to
t=2.8440 s, 3 droplets have impinged onto the weld pool forming
the peak of a ripple. The distance between the peaks of the ripple
formed during this time period and the previous one is about 0.72
mm.
4.4 The Weld Bead Shape. The base metal and the resulting
weld are shown in Fig. 10. The black zones in the base metal are
Mg2Si particles 关23兴. On the cross section near the fusion line, the
weld can be divided into three zones: fusion zone 共FZ兲, where the
metal was melted and then solidified, partial melted zone 共PMZ兲,
where the peak temperature was between the alloy’s melting point
and eutectic temperature, and heat-affected zone 共HAZ兲, where no
melting happened during welding but significant solid-phase
transformations took place. The FZ is characterized by columnar
dendrites. The dark interdendritic network in the FZ is aluminum-
silicon eutectic 关23兴. The PMZ has a coarse grain structure. In the
HAZ near the weld bead, there are fewer Mg2Si particles than in
the base metal since, near the weld bead, the peak temperature is
high enough for the particles to dissolve into the aluminum ma-
trix. The cross section of the weld bead at x=30 mm is compared
with the simulated results in Fig. 11 and Table 2. The zig-zag at
the bottom of the simulated weld bead is the result of computa-
tional grid. A good agreement between the experimental and cal-
culated results was obtained.
4.5 Microhardness. Knoop microhardness measurements
were conducted on the base metal and weld bead. The average
hardness is HK 82.17 with a standard deviation of HK 1.56 for the
base metal and HK 54.25 with a standard deviation of HK 3.779
for the weld bead. Knoop hardness in the HAZ was measured on
the x=30 mm cross section along a line 0.4 mm below the top
surface of the welding sample 共Fig. 12兲. The results are shown in
Fig. 13. It is observed that although the measurement was per-
Fig. 8 The corresponding temperature field of Fig. 7
Fig. 9 The corresponding velocity distributions of Fig. 7
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formed after 1000 h of natural aging at room temperature, the
hardness in the HAZ is still significantly lower than that of the
base metal.
The 6005 alloy used in this research is a heat-treatable alumi-
num alloy, which gains its strength primarily through the forma-
tion of precipitates in the aluminum matrix during heat treatment.
Four sequential precipitations may be formed in the alloy during
the aging process: the Guinier-Preston 共GP兲zones, the

⬙phase,
the

⬘Mg2Si phase, and the equilibrium phase

Mg2Si
关19,27,28兴. Among the four phases, the

⬙phase is the primary
strengthening phase in 6xxx series alloys 关29兴. It is observed from
Fig. 13 that for the whole microhardness measurement zone, the
peak temperature is above 523 K everywhere. When the tempera-
ture is between 523 K and 653 K, the

⬙phase coarsens and also
transforms to the

⬘phase, causing lower hardness than that of the
base metal. At 653 K, the size of the

⬙phase and the amount of
the

⬘phase reach the maximum, and the strength of the metal
decreases to a minimum value 关28兴. This corresponds to the low-
est hardness near 5 mm. In the region between 5.76 mm and 3.56
mm to the fusion line, where the temperature is between 653 K
and 773 K, dissolution of

⬙and

⬘occurs because the precipi-
tations are held at temperatures higher than the solvus. The disso-
lution process enriches the solid solution of the aluminum matrix
with alloying element Mg 关30兴. Therefore, this zone may undergo
a solution-hardening heat treatment during the heating and cooling
of the welding process, which contributes to the rise of local hard-
ness. Thus, a local hardness increase is found at about 3.5 mm.
Another contribution to the local hardness rise is that during the
postweld natural aging 共⬎3000 h兲, new precipitates are formed,
which can be either GP zones 关31兴or

⬙phases. When the dis-
tance to the fusion line is less than 3.56 mm, the temperature is
Fig. 10 Zones near the fusion line at the cross section of the
weld: „a…zones near the fusion line and „b…base metal
Fig. 11 Comparison of the experimental and calculated results
for a cross section at x=30 mm
Table 2 Dimensions of cross sections at x=30 mm
Expt.aSimulation
Pb共mm兲2.15 2.07
Wb共mm兲7.56 7.65
Rb共mm兲2.05 2.19
aAverage values are used for experimental results.
bP: penetration; W: width; R: reinforcement.
Fig. 12 Knoop hardness measurement positions
Fig. 13 Knoop hardness measurement results and peak tem-
perature along the hardness measurement line on cross sec-
tion at x=30 mm
021011-8 / Vol. 132, APRIL 2010 Transactions of the ASME
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higher than 773 K. There are no precipitates in this zone because
of the dissolution of the

⬙and

⬘phases 关30兴. The aluminum
matrix is therefore enriched with Mg. The possible reason for the
hardness drop may be the diffusion of alloy element Mg between
the solid and liquid metals at the interface between the weld pool
and solid metal. In the electrode material 4043, the Mg content is
far lower than in the base metal 关22兴. Since areas adjacent to the
fusion zone undergo high temperatures during the welding pro-
cess, the diffusion of Mg may not be negligible, inducing the
depletion of Mg in this zone and consequently resulting in the
hardness drop near the fusion line.
5 Conclusions
The fluid flow and heat and mass transfer in the weld pool for a
moving GMAW of aluminum alloy 6005 were analyzed. Weld
pool and weld bead shapes, temperature field, and velocity distri-
bution were obtained for the welding process. Experiments were
conducted on the formation of the weld. Metallurgical character-
izations together with microhardness measurements were per-
formed. It was found that due to the fast heat dissipation, the weld
pool is small compared with the typical GMAW process of steels,
and no vortex is formed. The drop impingement, surface tension,
and welding arc pressure force the fluid to flow away from the
welding arc center. A crater-shaped weld pool is formed as a re-
sult. Consecutive droplet impingements are needed for the fluid
level at the rear end of the weld pool to vary periodically and form
the ripples on the weld bead. Combining the metallurgical analy-
sis and mathematical modeling, it was found that the high peak
temperature near the fusion line causes the HAZ softening.
Acknowledgment
This work is partially supported by the General Motors Corpo-
ration, which is gratefully acknowledged.
Nomenclature
B
៝
⫽magnetic induction vector
c⫽specific heat
C⫽inertial coefficient
f⫽mass fraction
F⫽volume of fluid function
g⫽gravitational acceleration
h⫽enthalpy
hc⫽convective heat transfer coefficient
Hv⫽latent heat of vaporization
I⫽welding current
J
៝
⫽current density vector
k⫽thermal conductivity
K⫽permeability function
n
៝
⫽normal vector to the local surface
p⫽pressure
pv⫽vapor pressure or any other applied external
pressure
Pmax ⫽maximum arc pressure at the arc center
r−z⫽cylindrical coordinate system
s
៝
⫽local surface tangential vector
t⫽time
T⫽temperature
u⫽velocity in the xdirection
uw⫽arc voltage
v⫽velocity in the ydirection
V
៝
⫽velocity vector
V
៝
r⫽relative velocity vector between the liquid
phase and solid phase
w⫽velocity in the zdirection
W⫽melt mass evaporation rate
Greek Symbols

T⫽thermal expansion coefficient
⫽surface radiation emissivity
␥
⫽surface tension coefficient
⫽free surface curvature
⫽dynamic viscosity
⫽arc thermal efficiency
d⫽ratio of droplet thermal energy to the total arc
energy
⫽Stefan–Boltzmann constant
⫽density
p⫽arc pressure distribution parameter
q⫽arc heat flux distribution parameter
s
ជ
⫽Marangoni shear stress
Subscripts
0⫽initial condition
d⫽droplet
l⫽liquid phase
m⫽melting point of aluminum
s⫽solid phase
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