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Materials Science and Engineering A246 (1998) 4554
Numerical analysis of GTA welding process with emphasis onpost-solidification phase transformation effects on residual stresses1
B. Taljat *, B. Radhakrishnan, T. Zacharia
Oak Ridge National Laboratory, Metals and Ceramics Di6ision, Oak Ridge, TN 37831-6140, USA
Received 19 August 1997; received in revised form 3 October 1997
Abstract
The objective of this work was to analyze the residual stress state in spot welds made in an HY-100 steel disk by an autogenous
gas tungsten arc (GTA) welding process. An uncoupled thermal-mechanical finite element (FE) model was developed that took
into account the effects of liquid-to-solid and solid-state phase transformations. Effects of variations in mechanical properties due
to solid-state phase transformations on residual stresses in the weld were studied. Extensive experimental testing was carried out
to determine the mechanical properties of HY-100 steel. The residual stresses in the disk with the spot weld were measured by a
neutron diffraction (ND) technique. The FE results are in good agreement with the ND measurements. The results show that the
volumetric changes associated with the austenite to martensite phase transformation in HY-100 steel significantly affect residual
stresses in the weld fusion zone and the heat affected zone. 1998 Elsevier Science S.A. All rights reserved.
Keywords: Finite element method; Gas tungsten arc; Residual stress state; Neutron diffraction
1. Introduction
One of the major problems in welded structures is
residual stress and distortion. Residual stresses that
develop in and around the welded joint are detrimental
to the integrity and the service behavior of the welded
part. High residual tensile stresses in the region near the
weld might promote brittle fracture, reduce the fatigue
life, and promote stress corrosion cracking during ser-
vice. Residual tensile stresses also promote cold crack-
ing in association with hydrogen in certain steels, even
before the welded member is put in service.
Because a weldment is heated locally by the welding
heat source, temperatures in the vicinity of the weld-
ment are not uniform but change with distance from
the weld centerline. Due to localized heating, complex
thermal stresses are generated during welding. Residual
stresses are stresses that remain in a material as a result
of liquid-to-solid phase transformation associated with
weld solidification and the subsequent non-uniform
cooling of the weld altered by phase transformations in
the solid state.
Several factors may contribute to the formation of
residual stresses [1 7]. The plastic deformation pro-
duced in the base metal (BM) is a function of struc-
tural, material, and fabrication parameters. The
structural parameters include the geometry, thickness,
and joint design. The material parameters reflect the
metallurgical condition of the base material and the
weld metal. Fabrication parameters include the welding
process, procedure, parameters, and the degree of
restraint.
In steel weldments, the solid-state transformation on
cooling of austenite to martensite has a major influence
on the residual stresses. The volumetric expansion at a
given location in the heat-affected zone (HAZ) or the
fusion zone (FZ) depends upon the volume fraction of
martensite that forms. The extent of martensitic trans-
formation depends upon the kinetics of other diffu-
* Corresponding author. Tel.: +1 423 5744837; fax: +1 423
5744839; e-mail: taljatb@ornl.gov1 The submitted manuscript has been authored by a contractor of
the US Government under contract No. DE-AC05-96OR22464. Ac-
cordingly, the US Government retains a nonexclusive, royalty-free
license to publish or reproduce the published form of this contribu-
tion, or allow others to do so, for US Government purposes.
0921-5093/98/$19.00 1998 Elsevier Science S.A. All rights reserved.
PII S 0 9 2 1 - 50 9 3 9 7 0 0 7 2 9 - 6
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B. Taljat et al. /Materials Science and Engineering A246 (1998) 455446
Table 1
Chemical composition of HY-100 material (wt.%)
NiC Cr Mn Si Mo Cu P S Al
1.4 0.280.18 0.262.8 0.18 0.17 0.044 0.029 0.013
sional transformations. The diffusional transformationkinetics are complicated because the austenite composi-
tion in the HAZ is not homogeneous. This is due to the
rapid heating and cooling associated with the welding,
and insufficient time available for austenite homoge-
nization especially at those locations where the on-heat-
ing peak temperatures are just above the trans-
formation temperature. It is known that inhomoge-
neous austenite transforms more readily to diffusional
products because of the ease of nucleation of the equi-
librium phases. The diffusional transformation kinetics
also depend upon the austenite grain size, since austen-
ite grain boundaries are preferred nucleation sites forthe austeniteferrite transformation. The grain size
dependence becomes more complicated in the weld
HAZ because of the variation of grain size with posi-
tion in the HAZ. Solidification may introduce composi-
tion fluctuations in the FZ with respect to
substitutional elements. It is known that substitutional
elements play a major role in the kinetics of diffusional
transformations [8].
The objective of this study was to analyze the resid-
ual stress state in spot welds made in HY-100 steel by
an autogenous gas tungsten arc (GTA) welding process.
A finite element (FE) model for residual stress analysisin spot welds was developed. The analysis included
both the mechanical property changes and the volumet-
ric changes due to the austenitemartensite transfor-
mation. Effects of variation in mechanical properties at
high temperatures and the variation due to transforma-
tion of austenite to martensite on residual stresses were
evaluated. The results were compared with experimen-
tal measurements of residual stresses [9 11] in the
HY-100 steel weldment using the neutron diffraction
(ND) technique.
2. Experimental
The chemical composition of HY-100 steel is shown
in Table 1. The carbon equivalent (CE) of the steel
calculated using the formula: CE=C+Mn/6+(Cr+
Mo+V)/5+(Ni+Cu)/15 is 0.74 wt%. The engineering
stressstrain curves were determined by a conventional
tensile test for the temperature range between 293 and
1273 K (Fig. 1). To obtain true stress strain curves,
which are the required input to the FE code, a linear
work hardening was assumed with the rate of 500 MPa.
Thermal expansion of the material was determined inthe range between room temperature and the solidus
temperature. A high speed quenching dilatometer was
used to carry out these measurements. The mean coeffi-
cient of thermal expansion (CTE) was calculated from
the dilatometer data using the solidus temperature as a
reference (Fig. 2). The solidus and the liquidus temper-
atures for the HY-100 steel composition determined
using Thermocalc are 1741 and 1776 K, respectively.
Other properties, such as elastic modulus, Poissons
ratio, thermal conductivity, density, and latent heat
were found elsewhere [12,13].
An autogenous GTA welding process was used tomake a spot weld at the center of a HY-100 steel disk
(19 mm in height and 75 mm in diameter) with a
welding current of 320 A and a voltage of 15 V, using
4 mm diameter electrode. Welding arc time was 5 s with
argon shielding, followed by a 5 s postweld purge with
argon gas. During welding, the disk was set on a table
and no additional restraints were applied. Fig. 3 shows
the welding set-up.
The disk was sectioned along the z axis through the
center of the weld. One half was used for the ND
residual stress measurements and the other half was
used for microhardness measurements and metallogra-
phy. Redistribution of residual stresses due to section-
ing of the disk was not taken into account.
Fig. 1. Engineering tensile stressstrain curves for HY-100 measured
at various temperatures.
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B. Taljat et al. /Materials Science and Engineering A246 (1998) 4554 47
Fig. 2. Thermal expansion and coefficient of thermal expansion for
HY-100. Note the length of cylindrical specimens used to measure
CTE is 8 mm.
3. Fe modeling
Complex numerical approaches are required to accu-
rately model the welding process. In thermal analysis,
one should account for: (1) conductive and convective
heat transfer in the weld pool; (2) convective, radiative,
and evaporative heat losses at the weld pool surface; (3)
heat conduction into the surrounding solid material, aswell as the conductive and convective heat transfer to
ambient temperature. Furthermore, one needs to ac-
count for temperature dependent material properties
and the effects of liquid-to-solid and solid-state phase
transformations in the material. Capturing all of the
above effects results in a model that cannot always be
realistically solved. However, some of these effects may
not significantly influence the residual stress calcula-
tions, and yet they considerably complicate the analysis.
Therefore, simplifying assumptions should be used judi-
ciously for establishing a reasonably effective and accu-
rate FE model.
The residual stress distribution was computed usingan uncoupled thermo-mechanical FE formulation using
ABAQUS FE code [15]. The computations used temper-
ature-dependent thermo-physical and mechanical prop-
erties of the BM. The thermal analysis was based on the
heat conduction formulation with the Gaussian heat
input from the arc.
An axisymmetric FE model was developed using
linear four-noded finite elements, as shown in Fig. 7.
The core of the modeling effort was the development of
user subroutines to the ABAQUS code, which were used
to model the welding arc in the thermal analysis and to
incorporate the phase transformation effects in themechanical analysis. Thermal and mechanical analysis
were uncoupled and conducted sequentially. First, the
thermal analysis was carried out calculating the tran-
sient temperature distributions during welding. The me-
chanical part relied on the thermal analysis results and
calculated the stressstrain distribution on the basis of
the temperature history. The mechanical model was
similar to the thermal model, except for the type of finite
elements and the applied boundary conditions.
To justify the expensive and time-consuming experi-
mental work for determining the high temperature me-
chanical properties of regions that undergo theon-heating and on-cooling phase transformations, as
well as of regions that do not experience these transfor-
mations, a sensitivity analysis was carried out to deter-
mine the temperature and microstructure dependence of
yield strength on residual stresses in the weld.
3.1. Thermal analysis
The welding arc was modeled by introducing a heat
flux to the disk surface. To account for heat transfer
effects due to fluid flow in the weld pool, an increase in
Metallographic observations together with the
dilatometer measurements indicate a martensite mi-
crostructure in the HAZ and FZ, with extensive crack-
ing in the FZ. Fig. 4(a) and (b) show the r z and r
section of the weld structure, respectively.
Microhardness was measured in order to determine
the yield strength in the HAZ and the FZ. According to
Cahoon [14], the correlation between yield strength, |y,
and the Vickers hardness, Hv, can be expressed as:
|y(my=me+0.002)=Hv
3
my0.08
n$
Hv
30.1n (1)
where n is the strain hardening coefficient, me is the
elastic strain at yield stress (me=sy/E), and E is the
Youngs modulus.
Fig. 5 shows the measured Vickers hardness across
the FZ, HAZ and BM. Hardness of the FZ and HAZ
(425475 Hv) is considerably higher than that of the
BM (about 280 Hv). The hardness in the center of the
FZ is about 425 Hv and linearly increases to about 475
Hv in the HAZ. The strain hardening coefficient for the
BM was determined by Eq. (1), using the yield strength
obtained in tensile tests and the measured hardness of
the BM. The strain hardening coefficients of the HAZ
and FZ were assumed to be equal to that of the BM.
According to Eq. (1), the yield strength of the HAZ and
FZ that corresponds to a hardness of 425475 Hv is
12141357 MPa.
The ND measurements were carried out on the
BEAM Tube-6 (BT-6) triple-axis spectrometer at the
National Institute of Standard and Technology research
reactor [10,11]. The measurements were made using a
nominal gauge volume of 333 mm. Fig. 6 shows
the positions and relative sizes of the measurement
points which are located on the radial section plane.
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B. Taljat et al. /Materials Science and Engineering A246 (1998) 455448
Fig. 3. Welding setup (dimensions are in mm).
thermal conductivity above the melting temperature
was assumed. The thermal effects due to solidification
of the weld pool were modeled by taking into account
the latent heat of fusion. To account for heat losses,
both the radiative and convective heat transfer at the
weld surface were modeled.
The overall heat flux was calculated as:
F=pEI (2)
where p represents the efficiency factor, which accounts
for radiative and other losses from the arc to the
ambient environment, E is voltage, and I electric cur-
rent. Heat flux distribution at the disk surface was
defined by the equation:
f(r)=f1e3(r/r0)
2
(3)
where r is the radial coordinate with the origin at the
spot weld center. The constant r0 represents the charac-
teristic arc dimension in the r direction within which
95% of the energy is transferred. The constant f1 can be
derived by integrating the function f(r) at the material
surface:
f1=pEI 3yr20
(4)
To account for heat transfer due to fluid flow in the
weld pool, the thermal conductivity was assumed to
increase linearly between the solidus temperature and
3000 K by a factor of three [4] (Z. Feng, Edison
Welding Institute, 1997, personal communication). Fig.
8 shows the specific heat and thermal conductivity used
in the analysis.
The latent heat of fusion was specified to model the
heat released during solidification. The value of 247 J
g1 was used [13]. The tube-air convection coefficient
was calculated for the natural convection to the air at
293 K. Radiative heat transfer was assumed at the top
disk surface with an emissivity coefficient e=0.2 [16].
Two computational steps were carried out to com-
plete the thermal welding simulation. In the first step,
the heating/melting of the material was modeled by
applying the heat flux. Cooling transients were calcu-
lated in the second step, when the heat source was
removed and the disk was cooled to room temperature.
The heating time was 5 s, whereas the disk was cooled
until the ambient temperature was reached.
3.2. Mechanical analysis
Rate-independent elastic-plastic constitutive equa-
tions were constructed from the uniaxial tensile test
results of the BM at various temperatures. A linear
transition between the yield strength of the BM at 573
K, the beginning of the martensite transformation, and
the yield strength of martensite at room temperature, as
calculated from the hardness data, was assumed. Both
yield and ultimate strengths were reduced to 5.0 MPa at
the melting temperature to simulate low strength at
high temperatures. Elastic modulus and Poissons ratio
were also given as functions of temperature. The elastic
modulus was reduced to a small value (5.0 GPa) at high
temperatures.
The same FE mesh as in the thermal analysis was
used here, except for the element type and different
boundary conditions. The analysis is based on the
temperature history calculated in the thermal analysis
which represents the input information. The movement
in the axial direction of the bottom disk surface was
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B. Taljat et al. /Materials Science and Engineering A246 (1998) 4554 49
Fig. 4. Weld structure: (a) rz section; (b) r section.
restrained to appropriately model the actual welding
conditions.
A subroutine to ABAQUS code was developed that
accounts for changes in mechanical properties and vol-
umetric changes due to the phase transformation. The
program consists of two parts:
The thermo-physical and mechanical properties of
the BM were used for the entire model during heating.
The temperature history of each integration point in the
model was observed during cooling. Depending on the
peak temperature that a particular point reached during
the heating transient, and depending on the cooling
time, the decision was made whether the point under-
went the martensitic transformation or not. For each
point that underwent the transformation the material
properties of the martensitic phase were applied.
The subroutine also provided the basis for calculat-
ing the volume increase due to martensitic phase devel-
opment. At this stage, the volume change was
approximated by the introduction of a modified coeffi-
cient of thermal expansion. The program distinguished
between the heating and cooling cycle of each point and
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B. Taljat et al. /Materials Science and Engineering A246 (1998) 455450
Fig. 5. Vickers hardness of weld and base material.
Fig. 7. FE model (dimensions are in mm).
in Fig. 9, Case 1 considers all effects, which means
higher yield strength at lower temperatures for the
material that undergoes the phase transformation, the
experimentally determined mechanical properties athigh temperatures, and the assumption of lower yield
strength at temperatures close to the melting point.
Case 2 is the same as Case 1, except it does not consider
the change in the yield strength due to the phase
transformation. Case 3 assumes a linear decrease in
yield strength from room temperature to the melting
temperature.
4. Results and discussion
Fig. 10 shows the radial, axial, and tangential resid-ual stresses at the weld centerline and at a radius of 10
mm. The radial stresses in the FZ and HAZ at R=0
are as high as 580 MPa. Stresses in the BM adjacent to
HAZ increase to almost twice that value and then
the appropriate CTE curve was used (Fig. 2). Note thatthe part of the CTE curve that represents the austen-
itemartensite phase transformation was only used on
the cooling cycle for the points that satisfied the trans-
formation criteria explained above. The CTE values
were calculated with respect to the reference tempera-
ture of 1741 K (solidus temperature). Note that in this
case the CTE defines contraction of the material at
temperatures below the reference temperature. The
CTE value above the melting point was set to zero in
order to disable the calculation of thermal stresses in
the weld pool, whose values might otherwise be signifi-
cant due to high temperatures.Three different cases were studied to analyze the
effect of yield strength at high temperatures and the
effect of yield strength after the austenitemartensite
phase transformation on the residual stresses. As shown
Fig. 6. HY-100 disk with ND measurement locations.
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B. Taljat et al. /Materials Science and Engineering A246 (1998) 4554 51
Fig. 8. Specific heat and thermal conductivity for HY-100.
Fig. 10. Comparison of FE and ND results in radial, axial, and
tangential direction at R=0 mm and R=10 mm.
gradually decrease to compressive stress in the far BM.
Lower stresses in the FZ and HAZ can be explained by
the volume change of the material that undergoes the
austenitemartensite phase transformation. The tem-
peratures in the BM adjacent to the HAZ do not reach
the transformation temperature, therefore, no phase
transformation occurs there, which means no volume
change to offset high stresses. The tangential stress
distribution at R=0 is very similar. The axial stresses
are lower and reach the magnitude of 240 MPa. Calcu-
lated radial and tangential residual stresses agree well
with the ND measurement, whereas the calculated axial
stresses are lower than measured by about 200 MPa. In
comparing the results, one should remember that each
ND data point represents an average residual stress
over a 333 mm volume. The radial residual
stresses at R=10 mm are tensile and lower. The agree-
Fig. 9. Yield stress for the assumed cases.
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B. Taljat et al. /Materials Science and Engineering A246 (1998) 455452
ment with the ND results is very good. The magnitude
of axial stresses is very small, which is also shown by
the ND results. The tangential stresses are compressive
and of a low magnitude. They are not in agreement
with the first ND data point, but agree with the rest of
the ND results. Fig. 11 shows the radial, axial, and
tangential stress distribution in the weld region.
The results presented in Figs. 10 and 11 take intoaccount the phase transformation effects. Another anal-
Fig. 12. Residual stress comparison with the case of no phase
transformation effect at R=0 and R=10 mm.
Fig. 11. Residual stress distribution; radial, axial, and tangential
component (deformation is magnified 5). Note the different stress
scale for axial stresses.
ysis was carried out without considering these effects,
and the comparison is shown in Fig. 12. The results
show a significant effect of phase transformation on
residual stresses. This can be explained by the mi-
crostructural changes that occur during the austenite
martensite phase transformation in the FZ and HAZ
that affect both the yield strength and CTE, which, in
turn, have a significant effect on the residual stress. The
increased yield strength in the FZ and HAZ, as indi-
cated by the changes in hardness (Fig. 5), allows higher
residual stresses. On the other hand, the higher hard-
ness in the FZ and HAZ is related to the formation of
martensite in these locations, which is accompanied by
a volume expansion that reduces the thermal contrac-
tion. This effect tends to reduce the residual stress level
in the FZ and HAZ.
Several computations evaluating the influence of
variations in mechanical properties at high tempera-
tures, and the effect of higher yield strength due to
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B. Taljat et al. /Materials Science and Engineering A246 (1998) 4554 53
martensite formation during cooling, were carried out.
Three cases were analyzed, as described previously, and
the comparisons are shown in Fig. 13. The results show
that the effect of higher yield strength due to formationof martensite does not affect the residual stresses in the
weld. The assumption of linear decrease in yield
strength with temperature has a notable effect on theresidual stresses, which suggests that accurate tempera-
ture dependent mechanical properties are required.
One can conclude that in such analysis it is not asimportant to account for changes in the stressstrain
data due to the austenitemartensite phase transfor-mation, as it is to account for the volumetric changes in
the material caused by the phase transformation, and to
provide accurate, temperature-dependent stress straindata for the austenitic and ferritic phases.
There are several possibilities for improving the
present model. The thermal analysis is based on theconduction model and the assumption of a Gaussian
shape for the heat source. The accuracy of calculated
residual stresses depend on the calculated temperaturetransients; therefore, future efforts will concentrate on
implementation of the arc-pool interaction effect (the
effects of arc-to-weld pool evolution and free weldsurface deformation) into the current thermal model. A
convective heat transfer model, which includes the fluidflow effects in the FZ, is also being developed. These
changes would improve the calculated temperature
transients which have an effect on the calculated resid-ual stresses.
The current model relies upon experimentally deter-
mined transformation kinetics to incorporate the trans-formation plasticity effects. However, it is of
fundamental interest to develop modeling capabilities
that will predict the austenite transformation kineticsunder non-equilibrium welding conditions. As a first
step, it is necessary to model the HAZ grain structurefor a given weld thermal cycle. Previous studies [17]
using 2D Monte Carlo simulations captured the effect
of thermal pinning in the HAZ of a 1/2Cr-Mo-V steel.The simulations are now being extended to two-phase
microstructures where the second phase is an insoluble
inclusion. Both 2 and 3D Monte Carlo simulationshave been carried out in the past to predict the influ-
ence of inclusion volume fraction, size, shape, etc. on
the pinned grain size (unpublished research). The re-sults indicate that there is a significant difference in the
nature of grain boundary pinning by inclusions between
2 and 3D. Hence, in order to make a realistic predictionof grain size in the HAZ of materials containing second
phase particles, one has to resort to a 3D simulationthan a 2D simulation.
5. Conclusions
An FE model for residual stress analysis in spotwelds, which accounts for the phase transformation
effects, was developed. The computations were carried
out using ABAQUS code.Fig. 13. Residual stress comparisons of the three analyzed cases. Note
the results of Case 1 and 2 overlay.
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B. Taljat et al. /Materials Science and Engineering A246 (1998) 455454
An experimental program was carried out to deter-
mine material properties of HY-100 steel. These include
tensile testing, measurement of the CCT curve, metallo-
graphic observations, and hardness measurements. The
hardness measurements show increase in hardness in
the HAZ and the FZ, which indicate the phase trans-
formation from austenite to martensite. The hardness
values were used to determine the yield strength in theHAZ and the FZ. The metallographic observations
show the martensitic structure in the FZ.
The ND technique was used to measure residual
stresses in the spot weld. The FE results are generally in
good agreement with the ND results. The results show
a considerable effect of phase transformation on resid-
ual stresses, which cannot be neglected in such analysis.
The volume change during the austenitemartensite
phase transformation tends to relieve high tensile
stresses, and this is the reason that the magnitude of
radial and tangential stresses in the HAZ and FZ is
about one-half the stress magnitude in the BM adjacent
to the HAZ. The results also show that the effect of
volume change on residual stresses is more significant
than the effect of higher yield strength caused by the
phase transformation. The results also indicate the sig-
nificance of temperature dependent stress strain data
for accurate prediction of residual stresses.
Acknowledgements
The authors would like to thank Dr C.R. Hubbard
and Dr X.L. Wang for reviewing the paper. The re-
search was sponsored in part by an appointment to theOak Ridge National Laboratory Postdoctoral Research
Associates Program administered jointly by the Oak
Ridge Institute for Science and Education and Oak
Ridge National Laboratory. The research was also
sponsored by the US Navy, Office of Naval Research,
under interagency agreement DOE No. 1866-E126-A1,
Navy No. N000014-92-F-0063 under US Department
of Energy contract DE-AC05-96OR22464 with Lock-
heed Martin Energy Research Corporation.
References
[1] N.J. Smith, J.T. McGrath, J.A. Gianetto, R.F. Orr, Weld. J.
Res. Suppl., March 1989, 112.
[2] V.S.R. Murti, P.D. Srinivas, G.D.H. Banadeki, K.S. Raju, J.
Mater. Proc. Tech. 37 (1993) 723.
[3] J.P. Balaguer, Z. Wang, E.F. Nippes, Weld. J. Res. Suppl., April
1989, 121.
[4] K.W. Mahin, W. Winters, T.M. Holden, R.R. Hosbons, S.R.
MacEwen, Weld. J. Res. Suppl., September 1991, 245.
[5] J.B. Roelens, 8th Int. Conf. on Pressure Vessel Technology,
Montreal, Canada, July 1996.
[6] A. Jovanovic, A.C. Lucia, Int. J. Press. Vessels Pip. 22 (1986)
111.
[7] B. Taljat, T. Zacharia, X.-L. Wang, J.R. Keiser, Z. Feng, M.J.
Jirinec, Approximate methods in the design and analysis of
pressure vessels and piping components, PVP ASME 347 (1997)
83.
[8] J. Dobbs, Masters Thesis, University of Alabama at Birming-
ham, Alabama, 1987.
[9] Z. Feng, Y.Y. Zhu, T. Zacharia, R.J. Fields, P.C. Brand, H.J.
Prask, J.M. Blackburn, Proc. of 4th Int. Conf. on Trends in
Welding Research, Gatlinburg, TN, June 1995.
[10] P.C. Brand, H.J. Prask, J. Blackburn, R.J. Fields, T.M. Proctor,
1994 MRS Fall Meeting in Boston, Proceedings.
[11] H.J. Prask, C.C. Choi, in: C. Ruud (Ed.), Practical Applications
of Residual Stress Technology, ASM International, Metals Park,
OH, 1991, 87.
[12] ASME Boiler and Pressure Vessel Code, Section II Materials,
Part DProperties, 1995 ed., The ASME, New York, 1995.
[13] Touloukian, Y.S., Ho, C.Y., (Eds.), Properties of Selected Fer-
rous Alloying Elements, vol. 3, McGraw Hill, New York, 1981.[14] J.R. Cahoon, W.H. Broughton, A.R. Kutzak, Met. Tran., July
1971, 1979.
[15] ABAQUS Users Manual, Version 5.5. Hibbitt, Karlsson and
Sorensen, 1996.
[16] E.R.G. Eckert, Heat and Mass Transfer, McGraw Hill, New
York, 1959.
[17] B. Radhakrishnan, T. Zacharia, Metall. Trans. A 26 (1995) 2123.
.
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