Thermally induced residual stresses due to welding can significantly impair the performance and reliability of welded structures. From a structural integrity perspective of welded structures, it is necessary to have an accurate spatial and temporal thermal distribution in the welded structure before stress analysis is performed. Existing research has ignored the effect of fluid flow in the weld pool on the temperature field of the welded joint. Previous research has established that the weld pool depth/width (D/W) ratio and heat affected zone (HAZ) are significantly altered by the weld pool dynamics. Hence, for a more accurate estimation of the thermally induced stresses it is desired to incorporate the weld pool dynamics into the analysis. Moreover, the effects of microstructure evolution in the HAZ on the mechanical behavior of the structure need to be included in the analysis for better mechanical response prediction. In this study, a three-dimensional numerical model for the thermomechanical analysis of gas tungsten arc (GTA) welding of thin stainless steel butt-joint plates has been developed. The model incorporates the effects of thermal energy redistribution through weld pool dynamics into the structural behavior calculations. Through material modeling the effects of microstructure change/phase transformation are indirectly included in the model. The developed weld pool dynamics model includes the effects of current, arc length, and electrode angle on the heat flux and current density distributions. All the major weld pool driving forces are included, namely surface tension gradient induced convection, plasma induced drag force, electromagnetic force, and buoyancy. The weld D/W predictions are validated with experimental results. They agree well. The workpiece deformation and stress distributions are also highlighted. The mathematical framework developed here serves as a robust tool for better quantification of thermally induced stress evolution and distribution in a welded structure by coupling the different fields in a welding process.

References

1.
Hibbitt
,
H. D.
, and
Marcal
,
R. V.
,
1973
, “
A Numerical Thermo-Mechanical Model for the Welding and Subsequent Loading of a Fabricated Structures
,”
Comput. Struct.
,
3
, pp.
1145
1174
.10.1016/0045-7949(73)90043-6
2.
Lai
,
C. K. F.
,
Koeing
,
H. A.
, and
Morral
,
J. E.
,
1986
, “
Three Dimensional Thermal Stress Analysis of a Welded Plate by the FEM
,”
Trans. CSME
,
10
, pp.
153
165
.
3.
Sheppard
,
S. D.
,
1990
, “
Thermal and Mechanical Simulations of Resistance Spot Welding
,”
Weld. Res. Counc. Bull.
,
356
, pp.
34
41
.
4.
Sluzalec
,
A.
,
1990
, “
Thermal Effects in Friction Welding
,”
Int. J. Mech. Sci.
,
32
, pp.
467
478
.10.1016/0020-7403(90)90153-A
5.
Khandkar
,
M. H. Z.
, and
Khan
,
J. A.
,
2003
, “
Predicting Residual Thermal Stresses in Friction Stir Welding
,”
ASME
IMECE
,
Washington, DC
,
Nov. 15–21
, Vol.
3
, pp.
355
359
.10.1115/IMECE2003-55048
6.
Lin
,
Y. C.
, and
Lee
,
K. H.
,
1997
, “
Effect of Preheating on the Residual Stress in Type 304 Stainless Steel Weldment
,”
J. Mater. Process. Technol.
,
63
, pp.
797
801
.10.1016/S0924-0136(96)02727-6
7.
Yang
,
L. J.
, and
Xiao
,
Z. M.
,
1995
, “
Elastic-Plastic Modeling of the Residual Stress Caused by Welding
,”
J. Mater. Process. Technol.
,
48
, pp.
589
601
.10.1016/0924-0136(94)01698-Z
8.
Canas
,
J.
,
Picon
,
R.
,
Paris
,
F.
,
Blazquez
,
A.
, and
Marin
,
J. C.
,
1996
, “
A Simplified Numerical Analysis of Residual Stresses in Aluminum Welded Plates
,”
Comput. Struct.
,
58
(
1
), pp.
59
69
.10.1016/0045-7949(95)00112-T
9.
Goldak
,
J. A.
,
Breiguine
,
V.
,
Dai
,
N.
,
Hughes
,
E.
, and
Zhou
,
J.
,
1997
, “
Thermal Stress Analysis in Solids Near the Liquid Region in Welds
,”
Mathematical Modeling of Weld Phenomena
, 3rd ed.,
H.
Cerjak
, ed.,
The Institute of Materials
, London, UK, pp.
543
570
.
10.
Oddy
,
A. S.
,
Goldak
,
J. A.
, and
McDill
,
J. M. J.
,
1990
, “
Numerical Analysis of Transformation Plasticity Relation in 3D Finite Element Analysis of Welds
,”
Eur. J. Mech. A/Solids
,
9
(
3
), pp.
253
263
.
11.
Oddy
,
A. S.
,
McDill
,
J. M.
, and
Goldak
,
J. A.
,
1990
, “
Consistent Strain Fields in 3D Finite Element Analysis of Welds
,”
ASME J. Pressure Vessel Technol.
,
112
(
3
), pp.
309
311
.10.1115/1.2928631
12.
Yuan
,
F.
, and
Sun
,
H.
,
1991
, “
Transient Temperature Fields and Residual Stress Fields of Metallic Materials Under Welding
,”
Appl. Math. Mech.
,
12
, pp.
595
599
.10.1007/BF02015573
13.
Murakawa
,
H.
,
Luo
,
Y.
, and
Ueda
,
Y.
,
1998
, “
Theoretical Prediction of Welding Deformation at Groove in Narrow Gap Welding
,”
ASM Proceedings of the International Conference: Trends in Welding Research
,
Pine Mountain, GA
, pp.
993
998
.
14.
Chidiac
,
S. E.
, and
Mirza
,
F. A.
,
1993
, “
Thermal Stress Analysis Due to Welding Processes by the Finite Element Method
,”
Comput. Struct.
,
46
, pp.
407
412
.10.1016/0045-7949(93)90210-5
15.
Sunar
,
M.
,
Yilbas
,
B. S.
, and
Boran
,
K.
,
2006
, “
Thermal and Stress Analysis of a Sheet Metal in Welding
,”
J Mater. Process. Technol.
,
172
, pp.
123
129
.10.1016/j.jmatprotec.2005.09.008
16.
Kong
,
F.
, and
Kovacevic
,
R.
,
2010
, “
3D Finite Element Modeling of the Thermally Induced Residual Stress in the Hybrid Laser/Arc Welding of Lap Joint
,”
J. Mater. Process. Technol.
,
210
, pp.
941
950
.10.1016/j.jmatprotec.2010.02.006
17.
Del Coz Diaz
,
J. J.
,
Menendez Rodriguez
,
P.
,
Garcia Nieto
,
P. J.
, and
Castro-Fresno
,
D.
,
2010
, “
Comparative Analysis of TIG Welding Distortions Between Austenitic and Duplex Stainless Steels by FEM
,”
Appl. Therm. Eng.
,
30
(
16
), pp.
2448
2459
.10.1016/j.applthermaleng.2010.06.016
18.
Oreper
,
G. M.
,
Eagar
,
T. W.
, and
Szekely
,
J.
,
1983
, “
Convection in Arc Weld Pools
,”
Weld. J.
,
62
(
11
), pp.
307
312
.
19.
Kou
,
S.
, and
Wang
,
Y. H.
,
1986
, “
Weld Pool Convection and Its Effect
,”
Weld. J.
,
65
(
3
), pp.
63s
70s
.
20.
Heiple
,
C. R.
, and
Roper
,
J. R.
,
1982
, “
Mechanism for Minor Element Effect on GTA Fusion Zone Geometry
,”
Weld. J.
,
61
, pp.
97s
102s
.
21.
Heiple
,
C. R.
, and
Roper
,
J. R.
,
1982
, “
Effects of Minor Elements of GTAW Fusion Zone Shape
,”
Trends in Welding Research in the United States
,
ASM, Metals Park, OH
, pp.
489
520
.
22.
Heiple
,
C. R.
,
Roper
,
J. R.
,
Stagner
,
R. T.
, and
Aden
,
R. J.
,
1983
, “
Surface Active Element Effects on the Shape of GTA, Laser, and Electron Beam Welds
Weld. J.
,
62
, pp.
72s
77s
.
23.
Sheng
,
I. C.
, and
Chen
,
Y.
,
1992
, “
Modeling Welding by Surface Heating
,”
ASME J. Eng. Mater. Technol.
,
114
, pp.
439
449
.10.1115/1.2904197
24.
Chen
,
Y.
, and
Sheng
,
I. C.
,
1993
, “
On the Solid-Fluid Transition Zone in Welding Analysis
,”
ASME J. Eng. Mater. Technol.
,
115
, pp.
17
23
.10.1115/1.2902150
25.
Leblond
,
J. B.
, and
Devaux
,
J. C.
,
1984
, “
A Kinetic Model for Anisothermal Metallurgical Transformation in Steels Including Effect of Austenite Grain Size
,”
Acta Metall.
,
32
, pp.
137
146
.10.1016/0001-6160(84)90211-6
26.
Leblond
,
J. B.
,
Mottet
,
G.
, and
Devaux
,
J. C.
,
1986
, “
A Theoretical and Numerical Approach to the Plastic Behavior of Steels During Phase Transformations: I: Derivation of General Equations
,”
J. Mech. Phys. Solids
,
34
, pp.
395
409
.10.1016/0022-5096(86)90009-8
27.
Oddy
,
A. S.
,
Goldak
,
J. A.
, and
McDill
,
J. M.
,
1990
, “
A General Transformation Plasticity Relation for 3D Finite Element Analysis of Welds
,”
Eur. J. Mech. A/Solids
,
9
, pp.
253
263
.
28.
Oddy
,
A. S.
,
Goldak
,
J. A.
, and
McDill
,
J. M.
,
1992
, “
Transformation Plasticity and Residual Stresses in Single-Pass Repair Welds
,”
ASME J. Pressure Vessel Technol.
,
114
, pp.
33
38
.10.1115/1.2929009
29.
Ronda
,
J.
,
Murakawa
,
H.
,
Oliver
,
G. J.
, and
Ueda
,
Y.
,
1995
, “
Thermo-Mechano-Metallurgical Model of Welded Steel: II. Finite Element Formulation and Constitutive Equations
,”
Trans. JWRI
,
14
, pp.
1
21
.
30.
Kim
,
J. W.
,
Im
,
S. Y.
, and
Kim
,
H. G.
,
2005
, “
Numerical Implementation of a Thermo-Elastic–Plastic Constitutive Equation in Consideration of Transformation Plasticity in Welding
,”
Int. J. Plast.
,
21
, pp.
1383
1408
.10.1016/j.ijplas.2004.06.007
31.
Deng
,
D.
, and
Murakawa
,
H.
,
2006
, “
Prediction of Welding Residual Stress in Multi-Pass Butt-Welded Modified 9Cr–1Mo Steel Pipe Considering Phase Transformation Effects
,”
Comput. Mater. Sci.
,
37
, pp.
209
219
.10.1016/j.commatsci.2005.06.010
32.
Lee
,
C. H.
,
2008
, “
Computational Modeling of the Residual Stress Evolution Due to Solid-State Phase Transformation During Welding
,”
Modell. Simul. Mater. Sci. Eng.
,
16
, pp.
1
16
.10.1088/0965-0393/16/7/075003
33.
Sen
,
D.
,
Ball
,
K. S.
, and
Pierson
,
M. A.
,
2012
, “
A Comprehensive Study of Residual Stresses in a Gas Tungsten Arc Welded Butt Joint
,”
Proceedings of the ASME Summer Heat Transfer Conference
,
Rio Grande, Puerto Rico
,
July 8–12
(accepted).
34.
Kou
,
S.
,
2002
, Welding Metallurgy, 2nd ed.,
John Wiley & Sons
, New York.
35.
Lindgren
,
L. E.
,
2001
, “
Finite Element Modeling and Simulation of Welding. Part 1: Increased Complexity
,”
J. Therm. Stresses
,
24
(
2
), pp.
141
192
.10.1080/01495730150500442
36.
Lindgren
,
L. E.
,
2001
, “
Finite Element Modeling and Simulation of Welding. Part 2: Improved Material Modeling
,”
J. Therm. Stresses
,
24
(
3
), pp.
195
231
.10.1080/014957301300006380
37.
Lindgren
,
L. E.
,
2007
,
Computational Welding Mechanics—Thermomechanical and Microstructural Simulations
, 1st ed.,
Woodhead Publishing
, Cambridge, UK.
38.
Voller
,
V. R.
, and
Prakash
,
C.
,
1987
, “
A Fixed-Grid Numerical Modeling Methodology for Convection-Diffusion Mushy Region Phase-Change Problems
,”
Int. J. Heat Mass Transfer
,
30
, pp.
1709
1720
.10.1016/0017-9310(87)90317-6
39.
Lawson
,
W. H. S.
, and
Kerr
,
H. W.
,
1976
, “
Fluid Motion in GTA Weld Pools—1. Flow Patterns and Weld Pool Homogeneity
,”
Weld. Res. Int.
,
6
(
5
), pp.
63
77
.
40.
Lawson
,
W. H. S.
, and
Kerr
,
H. W.
,
1976
, “
Fluid Motion in GTA Weld Pools—2. Weld Pool Shapes
,”
Weld. Res. Int.
,
6
(
6
), pp.
1
17
.
41.
Lin
,
M. L.
, and
Eagar
,
T. W.
,
1985
, “
Influence of Arc Pressure on Weld Pool Geometry
,”
Weld. J.
,
64
(
6
), pp.
163s
169s
.
42.
Lin
,
M. L.
, and
Eagar
,
T. W.
,
1983
, “
Influence of Surface Depression and Convection on Arc Weld Pool Geometry
,”
Trans. ASME Transp. Phenom. Mater. Process.
,
10
, pp.
63s
69s
.
43.
Rokhlin
,
S. I.
, and
Guu
,
A. C.
,
1993
, “
A Study of Arc Force, Pool Depression, and Weld Pool Penetration During GTAW
,”
Weld. J.
,
72
(
8
), pp.
381s
390s
.
44.
Ko
,
S. H.
,
Choi
,
S. K.
, and
Yoo
,
C. D.
,
2001
, “
Effects of Surface Depression on Pool Convection and Geometry in Stationary GTAW
,”
Weld. J.
,
80
(
2
), pp.
39s
45s
.
45.
Dong
,
W.
,
Lu
,
S.
,
Li
,
D.
, and
Li
,
Y.
,
2009
, “
Numerical Study for GTA Weld Shape Variation by Coupling Welding Arc and Weld Pool
,”
Int. J. Mod. Phys. B
,
23
(
6–7
), pp.
1597
1602
.10.1142/S0217979209061329
46.
Sahoo
,
P.
,
Debroy
,
T.
, and
McNallan
,
M. J.
,
1988
, “
Surface Tension of Binary Metal—Surface Active Solute Systems Under Conditions Relevant to Welding Metallurgy
,”
Metall. Trans. B
,
19B
, pp.
483
491
.10.1007/BF02657748
47.
Tsai
,
N. S.
, and
Eagar
,
T. W.
,
1985
, “
Distribution of the Heat and Current Fluxes in Gas Tungsten Arcs
,”
Metall. Trans. B
,
16B
, pp.
841
846
.10.1007/BF02667521
48.
Dong
,
W.
,
Lu
,
S.
,
Li
,
D.
, and
Li
,
Y.
,
2009
, “
Modeling of the Weld Shape Development During the Autogenous Welding Process by Coupling Welding Arc With Weld Pool
,”
J. Mater. Eng. Perform.
,
19
(
7
), pp.
942
950
.10.1007/s11665-009-9570-z
49.
Kim
,
C. S.
,
1975
, “
Thermophysical Properties of Stainless Steels
,” Argonne National Laboratory, Report No. ANL-75-55.
50.
Deng
,
D.
, and
Kiyoshima
,
S.
,
2010
, “
FEM Prediction of Welding Residual Stresses in a SUS304 Girth-Welded Pipe With Emphasis on Stress Distribution Near Weld Start/End Location
,”
Comput. Mater. Sci.
,
50
, pp.
612
621
.10.1016/j.commatsci.2010.09.025
51.
Choo
,
R. T. C.
,
Szekely
,
J.
, and
David
,
S. A.
,
1992
, “
On the Calculation of the Free Surface Temperature of Gas-Tungsten-Arc Weld Pools From First Principals: Part II. Modeling the Weld Pool and Comparison With Experiments
,”
Metall. Trans. B
,
23
, pp.
371
384
.10.1007/BF02656292
52.
Nestor
,
O. H.
,
1962
, “
Heat Intensity and Current Density Distributions at the Anode of High Current, Inert Gas Arcs
,”
J. Appl. Phys.
,
33
(
5
), pp.
1638
1648
.10.1063/1.1728803
53.
Lu
,
S. P.
,
Fujii
,
H.
, and
Nogi
,
K.
,
2005
, “
Influence of Welding Parameters and Shielding Gas Composition on GTA Weld Shape
,”
ISIJ Int.
,
45
, pp.
66
70
.10.2355/isijinternational.45.66
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