Resistance Spot Welding: [607003]

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 resis­
tance spot welding has been conducted
both theoretically and experimentally. A
numerical solution based on a finite dif­
ference formulation of the heat equation
has been developed to predict tempera­
ture distributions as a function of both
time and position during the welding
process. The computer model also pre­
dicts the temperature distribution
through the copper electrodes. One
important feature of the program is that it
allows for variations in the physical prop­
erties 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 heat-
affected zone (HAZ) obtained by plotting
the lines of constant temperature is very
similar to that measured from actual
welds.
Introduction
Resistance spot welding is character­
ized as a rapid and clean process for
joining sheet steel. Despite its long and
wide commercial application, an ade-
KEY WORDS
Resistance Spot Weld
Spot Welding
HSLA Steels
Heat Transfer Model
Temperature Spread
Copper Electrodes
Nugget Size
Heat Conduction
Heat of Fusion
Computer Model
Z. HAN, J. OROZCO and). E. INDACOCHEA
are with the University of Illinois at Chicago,
Chicago, III. C. H. CHEN is with inland Steel
Laboratories, East Chicago, Ind. quate weld nugget size is still the primary
concern for spot welding qualification
procedures (Refs. 1, 2). Weld nugget
sizes have been estimated conventional­
ly, 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 pro­
cess are either too basic (one-dimension­
al) or do not include some of the funda­
mental variables. For instance, the varia­
tion 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 elec­
trodes. This heat transfer model takes
into account the following considera­
tions: conduction in the solid, convection,
heat of fusion due to solid-liquid phase
change, element heat content as a func­
tion 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 two sheet pieces meet. Con­
sequently, a cylindrical coordinate system
was selected (Fig. 1) with radial as well as
vertical variations in temperature and the
assumption of azimuthai symmetry in </>.
The basic equations and the correspond­ing boundary conditions are expressed in
finite difference forms. The solution to
the equations includes an explicit formu­
lation 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 resis­
tance spot welds were processed at the
Inland Steel Research Laboratories, while
the simulated weld HAZ's were pro­
duced at the University of Illinois at Chi­
cago Welding and joining Laboratories.
The temperature computations were
performed for different power levels,
several welding efficiencies, various elec­
trode forces and corresponding material
contact resistances. The model also
accounts for the temperature depen­
dence 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 vol­
ume 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

ST/6<t>=0 •
-KdT/Sr^d-T,,,),
-KST/Sz-huCT-T^)^
6T/6r=0 . 6T/<5z=0
6T/6*=0
K6T/6r=h„(T-Tj
6T/6z=0
Fig. 1 —Schematic describing thermal boundary conditions Fig. 2 – Schematic of the resistance spot welding process
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 elec­
trodes 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 elec­
trodes can conduct high currents to the
workpiece without significant )oule heat­
ing 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. 3 —Simplification of the resistance across
the electrodes
364-s | SEPTEMBER 1989 large current flow is needed to produce a
high-Joule heating effect in the work-
piece. 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 work-
piece, 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 elec­
trodes 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 elec­
trodes 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 condi­
tion 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 resis­
tances. However, this value drops to
zero (Appendix A) as the weld nugget is
formed.
Model Assumptions
In modeling the resistance spot weld­
ing process, several boundary conditions
and physical phenomena must be consid­
ered. In simplifying this thermal model,
the following assumptions are made: 1) A cylindrical coordinate system was
selected as illustrated in Fig. 1. The por­
tions of the coupon affected by the heat
and the immediate-adjacent areas of the
unaffected base metal have been repre­
sented by a disk of radius o> (w = 25 mm),
because of the temperature symmetry.
This selection reduces the geometrical
dependency to two dimensions, hence
T = T(r,z,4>) (1)
2) The temperature of the inner sur­
face of the electrodes is that of the
cooling water, Tw.
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 symme­
try 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 resis­
tivity (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 = K0[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,
Cp = CPo [1+ 0.000688(T – 20)] (3)
and
CPo = 4.65 X 108 erg/g • °C
(ii) 520°C < T < 770°C,
and CP CPo T"' (4)
CPo = 8.55 X 103 erg/f
(iii) 770°C < T < 850°C,
Cp = Cpo(T – 850)4 + 7.118 X 108 (5)
and
CPo = 13.716 erg/g • °C
(iv) T > 850°C
Cp = 6.25 X 108 erg/g • "C (6)
The equation developed for the resistivi­
ty is:
P = Po[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 equa­
tion that was derived from the informa­
tion provided by Fig. 4D for the low-
carbon steel is:
p' = p'0 (1 – 0.0004754 P) (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 resis­
tances, 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, Too-
Mathematical Model
Governing Differential Equation and
Conditions
The three-dimensional heat conduc­
tion equation is written in cylindrical coor­
dinates at an inner node as follows
p"Cp dT/dt = (1/rp/3r(rK<9T/dr)] +
(K/r2)(d2T/d<p2) + K(32T/dz2)+ g (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 sym­
metrical 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 400 800 1200
Temperature (*C) 2 6 10 14
Temperature'C (xlOO)
5000
3000
E 2000
1000
500
Temperature (*C)
100
10 15 20
Electrode Force. Lbs. (xlOO)
Fig. 4 — Physical properties of low-carbon steels of conductivity, specific heat, bulk resistivity and
contact resistance as a function of temperature and electrode force (Refs. 14, 16-19)
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
-KdT/dr = 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 elec­
trode are
—KdT/dr = hoo(T — Too) along the out­
er surface of the electrode (17)
—KdT/3r = hw(T — Tw) 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
dr2
^1 dz2 i,),n = (TT + '/2,J-TT-./2,J)/£ (19)
i,j,n = (TV + i,j + TV _ ,,j – 2TV,j)/S2
(20)
. =(TV,j + 1 + TV,j-l-2TT,j)/52
i,J,n
(21)
The derivative of temperature for a node
i, j with respect to time is written as
3T
3t i,J,n = 0"ni+j1- TV,,)/At (22)
where i, j and n are integers.
Equation 10 and Equations 19 through
22 are now substituted into Equation 9 to
yield
1\ TT + 1,j + TT_1,j+ 1
22Ln, + 1 + TV,-1-4TV,J
+ 8Vj = -1|-T"iV-TT,j-|
K a|_ At Z
a
o
X
o tr <
tn
z UJ
s a. O _i
u > UJ
a x o cc < UJ
tn
UJ
S a. o
5 a ~-> x o tr < UJ
tn UJ
CC
z UJ
s a O —i
ui > UJ
a o
cc < ui
V)
UJ
oc
Hi
a O -1
UJ
>
X
o oc < UJ
tn ui cc
(23)
WELDING RESEARCH SUPPLEMENT 1365-s

•OJ-1
'0.1
'QK Aw.
A^
•V TM,H IM.
I! T
Tu-1 ti
i.i-1/2
ILJ
TM. r
Fig. 5-Rectangular T0l
nef mes/i of s/ze 7
ana7 a node (ij) n
/ns/rJe f/ie matrix <" -> ->
\ Tr-1.0 TM.
??.i{ 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 I"'
value at any node i,j and moment n + 1
as follows >0 for 0 < i < 4, 0 < j < 2
= 0 everywhere else (25)
for node i, j located on outer surface, we
At h0
Tn. + ) _ 1 i i KAt
t P"CPC2"
Ti/T+1 + Ttf-nl TV + , i + TV – . i + qV, = ^(TT,j-Too) P CpV
g?,i = o (26)
At
+— g?,i + I P Cp [4KAt 1 n and finally, for node i, j located on the
inner surface of the electrodes, we
have
(24) At K
where qV,, is related to convective pro­
cess. If node i, j is located within the
system or on adiabatic boundaries, then qv.) =
gV.i = 0 (27)
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 JL -f^^?
I 1.5'-
WELDING FIXTURE U5
Electrode approaches zero (1/r) (3T/3r) would be
undefined. To deal with this situation, we
have that for r = 0
lim [(1/r)(3T/dr)] = d2T/dr2
r^O (28)
then the heat-conduction Equation 9 at
the location r = 0 takes the form
2d2T/<3r2 + 32T/3z2 + (1/K)g = (29)
(1/a)3T/at
similar formulations are also developed
for points along the boundaries. Howev­
er, for simplicity their development is
omitted.
Numerical Method
The governing differential equation
was written in finite difference form and
solved using an explicit method. The
explicit method is relatively straightfor­
ward but requires a large amount of
computing time because of the stringent
stability condition which is expressed as
At < (p"Cp/2Ar)2/[1 + (Ar)2/(rAt)2]. In
this study, the minimum time step used is
0.00015 s.
Experimental Procedures
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 two specimens into a special
welding fixture —Fig. 6. The fixture at­
taches to the lower copper electrode.
The spot welding was done on a
Sciaky press-type 100-kVA single-phase
resistance welding machine. The elec­
trode 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 Manu­
facturers' Association (RWMA) standard.
The electrode tips have a contact diame­
ter 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 dur­
ing resistance welding were measured by
spot welding a 0.254-mm (0.010-in.) ther­
mocouple (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 metallograph­
ic analysis on several preliminary spot
welds. The welds were sectioned
through the nugget normal to the plane
366-s I SEPTEMBER 1989

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 charac­
terized with a Leco 300 metallograph.
The nugget size, as well as HAZ measure­
ments, were made from the resulting
micrographs and Fig. 8 shows one of
several photo composites that were
assembled for the metallographic analy­
ses. The HAZ was observed to be the
widest at the faying interface. The ther­
mocouples were placed very close to this
faying surface, and its exact location was
later determined by metallographic eval­
uation after welding. The thermal mea­
surements were collected using a Hew­
lett-Packard Series 3000 personal com­
puter with a 3852 data acquisition unit
and a Xerox 6060 personal computer
interphased with a metrobyte data acqui­
sition 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 cool­
ing 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. it
5?
^E 30172"
L-0.346' to 0.365"
W= 0.032" to 0.045" Fig. 7 —Sheet steel
coupons for the
spot welds
Table 1-
C
0.06 -Composition of the HSLA-Sheet Steel wt-%
Mn Si Nb Ti Al
0.96 0.03 0.10 0.002 0.060 N
0.006 s
0.012 P
0.009
Effect of Current Level on Nugget Formation
Automotive companies' spot weld
qualification procedures (Refs. 1, 2) spec­
ify measuring the size of the weld nugget
in terms of one or more welding vari­
ables, depending on the specification
applied. The correlations of nugget size
with current or with current and time are
some of the most popular for qualifica­
tion procedures. The importance of the
current's influence on the soundness of
the weld nugget has led to the develop­ment of welding lobes to define the
current and time ranges where optimum
spot welds can consistently be produced.
However, this reproducibility is ham­
pered by inconsistencies in metal compo­
sition, 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. Conse­
quently, it can also define the time when
the weld nugget begins to form. Figure 9 I-
Z UJ
E Q.
o _l
UJ
>
o oc < UJ
tn ut
ac
*>.
o. o
X
o cc <
Ul
tn
UJ
ac
z
UJ
2
Q.
o > ui
a ~~^ x o oc
< UJ
tn
ui
ac
CROSS SECTION Or WELD
ECHANT: PICRIC ACID + SODIUM TRIDECYLBENZENE SULFONATE
«*^BwVVYT* .H*ffl^?SWf||jS% Fig. 8 —Micrograph
of a spot weld
cross-section
'"• ": *^mw a. O
o cc < UJ
tn UJ
oc
a. O
x o
rr
< UJ
CA
UJ
CC
WELDING RESEARCH SUPPLEMENT 1367-s

3000
2500 At the Center of
Weld Nugget Tr=29°c Tw = 14b
P=1600Lbs.
EF=70%
l = 14KA
l= 11.93KA 3000 At the Center of
Weld Nugget
0 0.15 0.3 0.45 0.6 0.75
TIME (Sec.)
Fig. 9 – Theoretical temperature distributions as a function of time for
three different currents Tr = 29*c, Tw = 14fc
P= 1600Lbs.
I =11.93KA
EF=90%
EF= 80%
0 0.15 0.3 0.45 0.6 0.75
TIME (Sec.)
Fig. 10— Theoretical temperature distributions as a function of time
for different efficiencies
presents temperature versus time predic­
tions at the center of the weld nugget at
the faying surface. Computation of this
information was done with the assump­
tion of a fixed electrode force of 1600 Ib
and efficiency factor of 70%.
At low currents, undersize and brittle
nuggets are formed because of the insuf­
ficient heat supplied to cause the asperity
collapse and surface film breakdown.
From the results observed in Fig. 9, it
seems that a welding current of 14.0 kA
will produce a larger nugget than 11.93
kA, since the supply of heat for the high
current is larger not only because of the
higher current, but also because of the
time spent at melting temperature or
above the melting point, as denoted by
AtLow i and AtHigh i- Correspondingly, the
time to reach the melting temperature
will be shorter for the high current than
for the low current. The model predicts a
Fig. 11— Theoretical
temperature
distributions and
heating and cooling
rates versus time at 2
the weld center s
nugget 1
6 time of 0.21 s for 14.0 kA versus 0.33 s
for 11.93 kA, as seen in Fig. 9.
The welding efficiency factor is an
important consideration in this model
because of its effect on the accuracy of
the model's predictions. Figure 10 reflects
its significance. The use of an incorrect
efficiency factor could either lengthen or
shorten the period for start of nugget
formation. The theoretical curves gener­
ated in Fig. 10 assume a constant elec­
trode load of 1600 Ib and current of
11.93 kA.
This heat transfer model has also been
used to determine the heating and cool­
ing rate as a function of time for any
location in the workpiece (Appendix B).
Figure 11 shows the heating and cooling
rate curves superimposed with the tem­
perature-time curve corresponding to
the center of the weld nugget. Notice
that the sudden drop in the heating rate
10000
5000
0
-5000
10000 At the Center of Weld Nugget
Heating Rate /—^
/ ' Tr = 28 C
Tw=14*C
. P=1600Lbs.
\ 1=11.79KA
\ EF=0.75
\ Melting Point
/ Cooling Rate
0.3 0.45
Time (Sec.) corresponds to a constant temperature
(melting point) of the workpiece (where
the nugget would be formed) as a result
of the heat absorption prior to melting.
The time at which such drop occurs
coincides with the time to reach the
melting temperature as seen in Fig. 11.
Effect of Electrode Force on Nugget
Formation
In order to examine the effect of
electrode force on the start of the nugget
formation, temperature-time curves
were calculated with this model using
three different electrode forces —Fig. 12.
All these curves correspond to a location
at the center of the weld nugget and right
at the faying interface.
As the electrode force was increased,
the time to reach the melting tempera­
ture was delayed because of the general
decrease in the resistance level. Such
reduction in total resistance is expected
because the increase in the applied pres­
sure will decrease the thickness of the
material between the electrodes and the
contact area, primarily at the faying inter­
face, will increase in view of the defor­
mation of the asperities. Recall that the
resistance is proportional to the length of
the conductor and inversely proportional
to the cross-sectional area (R a L/A).
Since all the curves were calculated at
the same current (11.93 kA and efficiency
value 70%), decreasing resistance results
in a decrease in the rate at which energy
is supplied to the weld (P = r/l2R). Thus
the time to reach the temperature for
melting is shifted to longer times and,
368-s | SEPTEMBER 1989

501 At the Center of
Weld Nugget
P = 1300Lbs.
P = 1600Lbs.
P = 1900Lbs.
a w
[5 15001- MELTING POINT
I Tr= 23b, Tw=14fc
EF=70%
1=1 1.93KA
TIME (SecJ
Fig. 12 — Theoretical temperature distributions as function of time for
different electrode forces """* £•
UJ
rr
< rr LU
0.
i
LU
F 2500
2000
1500
1000
500 At the Center of
Weld Nugget
i
1
-MELTING POINT f j
1 /
/ / / / / / / / / /
/ / / / / /
/ /
// // s '/ •
<s ^
2_ 1 L Tr » 2Sfb, Tw=14b
P = 1600,Lbs.,
EF =70%
1 = 11.93KA
A
\ FAYING SURFACE
\\/ \ <^ INNER LAYER
\ \ / \ \ / \ \J V A ELECTRODE-SHEET
""L \ INTERFACE
>v N /
\./> /v. ^
\ / \S
1 1 1
0.15 0.75 0.9 0.3 0.45 0.6
TIME (Sec.)
Fig. 13 – Predicted temperature distributions as a function of time at
different positions from the faying interface along the electrode axis
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.
Correlations of Theoretical and
Experimental Results
It has been indicated that this thermal
model is capable of predicting the tem­perature 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 thick­
ness of the sheet metal. Similar distribu­
tion of temperatures have been calculat­
ed 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 experi­
mental and theoretical temperature-time
curves is presented in Figs. 15 and 16.
The thermocouple for the experimental
curve was placed along the faying inter­
face at a distance of 53.8 mm (0.15 in.) from the center of the weld nugget.
Although the agreement is very reason­
able, discrepancies were found primarily
during the cooling cycle that could be
attributed to some of the original
assumptions made in the model's formu­
lation. The selection of a relatively large
grid size (1.0 mm) and the lack of an
efficiency factor were some of the prob­
lems 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 experimen­
tal and theoretical curves, as shown in
Figs. 15 and 16 for two different samples.
rr
i-< or.
UJ
o.
UJ 2500
2000
1500
1000
500 –
– MELTING POINT lj
if l/
' ///
• />'/
^s ^^ Tr-28fc Tw = 14fc
P=1600Lbs.
EF=70%
WELDING CENTER
/ L-1
fKV L-2
"A\/ L-3
K \Z
/ \ A- \
/~^\ /\ >\
J-^s^ll ~~ 3000
0.15 0.6 0.75 0.3 0.45
TIME (Sec.)
L: 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 LU
< cr LU
o. 2500
2000
1500
1000
500 L-3.8 (mm) Tr-29t;> Tw-14C
From Weld Nugget P-1600Lbs,
Center on Faying Surface … __ .
I =11.93KA
EF=75 %
bO.2 mm
4W).0OO15 S«c, \.
EF=70% //"v^ Experiment
I- 1 mrt 7^-/ • ^^^
ss" '^~-~^~~~~~~-
0.15 0.3 0.45
TIME (SecJ 0.6 0.75
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
2500
2000
LU
CC
Si tr LU
0.
LU 500
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 1000
500 L-4(mm)
FROM WELDING CENTER
ON FAYING SURFACE Tr=28C, Tw-KfC
P-1600Lbs,
M1.79KA
EF=75 %
• Model
Experimental
0.15 0.3 0.45
TIME (Sec.) 0.75
-Electrode-
I
T-=700'C T=600"C T=300-C T=100*C
T=500'C T=400"C T=200'C
7 (mm) r
Tr=28C, Tw=14C . P=1600Lbs.. 1=11.79KA, EF=75% t=0.38 Sec.
Fig. 17-Predicted temperature profiles around the weld nugget and heat-affected zone of the
spot weld
Tr-28"C, Tw-V4C
P-1600LDS,
M1.79KA
EF=75 % Model
Experiment
Distance from Weld Center 1 (mm)
Fig. 18 —Schematic comparing the predicted and experimental weld nugget cross-section
dimensions
370-s | SEPTEMBER 1989 The differences between the two curves
are more noticeable during cooling and
at the longer times, with the experimental
curve having a slower cooling rate — Figs.
15 and 16. This is probably caused by the
fact that material was removed to make a
notch where the thermocouple was spot
welded.
The model was used to map constant
temperature curves for the spot weld at
0.38 s into the welding cycle, when the
current was stopped at that instant.
These curves were plotted for one of the
quadrants of the spot welding system as
shown in Fig. 17. The temperature distri­
bution allows us to define the regions
that underwent melting (weld nugget)
and those that were affected by the heat
of the process (HAZ). Based on this, the
weld nugget size and HAZ were estimat­
ed, and these results have been schemat­
ically compared in Fig. 18 for a spot
weld.
Conclusions
1) A finite difference thermal model
was developed for resistance spot weld­
ing, capable of predicting the tempera­
ture as a function of time and location for
any position in the workpiece, and for
any low-carbon sheet steel. This model
could also be applied to any other metal
provided the physical properties of given
material are included in the model.
2) Acceptable correlations between
the theoretical and experimental temper­
atures have been made. The tempera­
tures in the spot welds were measured
using fine thermocouples imbedded in
the sheet-steel coupons near the faying
interface.
3) Improvement in the experimental
techniques to monitor the thermal cycles,
as well as the introduction of empirical
data in the model should reduce the
deviations that exist between the pre­
dicted and the experimental values.
4) This model can also predict indirect­
ly the weld nugget size and the width of
the HAZ. Work continues to improve the
model to predict the microstructures and
corresponding strengths of the HAZ.
A ckno wledgments
The authors wish to acknowledge the
financial support provided by Inland Steel
Company for the work performed at the
University of Illinois at Chicago. We are
also grateful to Michael Bjornson for the
extensive metallography and measure­
ments performed on this project. Mr.
Dan Caliher and Mr. Neal Saboff, who
carried out the spot welds at Inland Steel
Research Laboratories also are acknowl­
edged. This project could have not been
started without the tremendous support
and encouragement from the late William
Schumacher.

Appendix A
The Drop to Zero: an Explanation
The existence of a finite contact resis­
tance is due principally to surface rough­
ness effects. Heat transfer is therefore
due to conduction across the actual con­
tact 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
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 deriva­
tive of temperature with time for an 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
At _ Tjj.n + 5 ' Tj,j,n – 5
ti,j,n + 5 — ti,j,n – 5
TU<n j,n + 5 i,j,n — 5
10 X At*
Ti in + 5 — T| i.n-5
AT
At
AT
At 0.0015
> 0, in the heating stage
< 0, in the cooling stage
AT = o, in the constant temperature
^ of the melting temperature
References
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 param­
eter 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 weldabili­
ty. 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 tech­niques. 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 pro­
cess. 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 varia­
tions during spot welding. Welding Journal
30(11):1004-1019.
15. Savage, W. F., Nippes, E. F., and Was-
sell, 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, Worth Pub­
lishers, 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. Weld­
ing 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 Committee 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 Committee 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 1301, 345 E. 47th St., New York, NY 10017.
WELDING RESEARCH SUPPLEMENT 1371-s