T-joint ®llet welds are extensively used in ship engineering and bridge structures. Localized heating from the welding process and subsequent rapid cooling induce tensile residual stress near the toe of the T-joint in ®llet welds.

1. Analysis of residual stresses and distortions in
T-joint ®llet welds
Tso-Liang Tenga,*, Chin-Ping Fungb
, Peng-Hsiang Changb
, Wei-Chun Yangc
a
Department of Mechanical Engineering, Da-Yeh University, 112, Shan-Jiau Rd., Da-Tsuen, Changhua 515, Taiwan, ROC
b
Institute of System Engineering, Chung Cheng Institute of Technology, Ta-Shi, Tao-Yuan 335, Taiwan, ROC
c
Ordnance Readiness Development Center, Nantou, Taiwan, ROC
Received 5 December 2000; revised 1 August 2001; accepted 7 August 2001
Abstract
T-joint ®llet welds are extensively used in ship engineering and bridge structures. Localized heating from the welding process
and subsequent rapid cooling induce tensile residual stress near the toe of the T-joint in ®llet welds. Welding produces thermal
stresses that cause structural distortions, which in¯uence the buckling strength of the welded structures. This study describes the
thermal elasto-plastic analysis using ®nite element techniques to analyse the thermomechanical behaviour and evaluate the residual
stresses and angular distortions of the T-joint in ®llet welds. Furthermore, this work employs the technique of element birth and
death to simulate the weld ®ller variation with time in T-joint ®llet welds. Also discussed are the effects of ¯ange thickness,
welding penetration depth, and restraint condition of welding on the residual stresses and distortions. q 2001 Elsevier Science Ltd.
All rights reserved.
Keywords: T-joint ®llet weld; Residual stresses; Angular distortions
1. Introduction
Metallurgical joints made by welding are extensively
used in the fabrication industry, including ships, off-
shore structures, steel bridges and pressure vessels.
Among the merits of such welded structures are high
joint ef®ciency, water and air tightness, and low fabri-
cation cost. The types of welded joint can be classi®ed
into ®ve basic categories: butt, ®llet, corner, lap and
edge. T-joint ®llet welds are widely employed in
ships, bridge structures and supporting frames for pres-
sure vessels and piping. Due to localized heating by the
welding process and subsequent rapid cooling, residual
stresses and distortions can occur near the T-joint. High
residual stresses in regions near the weld may promote brit-
tle fracture, fatigue, or stress corrosion cracking. Mean-
while, distortion in the base plate may reduce the buckling
strength of structural members. To accurately evaluate T-
joint ®llet welds, predicting welding residual stresses and
distortion in relation to considerations of design and safety
is a relevant task.
For the prediction of the residual stresses and distor-
tions attributed to welding, previous investigations have
developed several experimental methods, including
stress±relaxation [1], X-ray diffraction [2,3], ultrasonic
[4] and cracking [5]. In these methods the stresses are
determined by experimental methods. With the develop-
ment of computer techniques, the ®nite element method
for analysing thermomechanical behaviour in welded
structures has been further enhanced. For an analysis
of T-joint ®llet welds, Sasayama et al. [6] used the
experimental method to determine the relation between
longitudinal shrinkage deformation and welding para-
meters on long T-joint ®llet welds. This work also
presented a formula describing the deformation process.
Meanwhile, Guyot [7] discussed the effect of transverse
shrinkage on different types of ®llet welds and deduced
the shrinkage formula. Furthermore, Kumose et al. [8]
developed an experimental method to measure angular
distortions in single pass T-joint ®llet welds with differ-
ent welding parameters. Their investigation also consid-
ered ways to improve angular distortion. Nagaraja [9]
examined how the T-joint ®llet welds can be treated as
International Journal of Pressure Vessels and Piping 78 (2001) 523±538
0308-0161/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved.
PII: S0308-0161(01)00074-6
www.elsevier.com/locate/ijpvp
* Corresponding author. Tel.: 1886-3-389-2131; fax: 1886-3-389-2131.
E-mail address: g910404@ccit.edu.tw (T.-L. Teng).

2. a pattern that was combined by a welding pass at the
middle and edge of a butt-welded plate. Michaleris and
DeBiccari [10] designed a computational model to esti-
mate buckling and deformation on large and complex T-
joint ®llet welds. Meanwhile, Arnold [11] estimated
residual stresses in multipass ®llet welds using the ®nite
element code PAFEC. Furthermore, Finch and Burdekin
[12] discussed the effects of residual stresses on differ-
ent kinds of T-joint ®llet weld defects using the ®nite
element code ABAQUS. Finally, Ueda and Ma et al.
[13] developed elastoplastic ®nite-element computer
programs to improve the accuracy of two-dimensional
symmetric ®nite-element models and help them
approach three-dimensional models on T-joint ®llet
welds. Their investigation also discussed the effect of
T-joint weld size, and welding parameters on the weld
residual stresses.
Residual stresses and distortions are unavoidable in
welding, and the effects of these stresses and distortions
on welded structures cannot be disregarded. Deter-
mining residual stresses and distortions is thus an
important problem. However, accurate prediction of
residual stresses and distortions induced by the welding
process is extremely dif®cult because the thermal and
mechanical behaviour in welding include local high
temperature, temperature dependence of material proper-
ties, and a moving heat source. Finite element simula-
tion of the welding process is highly effective in
predicting thermomechanical behaviour. This investiga-
tion performs thermal elasto-plastic analysis using ®nite
element techniques to analyse the thermomechanical
behaviour and evaluate the residual stresses and angular
distortions of the T-joint in ®llet welds. Additionally, it
also considers the effects of ¯ange thickness, welding
penetration depth, and restraint condition on residual
stresses and distortions. Information on how to improve
the fabrication process of welded structures is also
presented.
2. Analysis model
2.1. Thermo-mechanical model
Welding residual stress distributions are calculated by
a ®nite element method. Fig. 1 presents the analysis
procedures.
2.1.1. Thermal model
In the thermal analysis, a total of 160 load steps
increasing from 0.001 to 10 s were required to complete
the heating cycle. Only 30 load increments were typi-
cally required for the weldment to return to its initial
(room) temperature. The time increments were auto-
matically optimised for each time step by the computer
program. The modi®ed Newton±Raphson method was
used in each time step for the heat balance iteration.
This study simulates the weld thermal cycles for SAE
1020 steel shown in Fig. 2. The convective heat transfer
coef®cients on the surfaces were estimated (using engi-
neering formulae for natural convection) to be
15 W m2
K21
.
2.1.2. Mechanical model
In the mechanical analysis, the temperature history
obtained from the thermal analysis was input as a ther-
mal loading into the structural model. The thermal
strains and stresses can be calculated at each time
increment. Also, the ®nal state of residual stresses
will be accumulated by the thermal strains and stresses.
During each weld pass, thermal stresses are calculated
from the temperature distributions determined by the
thermal model. The residual stresses from each tempera-
ture increment are added to the nodal point location to
determine the updated behaviour of the model before
the next temperature increment. The material was
assumed to follow the von Mises yield criterion and
the associated ¯ow rules. Phase transformation effects
were not considered in the current analysis due to
lack of material information, especially at high tempera-
tures, such as the near-melting state.
2.2. Element birth and death
The model in this study adopts the technique of
T.-L. Teng et al. / International Journal of Pressure Vessels and Piping 78 (2001) 523±538524
Nomenclature
r density
C speci®c heat
T temperature
t time
{q} heat ¯ux
Q the rate of internal heat generation
h unit outward normal vector
hf ®lm coef®cient
TB bulk temperature of the adjacent ¯uid
TA temperature at the surface of the model
{Te} nodal temperature vector
{Dse} nodal stress increment matrix
{Dep
} {De
} 1 {Dp
}
{De
} elastic stiffness matrix
{Dp
} plastic stiffness matrix
{Ue} nodal displacement vector
‰BŠ strain-displacement matrix
{DT} temperature increment matrix
{Cth} thermal stiffness matrix
{DTe} nodal temperature increment matrix
‰MŠ temperature shape function
sz longitudinal residual stress
sX transverse residual stress

3. element `birth and death' to simulate the weld ®ller
variation with time in T-joint ®llet welds. All elements
must be created, including those weld ®llers to be
`born' in later stages of the analysis. The method
proposed does not remove elements to achieve the
`element death' effect. Instead, the method deactivates
them by multiplying their stiffness by a severe reduction
factor. Although zeroed out of the load vector, element
loads associated with deactivated elements still appear
in element-load lists. Similarly, mass, damping, speci®c
heat, and other such effects are set to zero for deacti-
vated elements. The mass and energy of deactivated
elements are excluded from the summations of the
model. An element's strain is also set to zero as soon
as that element is `killed'. Similarly, when elements are
born, they are not actually added to the model, but are
simply reactivated. When an element is reactivated, its
stiffness, mass, element loads, etc. return to their full
original values. Thermal strains are computed for newly
activated elements according to the current load step
temperature.
2.3. Veri®cation
The proposed method was compared with ®nite
T.-L. Teng et al. / International Journal of Pressure Vessels and Piping 78 (2001) 523±538 525
Fig. 1. Flow diagram of the analysis procedure.

4. element and experimental results taken from Ma et al.
[13] and Shim et al. [14] to con®rm its accuracy. Ma et
al.'s investigation computed the residual stress in T-
joint ®llet welds using thermal elastic plastic three-
dimensional FEM and generalized plane strain FEM.
Fig. 3 portrays the residual stress distributions across
the width of the ¯ange. The solid lines and broken
lines in Fig. 3 represent the residual stress computed
by Ma et al. and this work, respectively. According to
Fig. 3, the residual stress distributions computed by the
method proposed here show very good agreement with
those determined by three-dimensional FEM.
T.-L. Teng et al. / International Journal of Pressure Vessels and Piping 78 (2001) 523±538526
Fig. 3. Residual stress computed by Ma et al.'s three-dimensional FEM and present method.
Fig. 2. Simulated weld thermal cycles for SAE 1020 steel.

5. For Shim et al.'s investigation, a specimen was
constructed using multi-pass butt welding, with a length,
width and thickness of L ˆ 1000 mm; W ˆ 400 mm; t ˆ
25:4 mm; respectively, as shown in Fig. 4. The welding
used the submerged arc technique. Pass sequences and
welding parameters are shown in Table 1. Figs. 5 and 6
portray the distribution of the transverse and longitudi-
nal >residual stress on the thick plate computed by
Shim et al. and the present method. Shim et al. [14]
presented experimental results for the problem. Addi-
tionally, the ABAQUS ®nite element package is applied
as a comparison. As Fig. 5 indicate, the ABAQUS
package result showed slightly lower tensile transverse
stress near the weld centreline. The present method
tends to the experimental results near the surface. As
Fig. 6 indicate, both analysis results show tensile stress
near the weld centreline.
The residual stress calculated using the present method
T.-L. Teng et al. / International Journal of Pressure Vessels and Piping 78 (2001) 523±538 527
Fig. 4. Geometry of multipass butt weld.
Table 1
Schematics of pass sequences along with welding parameters for each pass
Pass no. (1±11) Voltage (V) Current (A) Speed (mm sec21
)
1 25 190 3.34
2±5 26 215 4.70
6 25 190 3.37
7±9 26 220 4.70
10±11 27 250 4.70

6. T.-L. Teng et al. / International Journal of Pressure Vessels and Piping 78 (2001) 523±538528
Fig. 6. Longitudinal residual stress at the top surface of plate.
Fig. 5. Transverse residual stress at the top surface of plate.

7. correlates well with that determined using Ma et al.'s
three-dimensional FEM and that found in Shim et al.'s
experiments. Therefore, the procedure proposed here is
considered appropriate for analysing residual stresses and
distortions due to welding.
3. Analysis of T-joint ®llet weld
3.1. Specimen and material properties
Fig. 7 depicts two plate ®llet weld. The length of the
®llet weld, the width of the ¯ange and height of the
web are assumed to be 500, 200 and 100 mm, respec-
tively. The plate thickness is 16 mm for the ¯ange and
12 mm for the web. The plate material is SAE 1020,
and the mechanical properties are dependent on the
temperature history, as Fig. 8 illustrates.
3.2. Welding conditions
The welding parameters chosen for this analysis
were as follows: welding method, single pass gas
tungsten-arc welding; welding current, I ˆ 260 A;
welding voltage, V ˆ 20 V; and welding speed,
v ˆ 5 mm sec21
. For practical welds, the heat sources
are applied along the weld path. However, this investi-
gation simulates the increment of heat loading on the
welding process via the lead temperature curve as
shown in Fig. 2.
3.3. Finite element model for T-joint ®llet welds
In the T-joint ®llet weld, the welds on both sides
of the webs are assumed to be simultaneously welded
under the same welding conditions. Therefore, the
T-joint ®llet weld can be considered to be symmetrical
with the Y±Z plane. his work develops a two-
dimensional symmetrical generalized plane strain model
to calculate the residual stresses of the T-joint ®llet
weld using the ®nite element method. With the aid
of this generalized plane strain condition, the three-
dimensional residual stress components distributed in
the transverse section can be computed by thermal
elasto-plastic analysis using ®nite element tech-
niques with unit thickness. The model employs two-
dimensional four node plane elements, including the
®nite element meshes for the ®llet weld, along with
re®ned meshes used in the weld area. The symmetric
model has 439 elements and 514 nodes as shown in
Fig. 9.
3.4. Mesh sensitivity study
To examine the adequacy of element sizes, the effect
of mesh re®nement in the weld area was studied. A new
model with re®ned meshes consists of 507 elements
and 585 nodes. Results from two mesh densities with
the same material model and geometry showed little
difference. Therefore, the original FEM model with-
out mesh re®nement in the weld joint is used for this
study.
3.5. Analysis procedure
During each weld pass, thermal stresses are cal-
culated from the temperature distributions deter-
mined by the thermal model. The residual stresses
T.-L. Teng et al. / International Journal of Pressure Vessels and Piping 78 (2001) 523±538 529
Fig. 7. Geometry of T-joint ®llet welds.

8. from each temperature increment are added to the
nodal point location to determine the updated beha-
viour of the model before the next temperature
increment.
4. Results and discussion
4.1. Transverse residual stresses
A stress acting normal to the direction of the weld
bead is known as a transverse residual stress, denoted
sx. Fig. 10 represents the distributions of the residual
stress sx along the X direction. A very large tensile
residual stress is produced at the surface of the base
plates near the ®llet weld toes. The value of the residual
stress near the weld toes is 25 MPa and decreases to
zero as the distance from the weld toes increases.
Owing to the locally concentrated heat source, the
temperature near the weld bead and heat-affected zone
rapidly changes with distance from the heat source, i.e.
the highest temperature is limited to the domain of the
heat source, from which lower temperature zones fan
out. According to Fig. 10 the temperature non-
uniformity varies the shrinkage through the weldment
thickness during cool-down and, consequently a high
tensile residual stress occurs on the surface of the
weld toes.
4.2. Longitudinal residual stresses
A stress acting parallel to the direction of the
T.-L. Teng et al. / International Journal of Pressure Vessels and Piping 78 (2001) 523±538530
Fig. 8. The mechanical properties of T-joint ®llet weld.

9. weld bead is termed a longitudinal residual stress,
denoted sz. Fig. 11 depicts the distributions of the
residual stress sz along the X-direction. The longi-
tudinal residual stress develops from longitudinal
expansion and contraction during the welding sequence.
Along the weld line, a high tensile residual stress
arises near the weld toes, and then decreases to zero,
®nally becoming compressive as distance from the
weld line on the ¯ange increases. The residual stress
value is 110 MPa, approaching the yield stress of the
material. Due to the self-equilibrium of the weldment,
tensile and compressive residual stress exists at
the weld toes and away from the welding line on the
¯ange.
4.3. Angular distortion
For the angular distortion of a T-joint ®llet weld, the
angular change Du of the ¯ange for T-type joints is
expressed by Du ˆ a=b (for small angular change),
where b is the half length of the ¯ange and a is
the displacement of the Y direction along the ¯ange
edge. This equation describes the angular change of
the ¯ange for the T-joint ®llet weld illustrated in
Fig. 12. In T-type ®llet welding, Fig. 13 represents
T.-L. Teng et al. / International Journal of Pressure Vessels and Piping 78 (2001) 523±538 531
Fig. 9. Finite element meshes for the T-joint ®llet welds of 439
elements.
Fig. 10. Transverse residual stress distribution along the X direction.

10. the changes of angular distortion (Du) with cooling
time. This ®gure reveals that the angular distortion
downward is about 0.006 rad when the weldment has
cooled for 2 s. This is because the thermal expansion
in the upper portion exceeds that in the lower one.
Fig. 13 reveals that, after 20 s of weldment cooling,
the angular distortion upward is approximately
0.003 rad, and almost does not change. This is because
the upwards bend of the ¯ange due to plastic deforma-
tion in the upper portion exceeds that in the lower
portion.
4.4. Effect of ¯ange thickness
Fig. 14 presents the transverse residual stress sx
along the X direction for 10, 16 and 22 mm, related to ¯ange
thickness. All of the stress distributions indicate
tensile stresses near the weld toes, which then decrease
to zero as distance from the weld toes increases. Fig. 15
depicts the longitudinal residual stress distributions
along the X direction, for 10, 16 and 22 mm, related
to ¯ange thickness. All of the stress distributions
show tensile stresses near the weld line, that then
decrease to become compressive with increasing
distance from the weld line. Figs. 14 and 15 reveal
that with increasing ¯ange thickness, the residual stress
increases. Thus, ¯ange thickness affects the maximum
residual stress near the weld toe of the ¯ange in the
following two ways: (1) With increasing ¯ange thick-
ness, the temperature nonuniformity varies the thermal
expansion and shrinkage during cool-down, and, conse-
quently, the residual stress increases. (2) A thicker
T.-L. Teng et al. / International Journal of Pressure Vessels and Piping 78 (2001) 523±538532
Fig. 11. Longitudinal residual stress distribution along the X direction.
Fig. 12. Angular distortion (Du) in T-joint ®llet welds.

11. T.-L. Teng et al. / International Journal of Pressure Vessels and Piping 78 (2001) 523±538 533
Fig. 13. Angular distortion of T-joint ®llet weld.
Fig. 14. Transverse residual stress distributions for different ¯ange thickness.

12. ¯ange strengthens the internal restraint and increases
residual stress.
4.5. Effect of welding penetration depth
In the welding process, different weldment thick-
nesses require different weld penetration depths to
avoid a non-penetration defect. This research selects
elements and controls the heat input to investigate the
effect of different weld penetration depths on residual
stresses and distortions. All simulation models have the
same dimensions and the same weld toe length. As Fig.
16 shows, the weld penetration depth is assumed to be 0
or 6 mm.
Figs. 17 and 18 present the distributions for the
different welding penetration depth of the residual
stresses sx and sz along the X direction. The resi-
dualstress for a 6 mm penetration depth ®llet weld
is smaller than that in a 0 mm penetration depth weld.
This difference is because the larger penetration
depth corresponds to an increase in heat input or a
reduction of the welding speed, enlarging the heat
affected zone and reducing the temperature variation
of the upper and lower surfaces of the ¯ange.
Furthermore, the distortion and welding residual stress
decrease.
4.6. Effect of restraint conditions
In order to reduce T-joint ®llet weld angular
distortion, an external clamp is frequently applied
to the ¯ange, as Fig. 19 illustrates. This research
T.-L. Teng et al. / International Journal of Pressure Vessels and Piping 78 (2001) 523±538534
Fig. 15. Longitudinal residual stress distributions for different ¯ange thickness.
Fig. 16. Different types of penetration depth.

13. investigates the effect of restraint conditions and
restraint position on angular distortions and residual
stresses.
Fig. 20 presents the angular distortion of the
¯ange with various restraint positions. The ®gure
reveals that the angular distortion with restraint is
smaller than when the ¯ange is unrestrained. When
the applied restraint position is ®xed at 39.8 mm, this
computation provides a minimum angular distortion
0.002 rad.
T.-L. Teng et al. / International Journal of Pressure Vessels and Piping 78 (2001) 523±538 535
Fig. 17. Transverse residual stress distribution for different penetration depths.
Fig. 18. Longitudinal residual stress distribution for different penetration depths.

14. Figs. 21 and 22 show the distribution of the
restrained and unrestrained residual stresses sx, sz
along the X direction. The value of the residual stress
in the restrained model is smaller than that in the
unrestrained model. This difference occurs because
when the restraint is removed after welding, the ¯ange
is slightly bent by the released restraint force, and this
induces compressive stress on the top surface of the ¯ange
and tensile stress on the bottom surface of the ¯ange. This
new pattern of stress allows the tensile residual stress near
the toe to be reduced. This phenomenon means that the
restraint used to prevent angular distortion is also effective
in reducing the tensile residual stress near the weld toe.
5. Conclusions
This research employs the ®nite element method
to evaluate residual stresses and angular distortions in
T-joint ®llet welds. The technique of element birth and
death is used to simulate the weld ®ller variation with
time in T-joint ®llet welds. Additionally, it discusses the
effects of ¯ange thickness, welding penetration depth
and restraint condition of welding on residual stresses.
Based on the results in this study, we conclude the
following:
1. For transverse residual stresses, a high tensile
stress is produced near the ®llet weld toe. As
distance from the weld toe increases the stress
approaches zero.
2. For longitudinal residual stresses, a very large
tensile stress occurs near the weld toe, and a
compressive stress appears away from the weld
bead.
3. The temperature distribution along the ¯ange thick-
ness causes ®llet weld angular distortions, which
bend the ¯ange up.
4. With increasing ¯ange thickness, the internal
restraints are increased and the tensile residual stress
near the ®llet weld toe increases.
5. With increasing penetration depth or heat input
in ®llet welding, the tensile residual stress near the
®llet weld toe decreases, and can also improve non-
penetration defects.
6. In a restrained ®llet weld, the tensile residual stress
T.-L. Teng et al. / International Journal of Pressure Vessels and Piping 78 (2001) 523±538536
Fig. 19. Restraint condition in T-joint ®llet welding.
Fig. 20. The angular distortion of the ¯ange with various restraint positions.

15. T.-L. Teng et al. / International Journal of Pressure Vessels and Piping 78 (2001) 523±538 537
Fig. 21. Transverse residual stress distribution with restraint and in the unrestrained condition.
Fig. 22. Longitudinal residual stress distribution with restraint and in the unrestrained condition.

16. and angular distortion near the toe can be reduced
after the restraint force is released. When the applied
restraint position is changed at the boundary, a mini-
mum angular distortion can be obtained.
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