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Heat Flow during the Autogenous GTA Welding of Pipes
SINDO KOU and Y. LE
A theoretical and experimental study of heat flow during the
welding of pipes was carried out. The theoretical part of the study
involves the development of two finite difference computer models:
one for describing steady state, 3-dimensional heat flow during
seam welding, the other for describing unsteady state,
3-dimensional heat flow during girth welding. The experimental part
of the study, on the other hand, includes: measurement of the
thermal response of the pipe with a high speed data acquisition
system, determination of the arc efficiency with a calorimeter, and
examination of the fusion boundary of the resultant weld. The
experimental results were compared with the calculated ones, and
the agreement was excellent in the case of seam welding and
reasonably good in the case of girth welding. Both the computer
models and experiments confirmed that, under a constant heat input
and welding speed, the size of the fusion zone remains unchanged in
seam welding but continues to increase in girth welding of pipes of
small diameters. It is expected that the unsteady state model
developed can be used to provide optimum conditions for girth
welding, so that uniform weld beads can be obtained and weld
defects such as lack of fusion and sagging can be avoided.
I. INTRODUCTION
HEAT flow during welding is of great interest to welding
engineers and metallurgists. It not only controls the size of the
fusion and heat-affected zones, but also strongly affects the
microstructure and properties of the resultant weld.
Heat flow during the autogenous (i.e., without filler metal) GTA
(i.e., gas tungsten arc) welding of plates has been studied
extensively in recent years. However, far less work has been
conducted on heat flow during the autoge- nous GTA welding of
pipes. No analytical solutions have been made available. In fact,
the only study known to the authors is the recent one by Grill, 1
in which heat flow during girth welding was calculated using the
finite difference method. A "temperature source" was assigned to
each grid point in the workpiece, and the solution was obtained by
using the alternating direction implicit scheme. No experi- ments
were carried out to verify the calculated results.
In the present study, both steady state, 3-dimensional heat flow
during seam welding and unsteady state, 3- dimensional heat flow
during girth welding were theo- retically calculated and
experimentally verified.
II. MATHEMATICAL MODEL
Shown in Figures l(a) and (b) are schematic sketches for seam
and girth welding, respectively. In the former, the pipe is
stationary while the heat source travels in the axial direc- tion
of the pipe at a constant speed U. In the latter, the pipe rotates
about its axis at a constant angular velocity lq, while the heat
source remains stationary. As a result of the heat input, a weld
pool is created under the heat source. The weld pool can be either
fully or partially penetrating, depending on the welding parameter
used. Behind the weld pool is the solidified structure of the
fusion zone, i.e., the weld bead.
The cylindrical coordinate system shown in Figure l(a) travels
with the heat source at the same velocity, while that in Figure
l(b) remains stationary with the heat source. In
SINDO KOU and Y. LE are, respectively, Associate Professor and
Graduate Student at the Department of Metallurgical and Mineral
Engineer- ing, University of Wisconsin, Madison, WI 53706.
Manuscript submitted October 24, 1983.
SEAM WELDING Heat Source
,- rl Weld Fusion -~ U/Pool / zone Velocity, u
(o) (a)
GIRTH WELDING Heat
Source Weld Pool 0/
Angular LYe I~ Q' I/Tt~" -'- z (0 )
(b) Fig. 1 --Schematic sketches of pipe welding: (a) seam
welding; (b) girth welding.
both cases, the origin of the coordinate system is located at
the intersection between the axis of the pipe and that of the
tungsten electrode of the GTA torch.
Due to the combined effects of the electromagnetic force, the
plasma jet force, and the surface tension of the liquid metal, the
convection of the liquid metal in the weld pool appears to be
rather complex in arc welding. No attempts were made to simulate
the weld pool convection. Rather, the effective thermal
conductivity 1'2 was used to account for the effect of convection
on heat flow during welding.
The following integral energy equation was used to describe the
energy balance in a volume element of the workpiece:
f f f o(p"). - - - -~-ar = jj (kVT - pHV)dS [1] T $
where H is the enthalpy, p the density, t time, k the
thermal
METALLURGICAL TRANSACTIONS A VOLUME 15A, JUNE 1984--1165
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conductivity, and T temperature. ~- and S are the volume and
surface area of the volume element, respectively. V is the velocity
of the workpiece material with respect to the volume element.
A. Seam Welding
Except during the initial and the final transients of the
welding process, the temperature distribution in a pipe of
sufficient length is steady with respect to the moving coordi- nate
system. Therefore, the time dependent term in Eq. [1] equals zero
and the process becomes a steady state heat flow problem. Since the
problem is equivalent to one in which the heat source remains
stationary while the pipe travels at a speed U in the z-direction,
the velocity of the material relative to the volume element is
V = Uz [2]
where z is the unit vector in the z-direction. From Eqs. [1] and
[2], the following finite difference
equation can be derived for the temperature at nodal point P
shown in Figure 2:
Tp = (aeTE + awTw + auTN + asTs + arTr + asTB + b)/at"
[3]
where
k,r~A OA z a E = _ _
rE - rp
kwrwA OA z aw-
re - rw
k, FAOAr au- - ZN -- Zp
k,7"AOAr as --
ze - Zs
k, ArAz aT r.( O~ - Oj
kbArAz
as = rt'( Ot" - On)
at, = ae + aw + aN + as + ar + aB
1 b = - --f p(HN - Hs) UT" A OA r
t" = (re + rw) /2
Far ahead of the heat source, the pipe is not affected by the
heat source and, therefore, its temperature remains unchanged. Far
behind the heat source, on the other hand, the temperature of the
workpiece levels off to a steady value, and OT/Oz approaches zero?
The outer surface (r -- R) of the pipe is subjected to a heat flux
q either due to the heat source or due to the surface heat loss,
depending on its location. In summary, the boundary condi- tions
are as follows:
i T=To as z---->-oo
ii OT/Oz =0 as z--*
7
B Fig. 2--Volume element for calculation of heat flow.
_._.._....7
3Q exp at r =R and d< a iii q = 7raZ
iv q = - [h (T - Ta) + o 'e (T 4 - Za4)] at
r = R and d> a, and at r =R '
In boundary condition (i), To is the initial pipe temperature.
In boundary condition (iii), Q is the power input of the heat
source. It equals ~lEI, where E is the arc voltage, I the welding
current, and 7/the efficiency of the arc, i .e., the percentage of
the arc power (El) absorbed by the pipe. d and a are the distance
from the center of the heat source and the radius of the heat
source, respectively. The Gaussian distri- bution of the heat
source shown in (iii) was first proposed by Pavelic 4 in 1969 and
has been used extensively since then. Experimental studies have
indicated that such a distribution is essentially correct. 5'6 In
boundary condition (iv) h is the heat transfer coefficient, Ta the
ambient temperature, o" the Stefan-Boltzmann constant, e the total
emissivity of the workpiece surface, and R' the radius of inner
surface of the pipe. As in a previous study, 2 it was found that,
due to the low melting point and the high thermal conductivity of
alu- minum alloys, the surface heat loss due to radiation and
convection during welding is less than 1 pct of the heat input.
Therefore, the surface heat loss was neglected. The above
equations, however, are general and can be applied to situations
where surface heat loss is important.
B. Girth Welding
Since the weld bead eventually forms a closed circle on the
pipe, heat continues to build up during girth welding. Therefore,
the heat flow problem is an unsteady state one. The energy balance
equation, Eq. [1], can be integrated over the time interval from t
to t + At as follows:
3, -~ dtd'; = (kVT - pHV) " dSdt
[41
The fully implicit scheme was employed in the present study,
which according to Patankar 7 can be expressed below:
f '+a'Tdt = T 1 At [5] lI66--VOLUME 15A, JUNE 1984 METALLURGICAL
TRANSACTIONS A
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where T 1 is the new value of T, i .e., at time t + At. The
velocity of the material relative to the volume ele-
ment is
V = - f l rO [6]
where 0 is the unit vector in the 0-direction. From Eqs. [4] to
[6], an equation identical to Eq. [3] can
be obtained for the temperature at nodal point P. However, all T
should be changed to T 1 and the variable b should be
1 b = -~prpfZ(H~ - Hi) ArAz
- p(H~ - l -~p)~ArAzAO/At
where H i and /~p denote the new and old values of lip,
respectively.
The initial condition is T = To at t = 0 for all positions of
the pipe. Since the end surfaces of the pipe are much smaller than
its outer and inner surfaces, and since the temperature gradients
near the end surfaces are very small, heat loss from the end
surfaces is negligible. Therefore, boundary conditions (i) and (ii)
shown previously should now be
OT/Oz = 0 at z = +-L/2
where L is the length of the pipe. Boundary conditions (iii) and
(iv), however, are still valid.
III. METHOD OF SOLUTION
Eq. [3], boundary conditions (i) to (iv), and the enthalpy-
temperature relationship 8 were used to solve the temperature
distribution during seam welding. The heat of fusion was included
in the enthalpy-temperature relationship. As ob- served previously,
2 the effect of the temperature dependence of the thermal
conductivity of solid aluminum on heat flow was very small and was,
therefore, neglected. Since heat flow is symmetrical with respect
to its axial plane, only the temperature distribution in one-half
of the pipe was calcu- lated in the case of seam welding. In order
to enhance the accuracy of calculation, a grid mesh of variable
spacing was used, i .e., finer spacing near the heat source and
coarser far away from it. An example of the grid meshes used is
shown in Figure 3. The successive overrelaxation method with a
relaxation parameter of 1.4 was used. The iterative procedure of
temperature calculation was carried out with a digital computer
until the following convergence criterion was satisfied:
T~ - T O maximum ~ 1 .0 ~ over r, 0, z
In the case of girth welding, Eq. [3] (with b defined in II-B),
the initial and boundary conditions, and the enthalpy- temperature
relationship were used to calculate the tem- perature distribution
in the pipe. A grid mesh of variable spacing was also used. Since
heat flow is symmetrical with respect to the central plane, i .e.,
the r-O plane passing through the centerline of the heat source,
only the tem- perature distribution on one side of the central
plane was calculated. The successive over relaxation method with a
relaxation parameter of 1.4 was used at any time step n until
the change in the total enthalpy content of the pipe becomes
smaller than or equal to 1 pct of the total heat input up to that
time step, i .e.,
Ee(n ' - n o) ~,QAt -< 1 pct
Comparing with the previous convergence criterion, this
convergence criterion is equivalent to a maximum tem- perature
change of 10 -2 to 10 -3 ~ Since the heat flow problem is now an
unsteady state one, a convergence crite- rion tighter than the
previous one is necessary for assuring the accuracy of the
calculated results.
Instead of treating the heat input Q as a step function, it was
assumed that Q increases from zero to its steady state value Qs in
a short time, say 0.1 second. This helped avoid divergence at the
initial stage of calculation. This is shown in Figure 4. The values
of At chosen for the calcu- lation of heat flow during the rising
period, the steady state period, and the power-off period were
0.025, 0.25, and 0.5 second, respectively.
IV. EXPERIMENTAL PROCEDURE
The composition of 6061-T6 aluminum pipes used is shown in Table
I. The length, outer diameter, and wall thickness of the pipes are
20.3 cm (8 inches), 3.81 cm (1.5 inches), and 3.2 mm (0.125 inch),
respectively. Oxide films were polished off the surface of the
pipe. The polished surface was then cleansed with acetone just
before welding. The workpiece was thermally insulated from the
fixture to avoid heat sinks during welding. In the case of girth
welding, an MBC welding positioner (model BP-1) with a maximum
rotation speed of 6 rpm was employed.
The power source was a Cybertig-300 D.C. program- mable machine.
Direct current, straight polarity GTA welding was used to produce
autogeneous GTA welds. All welds were made using argon shielding
gas and a 2.4 mm (0.09375 inch) tungsten-2 pct thoria electrode
with a 50 deg included angle. A Cyclomatic AVC 2 automatic arc
voltage controller was used, and the arc voltage was kept within
+--0.1 volt of the predetermined value during welding. This allowed
the precise control of the heat input during welding.
It should be pointed out that D.C. straight polarity weld- ing
of aluminum has recently been employed in situations where deeper
weld penetration is desired, 1~ though A.C. welding of aluminum is
no doubt more popular due to its surface cleaning ability. D.C.
welding was chosen in the present study since the Cybertig-300
machine available is a D.C. type power source. This, however, does
not imply that A.C. welds are expected to be equivalent to D.C.
welds or to be reproduced by D.C. welding procedures.
Table I. Nominal Composition and Physical Properties of 6061
Aluminum Alloy 9
Element Mg Si Cu Cr AI Wt Pct 1.0 0.60 0.28 0.20 balance
TL = 652 ~ k = 168 W/m ~ Cp = 1066 J/kg ~ Ts = 582 ~ p = 2700
Kg/m 3 AH = 3.95 105 J/kg
METALLURGICAL TRANSACTIONS A VOLUME 15A, JUNE 1984--1167
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Fig. 3- -An example of the grid mesh for calculating heat flow
during seam welding: (a) side view; (b) front view.
Qs
C~
,.=,
Steady CA
o, ,A 0 toff
T IME, t
off
Fig. 4--Power input vs time relationship used for calculating
heat flow during girth welding.
II68--VOLUME 15A, JUNE 1984
A high speed data acquisition system, consisting of an LSI 11
computer, an analog/digital convener, two floppy disc drives, a
graphics terminal, and a printer/plotter, was employed for thermal
rlcasurements during welding. This data acquisition system al,ows
as many as twenty thermo- couples to be used simultaneously.
Chromel-alumel thermo- couple wires of 0.13 mm (0.005 inch)
diameter were used. The tips of the thermocouples were sealed
tightly to the bottom of 0.5 mm-diameter holes drilled (with a
microdrill) at selected positions in the pipe. After welding the
weld bead was sectioned, polished, and etched with Keller's etching
solution to reveal the fusion boundary.
The Zuiko macrophoto system was employed to photo- graph the
arc, with a No. 5 filter and high contrast films. By using proper
references, such as the diameter of the tungsten electrode and the
inside diameter of the ceramic cup, the size of the arc was
determined. It was found that the size of the arc so determined was
relatively insensitive to the variations in the amount of
exposure.
In order to determine the arc efficiency, the simple cal-
orimeter shown in Figure 5 was used. The aluminum pipe was
thermally insulated to avoid heat sinks. The current and voltage
employed were essentially the same as those in welding experiments.
The temperatures of inlet and outlet water were recorded
continuously, as shown in Figure 6. The surface of the pipe was
covered with insulating mate- rials immediately after the heat
source passed by, in order to minimize the surface heat loss. The
following equation was used to determine the arc efficiency:
JoCp(Tout - - Tin) dt = rlElt [7] W
where W = mass flow rate of water Cp = specific heat of water
To,t = outlet water temperature Tin = inlet water temperature t =
welding time
METALLURGICAL TRANSACTIONS A
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4 I I HEAT U SOURCE
PIPE A i i
W ATER, N I q.OeeE. STOPPER T
L, l~C. '////////////////////////"
INSULATION
Fig. 5 - -A simple calorimeter for determining the arc
efficiency.
5O
o
tS n~ 40 l--
n~ ILl a.
30 b.I I--
I J I
I IOA, IOV, 15 IPM Water f low rate = 495ml /min Weld ing time
23.1 sec
20 I I I I 0 I00 200 SEAM WELDING
Front View T IME, sec
Fig. 6 - - Inlet and outlet water temperatures as a function of
welding time.
It is worth pointing out that Figure 6 does not imply that
steady conditions were not achieved in seam welding. The upper
curve shown in this figure is the typical response curve observed
by chemical reactor designers in their stimulus-response
experiments. ~3 In the present case, the stimulus, i.e., the heat
input from the arc, lasted for about 23 seconds, while the
response, i.e., the change in water temperature, lasted for more
than 100 seconds.
V. RESULTS AND DISCUSSION
As discussed previously, 8 many dimensionless variables are
necessary for completely defining heat flow during fu- sion
welding. Consequently, the presentation of general heat flow
information based on dimensionless variables is not feasible.
Therefore, no dimensionless variables will be em- ployed in the
following discussion.
A. Seam Welding
Figure 7 shows the calculated and the measured thermal cycles
for a pipe welded with a voltage of 10 V and a current of 120 A.
The welding speed was 5.50 mm per second (13 ipm), and the measured
radius of the arc was 3 ram. With an arc efficiency of 78 pct and
an effective liquid conductivity 1.5 times the value of the solid
thermal conduc- tivity, very good agreement between the calculated
and the measured thermal cycles was obtained. This arc efficiency
is less than 4 pct off the measured value, thus indicating the
validity of the heat flow calculation.
The calculated isotherms and fusion boundary (TD are shown in
Figure 8. As can be seen, the calculated and the observed fusion
boundaries are in excellent agreement.
800
LJ o
2 400
Q.
E
I Calculated
2- - - Observed
J
I I T.C. r (mm) O(radians)
I 17.5 0 .079 2 18.0 0 .594
Seam Welding
t
0 I I I 0 I 0 20 50
Time, Sec Fig. 7 - Comparison between calculated and measured
thermal cycles for the seam weld.
- -Ca lcu la ted - - - Observed
-20mm
IOmm
0 I?mm 120mm
(a)
SEAM WELDING
Side View
0 IOmrn 20mm
4000C
(b)
Fig. 8 --Calculated isotherms for the seam weld. The dashed
lines indicate the observed fusion boundary.
METALLURGICAL TRANSACTIONS A VOLUME 15A, JUNE 1984--1169
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It is worth pointing out that, comparing to D.C. welding, the
arc efficiency is lower and the arc is wider in A.C. welding.
Consequently, A.C. welds are shallower. The computer model can
readily reproduce the difference in weld geometry between D.C. and
A.C. welding by chang- ing the size and efficiency of the arc.
This, in fact, has been demonstrated in our previous work. z
B. Girth Welding
Figure 9 shows the calculated and the measured thermal cycles
for a pipe welded with a voltage of 10 V and a current of 110 A.
The rotation speed was 2.12 rpm. The effective radius of the arc,
the arc efficiency, and the effective con- ductivity of the liquid
pool used in the calculation were identical to those used
previously in the calculation of the seam weld. As can be seen in
Figure 9, the agreement between the calculated and the measured
thermal cycles is reasonably good.
It is interesting to note that thermocouple 1 showed a small but
positive rise in temperature around 28 seconds after welding began.
This is about the time when the pipe finished one rotation. Since
thermocouple 1 was approach- ing the heat source, the temperature
went up again. The rise in temperature, however, was interrupted
since the power was shut off subsequently.
The calculated isotherms and fusion boundary are shown in Figure
10. The dashed lines indicate the observed fusion boundary. As can
be seen, the calculated and the observed fusion boundaries are in
reasonable agreement.
It can be seen from Figure 10 that the fusion zone in- creased
significantly in size as welding proceeded. This is because heat
continued to build up during welding and the areas yet to be welded
were preheated, even though both the heat input and the rotation
speed were kept constant throughout the entire welding process. At
the beginning of welding, there was no preheating and the weld bead
was too small to have full penetration. However, at the end of
weld- ing, there was too much preheating and the weld pool was so
large that it sagged. The sagging of the weld pool appar- ently
caused the observed fusion boundary to deviate from the calculated
one.
Ca lcu la ted - - - Observed
8 = 0 .097
GIRTH WELDING
Front V iew
\ : L /T , ,,o~ I I
8mm 0 8mm
(a)
Front View
0 = 0 .487
I
8mm
\ \ , s ,so.c, 0 8mm
(b) Fig. 10--Calculated isotherms for the girth weld. The dashed
lines indi- cate the observed fusion boundary.
It is, therefore, clear from the above results and dis- cussion
that in girth welding, especially pipes of small di- ameters, the
heat input per unit length of weld should be high at the beginning
and reduced continuously as welding proceeds. In the case of
automatic girth welding, the weld- ing current and hence the heat
input can be preprogrammed through the use of a programmable power
source. The pre- programming of the welding current, however, has
been done on a trial-and-error basis so far. The unsteady state
model developed in the present study is expected to help preprogram
the power source more effectively, so that sound girth welds of
uniform size can be produced.
I 000 i I I I ]
] - - Calculated . . . . Observed Girth Welding 3 TC. r(mm)
z(mm) O(radians)
I ~, I 17.5 1.0 .097 V J 5 2 ,8.o 5.0 I
I/ /l' A e O0 4 18.0 6.0 . , ' ' ,,I, ,,,
2OO
0 I 0 20 30 40
T ime, Sec Fig. 9--Comparison between calculated and measured
thermal cycles for the girth weld.
VI. CONCLUSIONS
The conclusions of this study are summarized below. 1. The
computer model developed for steady state, 3-
dimensional heat flow during seam welding agrees very well with
the thermal cycles and fusion boundary ob- served in aluminum
pipes.
2. The computer model developed for unsteady state,
3-dimensional heat flow during girth welding agrees reasonably well
with the thermal cycles and fusion boundary observed in aluminum
pipes.
3. Both the computer models and experiments confirmed that,
under a constant heat input and welding speed, the size of the
fusion zone is uniform in seam welding but continues to increase in
girth welding of pipes of small diameters. It is expected that the
unsteady state model developed can be used to preprogram the power
source, so that sound girth welds of uniform size can be
produced.
I170--VOLUME 15A, JUNE 1984 METALLURGICAL TRANSACTIONS A
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ACKNOWLEDGMENTS
The authors gratefully acknowledge support for this study from
the National Science Foundation, under NSF Grant No. DMR83-19342.
The assistance of D.K. Sun in the computer work is appreciated.
REFERENCES 1. A. Grill: Int. J. Num. Methods in Engr., 1982,
vol. 18, p. 1031. 2. S. Kou and Y. Le: Metall. Trans. A, 1983, vol.
14A, p. 2245. 3. D. Rosenthal and R.H. Cameron: Trans. ASME, 1947,
vol. 69,,
p. 961.
4. V. Pavelic, L.R. Tanbakuchi, O.A. Uyehara, and P.S. Myers:
Weld. J., 1969, vol. 48, p. 295s.
5. O.H. Nestor: J. of Appl. Phys., 1962, vol. 33, p. 1638. 6.
C.B. Shaw, Jr.: Weld. J., 1980, vol. 59, p. 121s. 7. S.V.
Patartkar: Numerical Heat Transfer and Fluid Flow, McGraw-
Hill, New York, NY, 1980, p. 54. 8. S. Kou: Metall. Trans. A,
1982, vol. 13A, p. 363. 9. Aluminum Standards and Data, 5th ed.,
The Aluminum Association,
New York, NY, 1976, pp. 38 and 40. 10. M. Mizuno and H. Nagaoka:
lntn. Met. Reviews, Review 240, 1979,
no. 2, p. 68. 11. E.P. Vilkas: Weld. J., 1966, vol. 45, p. 410.
12. Y. Kuriyama et al.: IHI Eng. Rev., 1976, no. 4, p. 400. 13. O.
Levenspiel: Chemical Reaction Engineering, 2nd ed., John Wiley
and Sons, New York, NY, 1972, chapter 9.
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