Resistance Spot Welding:
A Heat Transfer Study
Real and simulated welds were used to develop a model
for predicting temperature distribution
BY Z. HAN, J. OROZCO, J. E. INDACOCHEA AND C. H. CHEN
ABSTRACT. A heat transfer study of resistance spot welding has been conducted
both theoretically and experimentally. A
numerical solution based on a finite difference formulation of the heat equation
has been developed to predict temperature distributions as a function of both
time and position during the welding
process. The computer model also predicts
the
temperature
distribution
through the copper electrodes. One
important feature of the program is that it
allows for variations in the physical properties of the metal workpiece.
Temperature
measurements
have
been made in real and simulated welds of
a high-strength low-alloy (HSLA) sheet
steel. Excellent agreement is obtained
between the numerical solution and the
experimental measurements. The heataffected zone (HAZ) obtained by plotting
the lines of constant temperature is very
similar to that measured from actual
welds.
Introduction
Resistance spot welding is characterized as a rapid and clean process for
joining sheet steel. Despite its long and
wide commercial application, an ade-
KEY W O R D S
Resistance Spot Weld
Spot Welding
HSLA Steels
Heat Transfer Model
Temperature Spread
Copper Electrodes
Nugget Size
Heat Conduction
Heat of Fusion
Computer Model
quate weld nugget size is still the primary
concern for spot welding qualification
procedures (Refs. 1, 2). Weld nugget
sizes have been estimated conventionally, using a number of destructive tests,
and recently using more sophisticated
techniques, such as ultrasonic and
dynamic resistivity profiles (Refs. 3-5).
However, it has been pointed out by
other investigators (Ref. 6) that seldom
has the nugget size been directly and
methodically correlated with the different
welding process parameters.
A survey of the literature on resistance
welding (Refs. 7-11) reveals that most of
the thermal models currently available to
describe the resistance spot welding process are either too basic (one-dimensional) or do not include some of the fundamental variables. For instance, the variation of contact resistance with applied
electrode force is not included in the heat
transfer formulation, nor is it the effect of
temperature on physical properties of
the material.
This investigation has been undertaken
to address some of these issues. Basically,
in this work a heat transfer model is
proposed for predicting the temperature
as a function of time, from the start of the
weld, and as a function of position, for
any location within the weld nugget,
adjacent heat-affected regions or electrodes. This heat transfer model takes
into account the following considerations: conduction in the solid, convection,
heat of fusion due to solid-liquid phase
change, element heat content as a function of time and temperature, conduction
in the weld pool, and heat of fusion on
resolidification.
For the analysis of the temperature
distribution in the sheet metal, it is known
that there is a symmetrical distribution of
temperatures through the thickness of
the material and along the interface
where the t w o sheet pieces meet. Consequently, a cylindrical coordinate system
was selected (Fig. 1) with radial as well as
Z. HAN, J. OROZCO and). E. INDACOCHEA
vertical variations in temperature and the
are with the University of Illinois at Chicago,
assumption of azimuthai symmetry in </>.
Chicago, III. C. H. CHEN is with inland Steel
The basic equations and the correspondLaboratories, East Chicago, Ind.
ing boundary conditions are expressed in
finite difference forms. The solution to
the equations includes an explicit formulation which incorporates the physical
properties of the HSLA (high-strength
low-alloy) sheet steel, the base metal.
The analytical thermal results have
been correlated with the information
obtained from real and simulated weld
heat-affected zones (HAZ). The real resistance spot welds were processed at the
Inland Steel Research Laboratories, while
the simulated weld HAZ's were produced at the University of Illinois at Chicago Welding and joining Laboratories.
The temperature computations were
performed for different power levels,
several welding efficiencies, various electrode forces and corresponding material
contact resistances. The model also
accounts for the temperature dependence of the physical properties of the
base metal.
Physical and Mathematical Formulation
The weld nugget in resistance spot
welding is produced by the melting and
subsequent coalescence of a small volume of material due to the heating
caused by the passage of the electric
current and the high contact resistance
between the sheet metals joined. Such
heating per unit time (Q) is defined as the
product of the current intensity (I)
squared, times the total resistance (R),
times the welding efficiency (17).
Several authors (Refs. 12-14) have
reported continuous variations in the
electrical parameters during welding of
mild steel sheet. After about the first
cycle, there is an increase in voltage
across the copper electrodes and a
reduction in current flowing through the
weld zone until a "peak state" is reached.
Throughout the remaining portion of the
weld cycle, the voltage decreases to a
constant value while the
current
increases also to a constant value. These
changes in voltage and current have also
been represented as dynamic resistance
(Refs. 12-14). Basic welding mechanisms
WELDING RESEARCH SUPPLEMENT I 363-s
6T/<5z=0
6T/6*=0
ST/6<t>=0 •
K6T/6r=h„(T-Tj
-KdT/Sr^d-T,,,),
-KST/Sz-huCT-T^)^
6T/6r=0 .
6T/6z=0
Fig. 1 —Schematic describing thermal boundary conditions
can be altered by changes in welding
variables such as weld time, electrode
force and overall weld current.
The components of the system for
resistance spot welding are schematically
represented in Fig. 2. The copper electrodes are water cooled; they exert a
concentrated force on the outer surfaces
of the metals to be joined. Because of
their low electric resistance, these electrodes can conduct high currents to the
workpiece without significant )oule heating losses. Further, their high thermal
conductivity permits closer control of the
nugget formation as well as the cooling
rate, by conducting heat away from the
workpiece (Ref. 15).
The resistances of the sheet steels to
be joined are relatively small, so that a
R4
Rl
R3
R5
Fig. 2 - Schematic of the resistance spot welding process
large current flow is needed to produce a
high-Joule heating effect in the workpiece. The largest voltage drop occurs in
the workpiece, because the resistivity of
the copper electrodes is an order of
magnitude lower than that of the carbon
steel (Ref. 16). This generates the highest
internal heat production in the workpiece, and melting takes place at the
common interface of the workpiece and
spreads to produce the weld nugget. This
phase change from solid to liquid will
cause a drastic change in the physical
properties of the sheet steel.
The total resistance across the electrodes could be considered as the sum of
five resistors in the series schematically
represented in Fig. 3. R-i and R5 are the
interface resistances between the electrodes and the sheet metal; R2 and R4
represent the metals' bulk resistance. R3 is
defined as the contact resistance at the
faying interface and is affected by the
electrical, mechanical and thermal condition of the surface. Since melting occurs
at this last interface, heat production is
the greatest at this location, implying that
R3 is much larger than the other resistances. However, this value drops to
zero (Appendix A) as the weld nugget is
formed.
M o d e l Assumptions
In modeling the resistance spot welding process, several boundary conditions
and physical phenomena must be considFig. 3 —Simplification of the resistance across ered. In simplifying this thermal model,
the following assumptions are made:
the electrodes
364-s | SEPTEMBER 1989
1) A cylindrical coordinate system was
selected as illustrated in Fig. 1. The portions of the coupon affected by the heat
and the immediate-adjacent areas of the
unaffected base metal have been represented by a disk of radius o> (w = 25 mm),
because of the temperature symmetry.
This selection reduces the geometrical
dependency to t w o dimensions, hence
T = T(r,z,4>)
(1)
2) The temperature of the inner surface of the electrodes is that of the
cooling water, T w .
3) Natural convection is the dominant
mechanism on the outer surface of the
electrodes as well as on the surface of
the workpiece.
4) Symmetry with respect to 4>, the
azimuthal angle, permits heat transfer in
the radial and vertical directions only. The
boundary conditions created by symmetry are indicated in Fig. 1.
5) The materials are subjected to a
wide range of temperatures. Properties
such as thermal conductivity (K), thermal
diffusivity (a), specific heat (Cp) and resistivity (p) must then be considered as
functions of temperatures. For our study,
the thermal properties considered were
those of low-carbon steel, as shown in
Fig. 4 (Refs. 14, 16-19). Equations have
been developed for these properties as
function of temperature from the data in
Fig. 4.
The thermal conductivity is expressed
as:
K = K 0 [1 - 0.0004528(T - 20)]
(2)
where
K0 = 5.4 X 107 erg/s • mm • °C
The equations for the specific heat
were derived taking into consideration
four temperature ranges as noted
below
(i) T < 520°C,
Z
a
C p = C P o [ 1 + 0.000688(T - 20)] (3)
o
and
C Po = 4.65 X 108 erg/g • °C
(ii) 520°C < T < 770°C,
C
C
(4)
P
P o T"'
and
C Po = 8.55 X 103 erg/f
(iii) 770°C < T < 850°C,
Cp = C po (T - 850)4 + 7.118 X 10 8 (5)
and
C Po = 13.716 erg/g • °C
(iv) T > 850°C
C p = 6.25 X 108 erg/g • "C
(6)
The equation developed for the resistivity is:
P = P o [1 + 0.005(T - 20)]
(7)
and
p0= 1.5 pfi-mm
6) The contact resistance at the faying
interface varies with electrode force as
shown in Fig. 4D (Ref. 14). At relatively
low electrode forces, this resistance is so
large that the bulk resistance of the sheet
metal is neglected. The empirical equation that was derived from the information provided by Fig. 4D for the lowcarbon steel is:
p ' = p'0 (1 - 0.0004754 P)
2
400
800
1200
6
10
tr
<
tn
14
Temperature'C (xlOO)
Temperature (*C)
z
UJ
5000
s
3000
O
E 2000
u
>
a.
_i
UJ
a
x
o
cc
<
1000
UJ
tn
UJ
S
a.
o
500
(8)
p'o = 15 p.Q-mm
where P is the electrode force on the
workpiece in units of pounds.
7) Since the tip surfaces of the copper
electrodes are not only easily deformed,
but also polished before welding, the
electrode/sheet metal interface resistances, RT and R5, are assumed to be
negligible.
8) Since the metal undergoes a phase
change, a latent heat of fusion evolves
which is assumed to be isothermally
absorbed.
9) The initial temperature of the metal
is the ambient temperature, TooMathematical M o d e l
Governing Differential Equation and
Conditions
The three-dimensional heat conduction equation is written in cylindrical coordinates at an inner node as follows
p"C p dT/dt = (1/rp/3r(rK<9T/dr)] +
(K/r2)(d2T/d<p2) + K(3 2 T/dz 2 )+ g
X
o
(9)
where p" is the density of the steel sheet
or copper electrode, and g is the heat
contribution due to the joule heating
effect. However, since the system is symmetrical with respect to <t> as assumed in
the model assumptions
d2T/d<p2 = 0
(10)
The initial temperature of the system is
that of the ambient, thus
Temperature (*C)
100
10
5
a
15 20
Electrode Force. Lbs. (xlOO)
Fig. 4 — Physical properties of low-carbon steels of conductivity, specific heat, bulk resistivity
contact resistance as a function of temperature and electrode force (Refs. 14, 16-19)
and
~->
x
o
tr
<
UJ
tn
T(r,z,t0) = ^
(constant)
(11)
The adiabatic boundary conditions on the
workpiece, as shown in Fig. 1, are
dl/dr = 0 at r = 0 for 0_< z < b (12)
3T/dz ^ 0 at z = L for R , <
r < R2
(13)
<9T/d0 = 0 everywhere
(14)
The convective boundary conditions on
the workpiece are
- K d T / d r = hoo (T - TOT) at r = w for
0 < z < a
(15)
-KST/dz = hoo (T - Too) at z = a for
e < r < w
(16)
The boundary conditions on the electrode are
—KdT/dr = hoo(T — Too) along the outer surface of the electrode
(17)
—KdT/3r = h w (T — T w ) along the inner
surface
(18)
All the boundary conditions are identified
in Fig. 1.
Finite Difference Representation of the Heat
Equation
Attention is now focused on the mesh
shown in Fig. 5. The first and second
derivatives of the temperature with
respect to position at a point i, j may be
written as
3T
dx
UJ
= (TT
i,),n
+
'/2,J-TT-./2,J)/£
(19)
CC
z
UJ
2
dr 2
= (TV + i,j + TV _ ,,j - 2TV,j)/S
i,j,n
(20)
s
a
O
—i
ui
>
^1
dz2
UJ
.
i,J,n
=(TV, j +
1
2
a
o
(21)
cc
<
+ TV,j-l-2TT,j)/5
The derivative of temperature for a node
i, j with respect to time is written as
3T
3t
= 0 " n i + j 1 - TV,,)/At
(22)
i,J,n
ui
V)
UJ
oc
Hi
a
O
where i, j and n are integers.
Equation 10 and Equations 19 through
22 are now substituted into Equation 9 to
yield
-1
UJ
>
X
o
oc
<
1\
TT + 1,j + T T _ 1 , j + 1
2 2 Ln, + 1 + TV,- 1 -4TV,J
UJ
tn
ui
cc
8Vj = -1|-T"iV-TT,j-|
+
K a|_
At
(23)
WELDING RESEARCH SUPPLEMENT 1365-s
approaches zero (1/r) (3T/3r) would be
undefined. To deal with this situation, w e
have that for r = 0
•OJ-1
A w.
ti
IM.
lim [(1/r)(3T/dr)] = d 2 T/dr 2
r^O
then the heat-conduction Equation 9 at
the location r = 0 takes the form
i.i-1/2
'0.1
I!
A^
T
•V
2d2T/<3r2 + 3 2 T/3z 2 + (1/K)g =
(1/a)3T/at
ILJ
Tu-1
TM,H
'QK
(28)
TM.
(29)
similar formulations are also developed
for points along the boundaries. However, for simplicity their development is
omitted.
r
Numerical Method
< "
Fig. 5-Rectangular
nef mes/i of s/ze 7
ana7 a node (ij)
/ns/rJe f/ie matrix
T 0l
n
i
i
KAt
??.i{
> 0 for 0 < i < 4, 0 < j < 2
= 0 everywhere else
(25)
for node i, j located on outer surface, we
I"'
(26)
P CpV
TV + , i + TV - . i +
g?,i = o
Ti/T+1 + T t f - n l
At
+—
g?,i + I
P Cp
[
4
KAt 1
and finally, for node i, j located on the
inner surface of the electrodes, we
have
n
At K
(24)
(27)
qv.) =
where qV,, is related to convective process. If node i, j is located within the
system or on adiabatic boundaries, then
gV.i = 0
At the origin, r = 0, Equation 9 would
have a singularity because as r
Fig. 6 - Welding
fixture used for
production of spot
welds
Thermocouple Location
?
ZL
E
I
JL
-f^^?
U5
1.5'-
WELDING
FIXTURE
Electrode
366-s I SEPTEMBER 1989
The governing differential equation
was written in finite difference form and
solved using an explicit method. The
explicit method is relatively straightforward but requires a large amount of
computing time because of the stringent
stability condition which is expressed as
At < (p"C p /2Ar) 2 /[1 + (Ar) 2 /(rAt) 2 ].
In
this study, the minimum time step used is
0.00015 s.
Experimental Procedures
At h 0
qV, = ^ ( T T , j - T o o )
t
P"CPC2"
- >
TM.
\
where gVj is the energy generation term
at node i,j and moment n. Applying the
above formulation to those nodes on
boundaries, we can develop a general
expression to obtain the temperature
value at any node i,j and moment n + 1
as follows
Tn.
+ ) _
1
- >
Tr-1.0
A cold-rolled HSLA sheet steel, 2.18
mm (0.086 in.) thick was used in this
investigation. Its composition is given in
Table 1. The material was cut to small
coupons of dimensions of 101.6 X 25.4
mm (4.0 X 1.0 in.). The surfaces of the
specimens were previously cleaned with
acetone. The spot welds were produced
by placing t w o specimens into a special
welding fixture —Fig. 6. The fixture attaches to the lower copper electrode.
The spot welding was done on a
Sciaky press-type 100-kVA single-phase
resistance welding machine. The electrode force on welding was 1600 Ibf
(7120 N). The electrodes used were a
Class II copper alloy (99.2% Cu, 0.8% Cr)
based on the Resistance Welder Manufacturers' Association (RWMA) standard.
The electrode tips have a contact diameter of 7.9 mm (0.31 in.) and 45-deg
truncated cone nose in accordance to
the Ford Motor Company manufacturing
standards. The welding time was held
fixed at 23 cycles (0.38 s) and the current
varied between 11 and 12 kA.
The thermal cycle measurements during resistance welding were measured by
spot welding a 0.254-mm (0.010-in.) thermocouple (either a chromel/alumel or a
platinum/platinum-10% rhodium) onto a
0.8-1.1-mm (0.032-0.045-in.) wide slot
machined on the upper coupon as
shown in Fig. 7. The slot was machined so
as to end in the HAZ, and its length was
estimated by performing a metallographic analysis on several preliminary spot
welds. The welds were sectioned
through the nugget normal to the plane
of the sheet. Samples were mechanically
polished and etched with a solution of
picric acid plus sodium tridecylbenzene
sulfonate. This etchant was very effective
in revealing the solidification structure of
the weld nugget. Samples were characterized with a Leco 300 metallograph.
The nugget size, as well as HAZ measurements, were made from the resulting
micrographs and Fig. 8 shows one of
several photo composites that were
assembled for the metallographic analyses. The HAZ was observed to be the
widest at the faying interface. The thermocouples were placed very close to this
faying surface, and its exact location was
later determined by metallographic evaluation after welding. The thermal measurements were collected using a Hewlett-Packard Series 3000 personal computer with a 3852 data acquisition unit
and a Xerox 6060 personal computer
interphased with a metrobyte data acquisition system. The thermocouple output
signal was distorted during the heating
cycle, but then it remained very smooth
during cooling, immediately after the end
of the weld cycle. The peak temperature
was obtained by extrapolating the cooling curve to a time coinciding with the
end of the weld time.
Results and Discussion
The heat transfer model developed in
this study includes in its formulation the
independent process parameters such as
current, electrode force and time, the
material's thermally dependent physical
properties and the weld efficiency factor.
The analytical results predicted by the
model are compared with those obtained
experimentally.
I-
Z
it
UJ
E
Q.
o
_l
UJ
5?
>
o
oc
<
UJ
^
tn
ut
30172"
E
ac
*>.
L - 0 . 3 4 6 ' to
0.365"
Fig. 7 —Sheet steel
coupons for the
spot welds
W= 0.032" to 0.045"
o.
o
X
Table 1 - -Composition of the HSLA-Sheet Steel wt-%
C
Mn
Si
Nb
Ti
Al
0.06
0.96
0.03
0.10
0.002
0.060
N
s
P
o
cc
<
0.006
0.012
0.009
tn
Ul
UJ
Effect of Current Level on Nugget Formation
Automotive companies' spot weld
qualification procedures (Refs. 1, 2) specify measuring the size of the weld nugget
in terms of one or more welding variables, depending on the specification
applied. The correlations of nugget size
with current or with current and time are
some of the most popular for qualification procedures. The importance of the
current's influence on the soundness of
the weld nugget has led to the develop-
ment of welding lobes to define the
current and time ranges where optimum
spot welds can consistently be produced.
However, this reproducibility is hampered by inconsistencies in metal composition, variation in surface finish and by
electrode tip mushrooming.
The heat transfer model proposed
defines the temperature of any location
in the workpiece as a function of time
from the start of the process. Consequently, it can also define the time when
the weld nugget begins to form. Figure 9
Fig. 8 —Micrograph
of a spot weld
cross-section
ac
z
UJ
2
Q.
o
>
ui
a
~~^
x
o
oc
<
UJ
tn
ui
ac
a.
O
CROSS SECTION Or WELD
o
cc
<
UJ
tn
UJ
oc
a.
O
ECHANT: PICRIC ACID + SODIUM TRIDECYLBENZENE SULFONATE
x
o
rr
<
«*^BwVVYT* .H*ffl^?SWf|| j S%
'"• " :
UJ
CA
UJ
CC
*^mw
W E L D I N G RESEARCH SUPPLEMENT 1367-s
3000
3000
At the Center of
Weld Nugget
Tr=29°c Tw = 14b
At the Center of
Weld Nugget
Tr = 29*c,
EF=70%
2500
Tw = 14fc
P = 1600Lbs.
P=1600Lbs.
I =11.93KA
EF=90%
l = 14KA
EF= 80%
l = 11.93KA
0
0.3
0.15
Fig. 9 - Theoretical temperature
three different currents
This heat transfer m o d e l has also b e e n
used t o d e t e r m i n e t h e heating and c o o l ing rate as a f u n c t i o n of t i m e f o r any
location in the w o r k p i e c e ( A p p e n d i x B).
Figure 11 s h o w s the heating a n d cooling
rate curves s u p e r i m p o s e d w i t h t h e t e m perature-time curve corresponding to
t h e center of t h e w e l d nugget. N o t i c e
that the s u d d e n d r o p in the heating rate
Tr = 28 C
Tw=14*C
P=1600Lbs.
1=11.79KA
EF=0.75
.
\
\
Heating Rate
Fig. 10— Theoretical temperature
for different efficiencies
t i m e o f 0.21 s f o r 14.0 k A versus 0.33 s
f o r 11.93 kA, as seen in Fig. 9.
The w e l d i n g efficiency factor is an
i m p o r t a n t consideration in this m o d e l
because o f its effect o n the accuracy o f
the m o d e l ' s predictions. Figure 10 reflects
its significance. T h e use o f an incorrect
efficiency f a c t o r c o u l d either lengthen o r
s h o r t e n t h e p e r i o d f o r start o f nugget
f o r m a t i o n . T h e theoretical curves genera t e d in Fig. 10 assume a constant elect r o d e l o a d o f 1600 Ib a n d current of
11.93 k A .
At the Center of Weld Nugget
5000
/—^
\
Melting Point
6
0
'
/
-5000
/
Cooling Rate
10000
0.3
0.45
Time (Sec.)
3 6 8 - s | SEPTEMBER 1 9 8 9
0.3
0.15
0.45
0.6
0.75
TIME ( S e c . )
distributions as a function of time for
10000
2
s
1
0
0.75
(Sec.)
presents t e m p e r a t u r e versus t i m e predictions at t h e center of t h e w e l d nugget at
the faying surface. C o m p u t a t i o n of this
i n f o r m a t i o n w a s d o n e w i t h t h e assumpt i o n of a fixed e l e c t r o d e f o r c e o f 1600 Ib
a n d efficiency factor of 7 0 % .
A t l o w currents, undersize a n d brittle
nuggets are f o r m e d because o f the insufficient heat supplied t o cause t h e asperity
collapse a n d surface film b r e a k d o w n .
From t h e results o b s e r v e d in Fig. 9, it
seems that a w e l d i n g c u r r e n t o f 14.0 k A
will p r o d u c e a larger nugget than 11.93
k A , since the supply of heat f o r the high
current is larger n o t o n l y because of t h e
higher c u r r e n t , b u t also because of the
t i m e spent at melting t e m p e r a t u r e or
a b o v e t h e melting point, as d e n o t e d by
AtLow i a n d At H i g h i- C o r r e s p o n d i n g l y , t h e
t i m e t o reach t h e melting t e m p e r a t u r e
will be shorter f o r the high current than
f o r the l o w c u r r e n t . The m o d e l predicts a
Fig. 11— Theoretical
temperature
distributions and
heating and cooling
rates versus time at
the weld center
nugget
0.6
0.45
TIME
distributions as a function of time
c o r r e s p o n d s t o a constant t e m p e r a t u r e
(melting point) of the w o r k p i e c e ( w h e r e
the nugget w o u l d b e f o r m e d ) as a result
of the heat a b s o r p t i o n prior t o melting.
T h e time at w h i c h such d r o p occurs
coincides w i t h the time t o reach t h e
m e l t i n g t e m p e r a t u r e as seen in Fig. 1 1 .
Effect of Electrode Force on Nugget
Formation
In o r d e r t o examine t h e effect o f
e l e c t r o d e f o r c e o n the start o f the nugget
formation,
temperature-time
curves
w e r e calculated w i t h this m o d e l using
three different e l e c t r o d e forces —Fig. 12.
All these curves c o r r e s p o n d t o a location
at the center of the w e l d nugget and right
at the f a y i n g interface.
As the e l e c t r o d e f o r c e w a s increased,
the time t o reach the melting t e m p e r a t u r e w a s d e l a y e d because of the general
decrease in t h e resistance level. Such
r e d u c t i o n in total resistance is e x p e c t e d
because the increase in t h e applied pressure will decrease the thickness of t h e
material b e t w e e n t h e electrodes and t h e
contact area, primarily at t h e faying interface, will increase in v i e w o f t h e d e f o r m a t i o n o f t h e asperities. Recall that the
resistance is p r o p o r t i o n a l t o t h e length o f
the c o n d u c t o r and inversely p r o p o r t i o n a l
t o the cross-sectional area (R a L/A).
Since all t h e curves w e r e calculated at
the same current (11.93 k A and efficiency
value 70%), decreasing resistance results
in a decrease in the rate at w h i c h e n e r g y
is supplied t o the w e l d (P = r/l2R). Thus
the t i m e t o reach t h e t e m p e r a t u r e f o r
melting is shifted t o longer times a n d ,
2500
50
1 At the Center of
Weld Nugget
P = 1300Lbs.
Tr= 23b, Tw=14fc
EF=70%
1=1 1.93KA
P = 1600Lbs.
At the Center of
Weld Nugget
Tr » 2Sfb, Tw=14b
P = 1600,Lbs.,
EF =70%
"""* 2000
£•
1 = 11.93KA
UJ
i
rr
P = 1900Lbs.
<
a
rr
LU
0.
i
LU
w
[5 15001- MELTING POINT
I
F
1500 -MELTING
POINT
1000
f
1
\ \ <^/
INNER LAYER
/ / \ \
/
/ /
\ \ /
/ /
V \J
A
ELECTRODE-SHEET
\
/ /
""L \
INTERFACE
/ /
/
/
>v
/
/ // /
/ /
\ ./v.
/> ^
//
\
/
\S
//
s
'
/
•
<s
2 _
^
1
0.15
L
Fig. 12 — Theoretical temperature
different electrode forces
1
0.45
distributions as function of time for
It has been indicated that this thermal
model is capable of predicting the tem-
P=1600Lbs.
EF=70%
2500 -
from the center of the weld nugget.
Although the agreement is very reasonable, discrepancies were found primarily
during the cooling cycle that could be
attributed to some of the original
assumptions made in the model's formulation. The selection of a relatively large
grid size (1.0 mm) and the lack of an
efficiency factor were some of the problems thought to be responsible for such
deviations. Reduction in the mesh size
and the step time, as well as the use of a
higher efficiency factor (75%) improved
the agreement between the experimental and theoretical curves, as shown in
Figs. 15 and 16 for t w o different samples.
L-3.8 (mm)
Tr-29t;> Tw-14C
From
Weld
Nugget
Center on Faying Surface
P-1600Lbs,
... __
.
I =11.93KA
2500
WELDING
/
lj
o.
if
UJ
CENTER
L-2
"A\/
LU
L-3
<
cr
K \Z
'
/
>
^ ^
0.15
L:
'
EF=75 %
/
/
\ A- \
/ ~ ^ \ / \
> \
EF=70%
J-^s^ll
0.45
0.6
/
I- 1 mrt
/
"
v
7^-/
^
•
Experiment
^ ^ ^
500
ss"
~~
0.3
\ .
1000
500
^ s
o.
bO.2 mm
4W).0OO15 S«c,
/ / /
•
1500
LU
l/
1000
2000
L-1
fKV
MELTING POINT
0.9
3000
Tr-28fc Tw = 14fc
rr
i<
0.75
Fig. 13 - Predicted temperature distributions as a function of time at
different positions from the faying interface along the electrode axis
perature as a function of time for any
location in the workpiece. Figure 13
shows the peak temperatures reached
along the vertical axis of the electrodes
for different locations through the thickness of the sheet metal. Similar distribution of temperatures have been calculated along the faying interface at 1.0-mm
(0.04-in.) steps from the electrode axis, as
shown in Fig. 14.
A direct correlation between experimental and theoretical temperature-time
curves is presented in Figs. 15 and 16.
The thermocouple for the experimental
curve was placed along the faying interface at a distance of 53.8 mm (0.15 in.)
Correlations of Theoretical and
Experimental Results
2000
1
0.6
TIME (Sec.)
consequently,
nugget
formation is
delayed as electrode force is increased.
Lower electrode forces, therefore,
should favor nugget formation and larger
nugget size in view of the longer time and
at or above the melting temperature for
the same current, as observed in Fig. 12.
At higher forces, the nuggets would be
smaller, which could affect the ductility
and soundness of the spot weld.
1500 -
1
0.3
TIME (SecJ
UJ
FAYING SURFACE
1
j
/ \
N
500
or.
A
\
'^~-~^~~~~~~-
0.75
TIME (Sec.)
DISTANCE FROM WELDING CENTER
ON FAYING SURFACE (mm)
Fig. 14 —Predicted temperature distributions as a function of time in
the workpiece for different points along the faying interface
0.15
0.3
0.45
0.6
0.75
TIME (SecJ
Fig. 15 — Comparison of theoretical and experimental
temperature
distributions for a point on the faying interface and 3.8 mm from the
weld nugget centerline
WELDING RESEARCH SUPPLEMENT 1 369-s
3000
L-4(mm)
FROM WELDING CENTER
ON FAYING SURFACE
2500
The differences b e t w e e n the t w o curves
are m o r e noticeable d u r i n g cooling a n d
at the longer times, w i t h the e x p e r i m e n t a l
c u r v e h a v i n g a s l o w e r c o o l i n g rate — Figs.
15 and 16. This is p r o b a b l y caused b y t h e
fact that material w a s r e m o v e d t o m a k e a
n o t c h w h e r e the t h e r m o c o u p l e w a s spot
welded.
Tr=28C, Tw-KfC
P-1600Lbs,
M1.79KA
EF=75 %
• Model
Experimental
2000
T h e m o d e l w a s used t o m a p constant
t e m p e r a t u r e curves f o r t h e spot w e l d at
0.38 s into the w e l d i n g cycle, w h e n the
current w a s s t o p p e d at that instant.
These curves w e r e p l o t t e d f o r o n e o f t h e
quadrants o f the spot w e l d i n g system as
s h o w n in Fig. 17. T h e t e m p e r a t u r e distrib u t i o n allows us t o d e f i n e t h e regions
that u n d e r w e n t melting ( w e l d nugget)
a n d t h o s e that w e r e a f f e c t e d b y t h e heat
o f t h e process (HAZ). Based o n this, t h e
w e l d nugget size and H A Z w e r e estimate d , a n d these results have b e e n schematically c o m p a r e d in Fig. 18 f o r a s p o t
weld.
LU
CC
S i 500
tr
LU
0.
LU
1000
Fig. 16 — Comparison
of theoretical and
experimental
temperature
distributions for a
point on the faying
interface and 4.0
mm from the weld
nugget centerline
h
500
0.15
0.3
0.75
0.45
Conclusions
TIME (Sec.)
1) A finite d i f f e r e n c e t h e r m a l m o d e l
w a s d e v e l o p e d f o r resistance spot w e l d ing, capable o f p r e d i c t i n g the t e m p e r a ture as a f u n c t i o n o f t i m e a n d location f o r
any position in t h e w o r k p i e c e , a n d f o r
any l o w - c a r b o n sheet steel. This m o d e l
c o u l d also b e applied t o any o t h e r metal
p r o v i d e d the physical p r o p e r t i e s of g i v e n
material are included in t h e m o d e l .
-ElectrodeI
T-=700'C
T=300-C
T=600"C
T=500'C T=400"C
T=100*C
T=200'C
7 (mm)
Fig. 17-Predicted
spot weld
r
Tr=28C, Tw=14C . P=1600Lbs.. 1=11.79KA, EF=75% t=0.38 Sec.
temperature profiles around the weld nugget and heat-affected zone of the
Tr-28"C, Tw-V4C
P-1600LDS,
M1.79KA
EF=75 %
Model
Experiment
2) A c c e p t a b l e correlations b e t w e e n
t h e theoretical a n d e x p e r i m e n t a l t e m p e r atures h a v e b e e n m a d e . T h e t e m p e r a tures in the spot w e l d s w e r e m e a s u r e d
using fine t h e r m o c o u p l e s i m b e d d e d in
t h e sheet-steel c o u p o n s near t h e faying
interface.
3) I m p r o v e m e n t in t h e e x p e r i m e n t a l
techniques t o m o n i t o r the t h e r m a l cycles,
as w e l l as t h e i n t r o d u c t i o n of empirical
data in t h e m o d e l should r e d u c e t h e
deviations that exist b e t w e e n t h e p r e d i c t e d and the experimental values.
4) This m o d e l can also p r e d i c t indirectly the w e l d nugget size a n d the w i d t h o f
the H A Z . W o r k continues t o i m p r o v e the
m o d e l t o p r e d i c t the microstructures a n d
c o r r e s p o n d i n g strengths o f the H A Z .
A ckno wledgments
Distance from Weld
Fig. 18 —Schematic comparing
dimensions
3 7 0 - s | SEPTEMBER
1989
the predicted
Center
and experimental
1 (mm)
weld nugget
cross-section
The authors wish t o a c k n o w l e d g e t h e
financial s u p p o r t p r o v i d e d b y Inland Steel
C o m p a n y f o r the w o r k p e r f o r m e d at the
University o f Illinois at C h i c a g o . W e are
also grateful t o Michael Bjornson f o r the
extensive m e t a l l o g r a p h y and measurements p e r f o r m e d o n this p r o j e c t . M r .
D a n Caliher a n d M r . Neal Saboff, w h o
carried out the spot w e l d s at Inland Steel
Research Laboratories also are a c k n o w l e d g e d . This p r o j e c t c o u l d h a v e not b e e n
started w i t h o u t the t r e m e n d o u s s u p p o r t
and e n c o u r a g e m e n t f r o m the late William
Schumacher.
Appendix A
The Drop to Zero: an Explanation
The existence of a finite contact resistance is due principally to surface roughness effects. Heat transfer is therefore
due to conduction across the actual contact area and to conduction (or natural
convection) and radiation across the
gaps. The contact resistance decreases
with decreasing surface roughness. Since
a more intimate contact is brought about
instant n, at a location i, j , either for
heating or cooling, can be defined as
dT/dt|j,j,n- This can be approximated as
AT/At around the moment n, as shown
in the following expression
AT
_ Tjj.n + 5 '
At
ti,j,n + 5
TU<j,n
n+5
—
Tj,j,n - 5
ti,j,n - 5
i,j,n — 5
10 X At*
Ti in + 5 — T| i.n-5
0.0015
AT
At
AT
> 0, in t h e heating stage
< 0, in the cooling stage
At
AT = o, in the constant temperature
^
of the melting temperature
References
when melting occurs at the interface, it is
reasonable to assume that the value of
the contact resistance drops to zero. For
additional information, the reviewer
might consult Fundamentals of Heat and
Mass Transfer, by Incropera and Dewitt,
2nd Edition, p. 67.
Appendix B
Based on the computer program
developed, the time step At* = 0.00015
s and mesh size C = 0.2 mm. The derivative of temperature with time for an
1. Ford Laboratory Test Methods, Schedule
BA 13-4, September 26, 1980.
2. Fisher Body Weld Lobe
Procedure,
December 1987.
3. Dickinson, D. W., Franklin, ). E., and
Stanya, A. 1980. Characterization of spot
welding behavior by dynamic electrical parameter monitoring. Welding Journal 59(6):170-s
to 176-s.
4. Dickinson, D. W „ and Natale, J. V. 1981.
The effect of sheet surface on spot weldability. Technological Impact of Surfaces, ASM,
Metals Park, Ohio, April 14-15.
5. Spot Welding Sheet Steel, AISI Technical
Report, SG-936, 282-10RM-RI.
6. Could, J. E. 1987. An examination of
nugget development during spot welding,
using both experimental and analytical tech-
niques. Welding lournal 66(1):1-s to 10-s.
7. Goldak, )., Bibby, M., Moore, ]., House,
R., and Patel, B. 1986. Computer modeling of
heat flow in welds. Metallurgical Transactions
B, 17B(9):587.
8. Rice, W., and Funk, E. ). An analytical
investigation of the temperature distributions
during resistance welding. Welding Journal 46
(4):175-s to 186-s.
9. Krutz, C. W., and Segerlind, L. ). 1978.
Finite element analysis of welded structures.
Welding Journal 57 (7):211-s to 216-s.
10. Salcudean, M., Choi, M., and Greif, R.
1986. A study of heat transfer during arc
welding. Int. J. Heat Mass Transfer 29 (2):215.
11. Nied, H. A. 1984. The finite element
modeling of the resistance spot welding process. Welding Journal 63 (4):123-s to 132-s.
12. Metals Handbook, 8th Ed., ASM, Metals
Park, Ohio, 6:408.
13. Bhattacharya, S., and Andrews. D. R.
1972. Resistance weld quality monitoring.
Sheet Metal Industries, (7):400-466.
14. Roberts, W . L. 1951. Resistance variations during spot welding. Welding Journal
30(11):1004-1019.
15. Savage, W . F., Nippes, E. F., and Wassell, F. A. 1978. Dynamic contact resistance of
series spot welds. Welding Journal 57 (2):43-s
to 50-s.
16. Tipler, P. A. 1982. Physics, W o r t h Publishers, Inc., p. 675.
17. Ozisik, M. N. 1985. Heat
Transfer-A
Basic Approach, McGraw-Hill Book Company,
p. 746.
18. Paley, Z., and Hibbert, P. D. 1975.
Computation of temperatures in actual weld
designs. Welding Journal 54 (11):385-s to
392-s.
19. Kaiser, |. G., Dunn, G. )., and Eagar, T.
W . 1982. The effect of electrical resistance on
nugget formation during spot welding. Welding Journal 61(6): 167-s to 174-s.
WRC Bulletin 343
May 1989
Destructive Examination of PVRC Weld Specimens 202, 203 and 251J
This Bulletin contains three reports:
( 1 ) Destructive Examination of PVRC Specimen 202 Weld Flaws by JPVRC
By Y. Saiga
( 2 ) Destructive Examination of PVRC Nozzle Weld Specimen 203 Weld Flaws by JPVRC
By Y. Saiga
( 3 ) Destructive Examination of PVRC Specimen 251J Weld Flaws
By S. Yukawa
The sectioning and examination of Specimens 202 and 203 were sponsored by the Nondestructive
Examination C o m m i t t e e of the Japan Pressure Vessel Research Council. The destructive examination of
Specimen 251J was performed at the General Electric Company in Schenectady, N.Y., under the
sponsorship of the Subcommittee on Nondestructive Examination of Pressure Components of the
Pressure Vessel Research C o m m i t t e e of the Welding Research Council. The price of WRC Bulletin 343 is
$24.00 per copy, plus $5.00 for U.S., or $8.00 for overseas, postage and handling. Orders should be sent
with payment to the Welding Research Council, Room 1 3 0 1 , 345 E. 4 7 t h St., New York, NY 10017.
WELDING RESEARCH SUPPLEMENT 1371-s