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E. FilEDiAN Westinghouse Electric Corp.,
Bettis Atomic Power Laboratory, West Miff l in, Pa.
Thermomechanical Analysis i f t ie Welding Process Using t ie
Finite Element Method Analytical models are developed for
calculating temperatures, stresses and distortions resulting from
the welding process. The models are implemented in finite element
formulations and applied to a longitudinal butt weld. Nonuniform
temperature transients are shown to result in the characteristic
transverse bending distortions. Residual stresses are greatest in
the weld metal and heat-affected zones, while the ac-cumulated
plastic strain is maximum at the interface of tliese two zones on
tlie under-side of the weldment.
Introduction The welding of metal structures is aimed at
providing a means
of joining together a number of components in such a way as to
minimize the impairment of the properties of those components.
Considerable effort has been expended on developing effective
welding techniques for a large number of metals and alloys.
Con-current with these developments have been efforts aimed at
identifying the various problems that result from welding
proces-ses, determining the strength of welded joints and
structures subject to specified loading conditions, and
establishing guide-lines and criteria for most effective joint
design. The information accumulated in these areas over the years
has been overwhelming-ly experimental. Though attempts have been
made to establish empirical approaches toward understanding the
complex be-havior of materials due to welding, comparatively little
effort has been expended in developing and applying analytical
models to explain and predict the transient thermal response and
the transient and residual mechanical response. Survey papers that
deal with many of the analysis methods that do exist have been
published by the Welding Research Council on heat flow due to
welding [l]1 and welding-induced stresses and distortions [2].
Analytical treatments of temperature transients during welding
have most often been considered by assuming the effective thermal
energy supplied by the heat source to be deposited in such a narrow
band of material that it may be idealized as a point, or a line
source, depending on the geometry of the weld. The early work done
in this area was concerned with the quasi-stationary transient
temperature solution (steady-state with respect to a moving
coordinate system) resulting from a line source of heat traveling
on a straight path at a constant speed
Numbers in brackets designate References at end of paper.
Contributed by the Pressure Vessels and Piping Division and
presented at the Second National Congress on Pressure Vessels and
Piping, San Francisco, Calif., June 23-27, 1975, of THE AMERICAN
SOCIETY OF MECHANICAL EN-GINEERS. Manuscript Teeeived at ASME
Headquarters, March 28, 1975. Paper No. 75-PVP 27.
through an infinite plate. The classical line source solution,
which was determined independently by Boulton and Lance-Martjn [3]
and Rosenthal and Schmerber [4], has been used by Tallp] in the
development of a numerical model to calculate the longitudinal
stresses (stresses in the direction of the weld line) at a section
of the plate normal to the weld line. Plastic flow near the weld
line was included in the calculation, and mechanical
propertiesthough not thermal propertieswere taken to be
temperature-dependent. Masubuchi, Simmons, and Monroe [6] used
Tail's method of analysis to write a digital computer pro-gram to
calculate temperatures and stresses in welded plates.
Because of computational difficulties encountered when
at-tempting to include inelastic strains in an analysis in which
rapid temperature changes take place, little analytical work has
been carried out which goes significantly beyond Tail's
one-dimensional analysis of longitudinal stress. The complexity of
performing analytical studies of welding stresses and distortions
for various weldment configurations, when considering factors such
as tran-sient multidimensional temperature distributions, effects
of weldment fixturing and surrounding structure on heat sink and
constraint characteristics, and realistic models of inelastic
ma-terial behavior in the vicinity of the weld line, among others,
suggests the use of numerical methods of analysisin particular, the
widely adaptable finite element methodfor predicting tran-sient and
residual stresses and distortions.
Though a determination of the complete thermomechanical response
due to welding would require a full three-dimensional, inelastic
analysis of mechanical behavior, accompanied by com-putation of the
three-dimensional transient temperature dis-tribution, computer run
times would be very large and the resulting costs perhaps
prohibitive. I t is therefore reasonable at this time to first
develop, for weldments under quasi-stationary thermal conditions,
numerical techniques for planar analysis in sections normal to the
weld direction. Applications of these techniques yield valuable
data that have heretofore been un-obtainable, both in the fusion
and heat-affected zones, and in the weldment itself.
The recent paper by Hibbitt and Marcal [7] represents an initial
step in the development of numerical analysis techniques
206 / A U G U S T 1975 Transactions of the ASME Copyright 1975
by ASME
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that will simultaneously account for many welding parameters
iind factors that previously had been considered piecemeal or not a
t all. I " this work, the thermal input for the finite element
stress analysis is developed by use of a finite element transient
thermal analysis. The thermal model formulated by Hibbitt and
Marcal is designed to simulate the gas-metal arc welding process,
in which consumable electrodes are employed. The numerical thermal
analysis is required to account for such phenomena as
temperature-dependent material properties, phase change,
through-the-thickness temperature variations, irregular weldment
geometries, nonuniform distribution of energy from the heat source,
and deposition of filler metal, among others. The line source
solution [3-6] clearly cannot be used to model any of these
phenomena.
The weld thermomechanical model described in the present work
has been developed generally along the lines of Hibbitt and Marcal
[7]; i.e., the finite element method is utilized to model both the
thermal and the mechanical behavior. Emphasis, however, is placed
on applying the analysis technique to gas-timgsten arc welding,
although suitable modification of the thermal model will enable the
method to be applied to other welding processes, as well. Though
the purpose here is to develop a capability for predicting the
weld-induced transient and residual stresses and distortions, the
nature and characteristics of the thermal model by itself are
obviously of great importance, since the model can be used, for
example, to predict cooling rates, peak temperature distributions,
changes in metallurgical struc-ture, and effects of chill block
placement and other fixturing, as well as to provide input for the
mechanical model. Since strain rates induced by welding are
expected to be of the same order of magnitude as the free thermal
expansion rates and since the (hermoelastic coupling coefficient
[8] is small, thermomechanical coupling is neglected. On this
basis, descriptions of first the thermal model and then the
procedure for calculating stresses and distortions are presented.
An application of the thermo-mechanical welding analysis method is
then given for a simple butt weld.
Thermal Model Calculation of the transient temperature
distribution is based
on the attainment of quasi-stationary conditions, which are
de-veloped when the welding heat source is moving at constant speed
on a regular path (i.e., a straight line in a planar weld, or a
circle in an axisymmetric weld), and end effects resulting from
either initiation or termination of the heat source are neglected.
The temperature distribution is then stationary with respect to a
moving coordinate system whose origin coincides with the point of
application of the heat source. Consider the planar weld
illustrated in Fig. 1. The temperature at any point in the weldment
is expressed functionally as:
T(xs, x%, Xz, t) = T(xi, xi, x3 vt), (1)
where v is the welding speed. Thus, given the transient
tempera-ture distribution at any one section of the weldment
defined, say, by x3 = 0, the temperature at any other section is
determined by an appropriate shift of the time scale as
follows:
T(xu xt, x3, t) = T(xu xi, 0, t - x3/i>). (2)
The problem is, therefore, reduced to finding the
two-dimen-sional, unsteady temperature field at a section normal to
the weld line. A planar analysis may be used for this purpose when
the weld speed, relative to a characteristic diffusion rate for the
material, is sufficiently high so that the amount of heat
con-ducted ahead of the weld torch is very small relative to the
total heat input. In this case, the net heat flow across any
infmitesi-mally thin slice of the weldment normal to the weld line
is as-sumed to be negligible relative to the heat being diffused
within
the slice itself; tha t is, the term dx3
k(T) dxz
/ _ - - WELD LINE
/ f /
/ / /
DIRECTION OF / / ELECTRODE TRAVEL / / //
I I
T
-AAJSA-YAAAA^
-SECTION ANALYZED
150 mm mrf
Flf. 1 Weldment configuration
the heat conduction equation. Two-dimensional thermal analysis
at the section x3 = 0, normal to the direction of welding, is thus
treated in the present work.
Perhaps the most critical input data required for welding
thermal analysis are the parameters necessary to describe the heat
input to the weldment from the arc. Not only the magni-tude, but
the distribution of heat input will influence the dimen-sions of
the weld metal and heat-affected zones, the cooling rates, and the
peak temperature distribution, as well as the temperature gradients
necessary to calculate stresses and distortions. The welding
parameters required to formulate the heat flux boundary conditions
are the magnitude of heat input from the arc Q, the distribution of
the heat input, characterized by a length param-eter f, and the
weld speed v. Introducing the arc efficiency !j, Q is found simply
from the formula
Q = r]EI , (3)
where E and / are the arc voltage and current, respectively. The
heat deposited per linear inch of weld is merely Q/v. I t must be
recognized that an a priori determination of the magnitude and
distribution of heat input cannot, in general, be made due to the
lack of knowledge regarding energy transfer from the arc to the
workpiece. Investigations of the physics of the welding arc are
required to shed light on this area.
Following the approach of Pavelic, et al. [9], the heat from the
welding arc is, at any given time, assumed to be deposited on the
surface of the weldment as a radially symmetric normal
distribu-tion function. Letting r be the distance from the center
of the heat source, which is coincident with the axis of the
electrode, the heat flux q is given by:
q(r) = qoC -Cr2 (4)
where q0 and C are constants determined by the magnitude and
distribution of the heat input. The heat input parameters Q and f
are defined by:
is neglected in
Q '2w I q(r) r dr */ o
q(f) = 0.05 g0.
(5)
(6)
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Equation (4) then becomes
9 ( r ) = ^
-
jV-1 increments. Consider yielding to be governed by the Mises
criterion and plastic flow by the Prandtl-Reuss law. Then, as for
example derived by Hill [14], the increment of plastic strain may
be expressed in the form
3 < 3 . .
2er (15)
where $,/ = a,/ 1/3 ov* 8,7 is a component of deviatoric
stress,
is the generalized stress, and &ePL is an in-* = (fSSj
crement of the generalized plastic strain. A conventional power law
relation is postulated to characterize the generalized plastic
strain increment, such that
AePL(l) = maximum {(a(t)/KY -^PL(t - At); 0)] , (16)
where K and n are material parameters obtained from the
uni-axial stress-strain curve and, in general, are
temperature-depend-ent. Defining the yield strength cr, as the
stress level at which the plastic strain in a uniaxial, isothermal
test is 0.2 percent, K is evaluated by
K(T) =
-
Solid lines are representative of known data, while dashed lines
depict assumed high temperature properties. The density of Alloy
600 is 8430 kg/m 3 and its melting range is 1630 K - 1690 K [16].
The latent heat of nickel, which is 309 kj /kg, is used for phase
change calculations.
The thermal properties are extrapolated linearly to the melting
temperature. The adequacy of this assumption is of course open to
question, and only the experimental determination of the required
high temperature data can serve to test its validity. The
characterization of heat transfer in the weld puddle itself is an
even more formidable problem. Until more is known about the
mechanisms of heat flow in the puddle, only estimates of the molten
metal thermal characteristics can be made by specifi-cation of
appropriate values of conductivity and specific heat to be used in
the finite element analysis. The heat capacity of the molten metal
is assumed to be equal to its value at the melting point. The
thermal conductivity, on the other hand, has been taken to be half
that of the solid material at the solidus tempera-ture. This is
based on the expected behavior of molten metal that is not in
motion. The motion of the weld puddle, however, results in
temperatures that do not greatly exceed the melting temperature.
The relatively low puddle conductivity used ap-pears to have caused
excessive temperatures to be computed, as will be seen in the next
section. The effective conductivity above the melting point should
realistically be somewhat greater than that of the solid material,
in order to simulate the heat transfer mechanisms in the puddle,
and thus to lower the molten weld metal temperatures to more
realistic levels.
Since the strength and elastic modulus are negligible at the
melting point, both these properties are assumed to decrease
linearly from their respective values at the highest temperatures
at which data are available, to extremely low values at 1630 K, The
strain hardening characteristics of the material, character-ized by
the parameter n, are not known at very high tempera-tures. A value
of n 11, however, yields an analytical stress-strain relationship
in good agreement with test data at 590 K, and is used to
characterize hardening at all temperatures. Though the uniaxial
stiffness becomes negligible as the melting range is approached,
the material is relatively incompressible in the molten state. In
order to model this behavior and, at the same time, to avoid
possible ill-behavior of the solution process and thus facilitate
convergence, the elastic modulus approaches zero and the Poisson's
ratio one-half, in such a way that the bulk modulus is maintained
at its room temperature value through the entire high temperature
range, including the phase transition and the liquid state. Since
compressibility has no effect on the generalized plastic strain, no
plastic strain is, as expected, ac-cumulated in the weld
puddle.
Analysis of a Butt Weld Consider a 2.54-mm thick flat weldment
whose configuration
is shown in Fig. 1. Since the temperature distribution is
sym-metric about the weld line xi = 0, only half the weldment need
be modelled. The plane section normal to the direction of travel of
the electrode is assumed to be in a state of plane strain. Thus
motion is completely restrained in the weld, or longitudinal,
direction. To illustrate transverse bending distortions that are
characteristic of thin weldments of this type, the weldment is
completely free to expand and bend in the transverse direction.
Though the plane strain approach prevents characterization of
the longitudinal bow mode of distortion also common to these types
of welds, the method nevertheless enables one to determine complete
residual stress distributions, transverse distortions, and
estimates of damage accumulated as a result of the welding process.
I t should be noted, however, tha t longitudinal extension and
bowing could be considered without resorting to a three-dimensional
analysis by introducing up to three additional degrees of freedom
to the system. This approach, called generalized plane strain, and
used by Marcal in his analysis of curved pipe
bends [17], consists of relaxing the plane strain requirement by
letting the longitudinal strain be a linear function of these added
degrees of freedom, which represent longitudinal extension, and
rotation about the xt and x2 axes of Fig. 1. For the present,
however, the constraints associated with plane strain are main,
tained.
The welding parameters chosen for this analysis are as follows:
heat input Q = 703 W, characteristic radius of heat flux distribn.
tion f = 5.08 mm, weld speed v = 2.12 mm/s. An accurate
determination of both the magnitude and distribution of heat input
from the welding arc is predicated upon knowledge of the heat
transfer mechanisms from the arc to the workpiece. These values,
however, were selected to illustrate the thermomechanical response
of a full-penetration weld with a weld metal cross-section that
varies in width through the weldment thickness.
The transient thermal analysis was performed using the finite
element mesh shown in Fig. 3(a). A total of 47 time steps was used
in the analysis from the time the section being analyzed (x3 = 0)
is initially subject to heating from the welding arc, to complete
cool-down. Temperature transients are plotted in Fig. 4, while the
resulting weld metal zone, which is by definition that portion of
the weldment in which the peak temperatures exceed the liquidus
temperature, is depicted in Fig. 5. Tliese two figures demonstrate
the variation through the thickness of the thermal response,
resulting from the thermal energy from the welding arc being
distributed over a finite portion of the
^ ^ H E A T FLUX ^ ^ - ^ X ^ ^ ,
(a)
y i i i i r i ~i ~i
(b)
Fig. 3 Finite element mesh: (a) Temperature analysis; (fa)
Stress and distortion analysis
\ I ^ TOP SURFACE OF WELD J 1 __ BOTTOM SURFACE OF WELD
-0.1 0 0.1 0.2 0.3 0.4 0.5 TIME-MIN
f i g . 4 Temperature histories at various distances from the we
IP certterlins
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WELD
WELD
Fig, 5 Weld metal zone
-ORIGINAL GEOMETRY
^-DISTORTED GEOMETRY
F ig . 6 T r a n s v e r s e d i s t o r t i o n of w e i d m e
n t
heated surface of the weldment (as opposed to a line source of
heat, which yields no thickness variations whatsoever, employed in
previous investigations [3-6]). This localized temperature
non-uniformity yields a variation of shrinkage through the
thickness during cool-down, thus causing the characteristic bending
dis-tortions, which are accompanied by a nonuniform accumulation of
plastic strain in the weld metal and heat-affected zones.
In the weld puddle, calculated peak temperatures are
con-siderably higher than the melting temperature (Fig. 4). As
pointed out in the previous section, these apparently excessive
temperatures arise from the relatively low value of molten metal
conductivity used in the analysis. The cooling curves for weld
metal material passing through the liquid-solid phase transition
range are characteristic of solidifying alloys, in that the latent
heat liberated as a result of the phase transformation results in a
momentary cooling rate decrease during the freezing period.
The incremental elastoplastic stress and distortion analysis was
carried out using the finite element mesh shown in Fig. 3(6). A
total of 24 loading increments was used for the entire weld cycle,
from initial heatup to final cooldown. Proper modelling of the
bending distortion mode in the region in close proximity to the
weld centerline requires a relatively fine grid both in the
thickness and transverse directions. The final (residual)
dis-torted shape of the weldment cross-section, evaluated when
cool-down is complete and the temperature is uniform at its room
temperature value, is shown in Fig. 6. The maximum deflection (at
the weld centerline) is 0.066 mm.
The unconstrained motion of the weldment in the plane normal to
the weld line produces transient and residual stress patterns that
are dominated by the longitudinal stress. Longitudinal stress
distributions at a number of points in time, including the residual
stress distribution at final cool-down, are plotted in Fig. 7.
Stress histories at various locations are plotted in Fig. 8. I t is
of interest to note some of the characteristics of the transient
stress distribution.
Upon initial heatup (prior to the time at which the center of
the electrode passes over the section x3 0, being analyzed), the
localization of severe temperature gradients in the immediate
vicinity of the weld line produces compressive yielding in this
O 10 20 30 40
DISTANCE FROM WELD LINE-mm
F ig . 7 T r a n s i e n t a n d r e s i d u a l l o n g i t u d
i n a l s t ress d i s t r i b u t i o n s
region. As more energy is being supplied by the arc and
tem-peratures increase, the yield strength quickly decreases until,
at the melting point, it is negligible. During the time period
prior to solidification of the weld metal, all material outside the
puddle is in compression with that region immediately adjacent to t
h e molten zone in a plastic state of stress. Since temperatures in
this region are extremely nonuniform, the yield stresses vary from
zero at the melting point to about 260 MN/m 1 , which is only
slightly lower than the room temperature yield strength (291 MN/m 2
) . Plastic deformation in molten material has been completely
relieved.
Upon solidification, the fusion zone material yields initially
in compression at rather low stress levels. Upon further cooling,
yield strength is increased and unloading from the yield surface
proceeds elastically until the material yields in tension. In the
weld metal and heat-affected zones, unloading and reversed yielding
occur over a very narrow stress range. Hence, as cool-down
proceeds, tha t portion of the weldment that is in tension
longitudinally grows steadily until, at final cool-down, the
residual longitudinal stresses, which are appreciable only in the
region within about 50 mm of the weld centerline, are completely
tensile. This is due to the plane strain restrictions placed on the
analysis. Though relaxation of this constraint would yield residual
stresses in compression outside this region, it is important to
note that the tensile stresses in the highly stressed region of
interest (within about 25 mm of the centerline) are governed
primarily by plastic behavior and should change little.
The residual stress distribution is such that there is little
variation of stress through the thickness. The residual stresses
are essentially uniform at 390 M N / m 2 in the weld metal and
heat-affected zones and then decrease uniformly to the room
tempera-ture yield strength at a location 23 mm from the weld
centerline. In the elastic region beyond this location, the
stresses drop off quite rapidly. The residual stresses in the
plastic region exceed the room temperature yield strength because
of material strain hardening, which is such that the initial
short-time compressive yielding produces an expansion of the yield
surface followed, during cool-down, by yielding in tension at a
stress level higher than the mono tonic yield strength. This type
of behavior is consistent with the residual stresses measured for
bead-on-plate welds by Nagaraja Rao and Tall [18]. I t was noted in
this study that residual stresses in (or in the close vicinity of)
the weld metal zone are usually about 50 percent above the yield
strength of the base metal. The results presented here, therefore,
appear to be in good qualitative agreement with these test
data.
Plastic deformations are confined to a localized region as
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300
ZOO
100
0
100
200
-
-
-
STRESSES AT MfOSURFACE
SOLIDIFICATION, / i f MELTfNG^ \ /Jf
.,-0 25-, \ X/jr
\\ \ 1 f\ / "i"3 72 \
\ \ \ / / V / *,-U.43v /
v ~ r ~~ i
> ' ' ' ^ H ^ ^ ^ i i U U
/ / / - "
. y.1-31.75 /
\ _ _ ^ / , , , , , , , i , , , |
Fig. 8 Longitudinal stress histories at various distances from
the weld center!?!?
0 5 IO 15 20 25 DISTANCE FROM WELD L I N E - m m
Fig. 8 Transient and residua! generalized plastic strain
distributions
illustrated by Fig. 9, in which transient and residual
generalized plastic strain distributions are plotted. Consistent
with the plastic zone associated with the residual stress
distribution, plastic strains greater than 0.2 percent are
generated within 23 mm of the weld centerline. The highest plastic
strain levels exist in the weld metal and heat-affected zones
throughout the entire welding cycle, with the exception of that
time period in which the weld metal is molten and the plastic
strain nonexistent. Beyond the heat-affected zone the plastic
strain decreases quite rapidly. The plots of plastic strain against
time at various loca-tions in Fig. 10 illustrate the manner in
which plastic deforma-tion is accumulated in the weld. In the weld
metal zone, plastic strain is accumulated rapidly as the material
yields in compres-sion. At the melting point, the plastic strain,
which has reached a level of 2.3 percent, is completely relieved.
Upon solidification, the plastic strain very rapidly reaches a
level in close proximity to that existing just prior to melting. As
cooling continues and yielding in tension progresses, the plastic
strain steadily in-creases to its final value of 4.3 percent. In
the heat-affected zone, plastic strain is accumulated during
heat-up in much the same way as in the weld metal zone, but not
quite as rapidly. At the very high temperature levels just below
the solidus, the accumu-lated plastic strain is partially relieved.
As the material cools, it yields in tension and further plastic
strain is accumulated. In regions removed from the weld metal and
heat-affected zones, there is no relief of plastic strain and
elastic withdrawal from a plastic state of compressive stress is
characterized by no accumu-lation of plastic strain until yielding
in tension commences.
The generalized plastic strain, which characterizes permanent
deformation, may be used as an indicator of cumulative "dam-age" in
the weld metal and heat-affected zones during the welding process.
Contours of the accumulated generalized plastic strain at final
cool-down are plotted in Fig. 11 and, superposed with
curves defining the farthest extent of the liquidus and solidus
isotherms (recall that the former defines the weld metal zone),
indicate that there is considerable variation of plastic strain
through the thickness of the weld in the fusion and heat-affected
zones. The maximum residual plastic strain exists on the under-side
of the weldment at the weld metal/heat-affected zone inter-face and
reaches a level of 4.5 percent. Maximum damage can thus be expected
to occur in this vicinity. This agrees qualita-tively with
conclusions based on plastic strain distributions cal-culated by
Hibbitt and Marcal [7],
Conclusions
A thermomechanical model of the welding process has been
developed using the finite element method of analysis. The finite
element approach has been shown to be a powerful tool both for
determining the welding thermal cycle and for evaluating the
stresses and distortions generated as a result of the tempera-ture
transients. The analysis procedures are applicable to planar or
axisymmetric welds under quasistationary conditions.
The method used for determining temperatures is featured by a
direct iteration procedure to accurately account for the latent
heat liberated during solidification of the weld. The finite
ele-ment calculations enable, in particular, the effects of the
heat input distribution on the heat flow patterns through the
thick-ness of the weldment to be determined. The short-time thermal
response, which yields the dimensions of the fusion and
heat-affected zones, thus greatly affects the resulting nonuniform
shrinkage in these zones.
The mechanical response is calculated by implementing the
equations of time-independent incremental plasticity with
tem-perature-dependent material properties. The transient
longi-tudinal stress history of compressive loading followed by
load reversal and a tensile residual stress state is produced. Peak
residual stresses 30 percent in excess of the room temperature
yield strength are predicted both in the fusion zone and in the
heat-affected zone. A significant portion of the weldment outside
these zones is in a plastic state of stress as well. Nonuniform
shrinkage in the vicinity of the weld centerline produces the
transverse bending distortions typical of these types of welds.
The plastic strains, or permanent deformations, accumulated
during welding are maximum at the interface of the weld metal and
heat-affected zones on the underside of the weldment. With plastic
strain as an indicator of "damage" generated during welding, the
analytical prediction that maximum damage occurs in this region is
consistent with expected damage in full-penetra-tion welds. Thus,
in addition to predicting residual stresses and distortions due to
welding, the analytical technique can poten-tially be used for
damage assessments as well.
Though experimental studies of weld temperatures, residual
stresses and distortions have been made, none appears to de-scribe
the weld process and the material properties in sutficient detail
to adequately define the finite element thermal and me-
212 / A U G U S T 1975 Transactions of the ASME
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~
1 1 ' 1 PLASTIC STRAINS AT MIDSURFACE
MELTING.
,=0 25-v / /
J/y
SOLIDIFICATION-v /
^ - - . , - 2 79
^ , = 2 ? 9 mm
. , 3 ! 75-,
_ _ ^ ^ H
Fig. U Generalized plastic strain histories at various distances
from th wId e tnMf -Htte
FARTHEST EXTENT OF UOUIDUS (I), SOUDUS 12) CONTOURS
043 .042 .Q4* 04g \ \ 043 .041 .038 .036 .034 .032 .030
Fig. U Contours of residual generaiized plastic strain
chanical models. I t is clear that further assessments of both
models can be made only when numerical results are correlated with
experimental data generated from test welds designed specifically
for this purpose. Nevertheless, the potential of utilizing finite
element, methods of analysis for determining the effects of the
welding parameters, weldment geometry, material properties, heat
sink and constraint conditions, etc. on the thermomechanical
response, is evident.
Development of the weld thermomechanical model has also served
to identify other areas of work that would yield a more thorough
understanding of the welding process, in addition to providing more
reliable input data to the finite element analyses. Among these are
determinations of material properties at very high temperatures,
studies of heat transfer mechanisms in the weld puddle, and
investigations of the physics of the welding arc to determine the
means by which thermal energy is trans-ferred from the arc to the
workpiece.
Acknowledgment The author acknowledges the contributions of Dr.
C. M.
Friedrich in the development of the incremental plasticity
formulations employed for stress and distortion analysis.
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