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CHAPTER 5
EVALUATION OF RESIDUAL STRESS IN WELDED
PLATES
Finite element simulation of residual stresses due to welding
involves in general many phenomena, e.g. nonlinear temperature dependent
material behavior, 3D nature of weld-pool and the welding processes and
micro structural phase transformation. Even though the 3D FEA is more
accurate and realistic in nature, it is not possible to model very large
structures and the analysis involved huge computational time. Hence there is a
need of simplification of the problem without affecting the accuracy of
results. The most powerful strategy to reduce the cost of thermo-mechanical
simulations of welding has been to reduce the dimension of the problem from
three to two or one. Two-dimensional models can often be useful when
evaluating strains and stresses and it is always a good practice to start with
simple model in initial evaluations.
Different geometric models viz., 2D-X, 2D-P, 3D-shell and 3D-
solid are being used in the thermo-mechanical simulations of welding. 2D-X
ignores the heat conduction in the welding direction. This corresponds to
plane strain, generalized plane deformation and axisymmetric models. They
can also be used for very accurate modeling when studying stress-strain
behavior near the weld with very small elements and time steps. 2D-P
assumes constant temperature over the weld plate thickness. The model is a
plane stress model where the heat source is moving in the plane of the model.
45
Two-dimensional plane stress, 2D-P, is useful when the in-plane deformations
are of major concern. Multi-pass welds can be accommodated approximately
by changing thickness of elements. 3D-shell can have varying assumptions
about possible temperature variation over the thickness are possible. The total
bending strain varies linearly over the thickness according to shell theory. 3D-
shell models are useful when simulating the welding of thin-walled structures
in order to obtain the overall deformation behavior and stresses. It is possible
to combine them with 3D solids near the weld for better representation of
thermal and mechanical fields. In general, industrial applications require 3D
models using shell and/or solid elements.
Despite the simplification by excluding various effects, welding
simulation is still CPU time demanding and complex. Hence, simplified 2D
welding simulation procedures are required in order to reduce the complexity
and maintain the accuracy of the residual stress predictions. This chapter
presents the details of welding simulation studies made for evaluation of
residual stresses in welded plates. Finite element analysis of residual stresses
in butt welding is performed utilizing the finite element package ANSYS with
plane stress model. For an efficient comparison of this 2D model, a 3D
analysis has also performed. The present analysis results are found to be in
good agreement with the existing complex 3D finite element analysis and
experiments results.
5.1 WELDING SIMULATION
In general, the thermal history of welded joints can be predicted by
heat transfer analysis. Subsequently, the calculated thermal history can be
used for thermal stress analysis to determine the residual stress fields in the
welded joints. During welding processes, heat can be transmitted by
conduction, convection and radiation. For welding processes where an electric
arc is used as the welding source, heat conduction through the metal body is
46
the major mode of heat transfer and heat convection is less significant as far
as the temperature field in the welded body is concerned. The partial
differential equation for transient heat conduction is
fTt
Tc . (5.1)
where the density ( ), specific heat (c) and the thermal conductivity ( ) are
dependent on temperature (T). t is the time and f represents the additional
heat-generation function in the body.
The heat flux vector,
Tq (5.2)
The enthalpy is related to the temperature by
T
refTdcH )( (5.3)
which implies that
dT
dHc (5.4)
From Equations (5.1) and (5.4), one can write the apparent heat
capacity equation in the form
fTt
H. (5.5)
The heat conduction equation together with initial and boundary
conditions, defines the problem to be solved. Simple boundary conditions are
47
prescribed temperature or prescribed heat flux. The surface heat flux, qn is
defined as positive when directed in the outward normal direction. It is zero in
the case of an isolated, adiabatic boundary. Convective and radiation heat
losses are more complex boundary conditions for the outward flux. Then the
surface heat flux depends on the temperature of the body and the surrounding
and is written as (Fanous et al 2003)
44. refbfrefcn TTseTThn
TnTq (5.6)
where the first term is convective heat loss and hc is the heat transfer
coefficient. The second term is the heat loss due to radiation and bs is Stefan-
Bolzmann’s constant and fe is the emissivity factor. The second term is a
nonlinear boundary condition. The total heat loss in Equation (5.6) can be
written in a format more convenient for finite element implementation as
refeffrefrefrefbfcn TThTTTTTTsehq 22(5.7)
The effective heat transfer coefficient ( heff ) is a combination of
both the convection and radiation coefficients:
3223
refrefrefbfceff TTTTTTsehh (5.8)
The most important parameter to determine the temperature
distribution in the welded components is the heat input. This heat quantity is
the output from a particular heat source used to fabricate the welded joints. In
all the welding processes, heat source provides the required energy and causes
localized high temperature spot. In arc-welding with constant voltage (V) and
amperage (I), the efficiency of the heat source would be (Nguyen 2004)
48
IV
Q
tIV
tQ S
weld
weldS (5.9)
where QS is the heat generating rate and tweld is the welding time and is the
thermal efficiency. The Gaussian-distributed heat source (see Figure 5.1) can
be used to simulate the welding heat source to give a better prediction of the
temperature field near the source center.
Figure 5.1 Gaussian distributed heat flux, q
The heat source density, q(x, y) at an arbitrary point (x, y) is
represented by
2
0 exp, rkqyxq (5.10)
Here 0q is the maximum value of the heat source density. The
distance r in Equation (5.10) is the distance from the center point of the heat
source to the point for which the heat flux is being calculated. The coefficient
49
‘k’ determines the concentration of the heat source. It is also known as the
distribution parameter representing the width of the Gaussian distribution
curve. Higher value of k corresponds to a more concentrated heat source.
From the heat equilibrium condition
kqdykydxkxqdydxyxqQS 0
22
0 )exp()exp(, (5.11)
If the heat density at brr drops to only 5% of the maximum heat
density, i.e.,
)exp(05.0 2
00 brkqq (5.12)
The heat input parameter (k) can be evaluated from the heat source
radius as
222
39957.2)05.0(ln
bbb rrrk (5.13)
Using Equations (5.11) and (5.13) in Equation (5.10), one can write
2
2
23exp
3),(
bb
S
r
r
r
Qyxq (5.14)
The distribution of q(x, y) in Equation (5.14) represents 95% of the
total heat QS when applied within a circle with radius br . The distance,
22yxxr h ; )( 0ttvxh ; and v is the welding speed.
The time between the onset of welding and the end of the cooling to
ambient temperature can be divided into sufficiently small intervals so that
the temperature and thermal stresses for each interval may be regarded as
50
constant. Since the temperature change is rapid at the beginning of welding
and continuously decreases with time, the time step increment should be
sufficiently small at the beginning of the weld and relatively large as the time
increases. The calculation of welding residual stresses is usually based on the
temperature distribution and the thermal stress increment
)( TE is calculated from the incremental thermal strain T . Here
is the thermal expansion and E is the Young’s modulus. The residual
stresses arise not only from the welding shrinkage but also from the surface
quenching (rapid cooling of the weld surface layers) and phase transformation
(transformation of austenite during the cooling cycle).
The calculation starts with time t=0 and the thermal stress was
calculated for the initial temperature distribution of the welded components.
At the next time step, the thermal stress increment was added to the initial
stress at step t =0. The magnitude of the cumulative thermal stress was
limited to the yield strength of the material at actual temperatures. It should be
noted that at each step, the forces caused by the induced thermal stresses must
be in equilibrium. This procedure was repeated until the last step at which the
thermal stress is that at ambient temperature, i.e. the residual stress. This
numerical procedure for residual stress evaluation involves adding together
the incremental thermal stresses, previous thermal stresses and the
equilibrium stresses.
The equilibrium and compatibility equations are
023 ,,, ikikkki Tuu (5.15)
0,,,, ikjljlikijklklij (5.16)
Here, the Lame’s coefficients are:
51
)21()1(
E(5.17)
)1(2
E(5.18)
Where is the thermal expansion; iu s are displacements,
ijjiij uu ,,2
1, is the strain; E is the Young’s modulus; and is the
Poisson’s ratio. These equations, together with the defined boundary
conditions provide the residual stress field in the welded joints. The term
‘simulation’ is often used synonymously with modeling, but there are
differences in meaning (Lindgren 2001). A simulation should imitate the
internal processes and not merely the result of the thing being simulated. This
gives an association into a simulation as a model that imitates the evolution in
time of a studied process. For example, a simplified model directly giving
residual stresses due to a welding procedure will not qualify as a welding
simulation. However, the term ‘simulation’ is often used to denote the actual
computation. Simulation errors will then be those errors related to the solution
of nonlinear equations as well as the time stepping procedure.
It has been reported that the thermal analysis was straightforward
when compared with the mechanical analysis. The mechanical properties
were more difficult to obtain than the thermal properties, especially at high
temperatures (Lindgran 2001, 2007). Many analyses use a cut-off temperature
above which no changes in the mechanical properties are accounted for (Ueda
and Yamakawa 1971). It serves as an upper limit of the temperature in the
mechanical analysis. Tekriwal and Mazumder (1991) varied the cut-off
temperature up to the melting temperature. The residual transverse stress was
overestimated by 2-15% when the cut-off temperature was lowered. It should
52
be noted that all material models need to have good thermo-elasto-plastic
properties up to the cut-off temperature.
5.2 2D ANALYSIS OF BUTT-WELDED JOINT OF 2.25CR 1MO
LOW-ALLOY-FERRITIC STEEL PLATES
Tahami and Sorkhabi (2009) performed a 3D residual stress
analysis by FEA in a butt-welded joint of 2.25 Cr 1 Mo low-alloys – ferritic
steel plates (150 x 72 x 6mm) as shown in Figure 5.2. In this work the same
analysis is performed with 2D. The commercial finite element code ANSYS
has been used to carry out the thermal and mechanical analyses. For thermal
analysis, 2D element Plane 77 is used. It is an 8 node thermal solid (8 node
quadrilateral element) with single degree of freedom having temperature at
each node. Generally, temperature around the arc is higher than the melting
temperature of materials and drops sharply in regions away from weld pool.
In high temperature gradient regions of FZ and HAZ, more refined mesh
close to weld line is essential for obtaining accurate temperature field.
Figure 5.2 Butt-welded 2.25Cr1Mo steel plates
53
For structural analysis, 2D element Plane 82 is used. It is an 8 node
structural solid (8 node quadrilateral element) having two degrees of freedom
at each node, translation in the nodal x and y directions. The overall input of
heat flux QS is evaluated from Equation (5.9) specifying the arc efficiency,
= 0.7; arc voltage, V = 30V; and the current, I = 200A. The radial heat flux
distribution in Equation (5.14) is considered on the top surface of the
weldment. The heat density drops to 5% of its maximum value at brr . In the
present analysis, br is set to 3 mm. Welding speed = 3 mm/sec. When the
value of r is less than or equal to br , the heat flux is calculated according to the
Equation (5.14). Otherwise, the heat load is set to zero. Due to symmetry,
only half of the weld and plate were modeled.
Table 5.1 shows the temperature dependent thermal and mechanical
properties of 2.25Cr1Mo low alloy steel. Filler weld material is assumed to
have the same chemical composition of the parent material. The melting
temperature of the filler material is 1783K. A cut-off temperature (Tcut-off) is
set to 1073K. The material properties at Tcut-off are specified in the regions
where the temperature is higher than Tcut-off. For convective and radiative heat
losses, the constants in the complex boundary conditions for the outward flux
in Equation (5.6) are: Stefan-Boltzmann constant, Sb = 428/1067.5 KmWX ;
convection coefficient, KmWhc
2/15 ; and the emissivity factor, fe = 0.2. To
obtain thermal history, transient, non–linear thermal problem is solved using
temperature dependent thermal properties and considering heat conduction,
convective and radiative boundary conditions.
54
Table 5.1 Temperature dependent properties of 2.25Cr1Mo low-alloy-
ferritic steel, Chemical composition (%wt) (Tahami et al 2009)
C Si Mn P S Cr Mo Cu
0.06-0.15 0.5 0.4-0.7 0.035 0.03 2.0-2.5 0.9-1.1 0.3
Temp (K) 298 477 700 1033 1477 1589
Yield stress
(MPa) 248 200 152 40 4.8 0.7
Temp
(K)
Density
(kg/m3)
Elastic
modulus
(GPa)
Poisson’s
ratio
Thermal
expansion
coefficient
(K-1
)X10-6
Thermal
conductivity
W/(m-K)
Specific
heat
(J/(kg-K))
298 7852.50 215.0 0.288 11.60 35.0 467.07
323 7850.35 212.5 0.289 12.50 36.0 473.67
373 7835.30 209.0 0.290 12.70 36.5 481.41
423 7818.65 206.0 0.292 13.30 36.5 492.53
473 7801.46 197.0 0.294 13.70 37.0 507.02
523 7782.87 194.0 0.295 14.20 36.5 524.88
573 7764.78 189.5 0.296 14.45 36.0 546.12
623 7746.16 185.0 0.297 14.70 35.5 570.74
673 7726.60 180.5 0.298 15.00 35.0 598.73
723 7706.40 177.0 0. 299 15.30 34.0 630.09
773 7687.22 170.0 0.302 15.45 33.0 664.83
823 7668.35 165.0 0.305 15.55 32.0 702.95
873 7648.70 160.0 0.308 15.70 30.5 744.44
923 7630.16 155.0 0.314 15.75 28.0 784.30
973 7599.70 148.0 0.320 15.75 27.0 837.54
1023 7575.98 142.0 0.330 15.75 26.0 889.16
1073 7551.67 142.0 0.330 15.75 25.5 944.15
1123 7526.97 142.0 0.330 15.75 25.5 1002.51
1173 7501.32 142.0 0.330 15.75 25.5 1064.25
1223 7475.28 142.0 0.330 15.75 25.5 1160.87
1273 7448.68 142.0 0.330 15.75 25.5 1197.88
1323 7421.54 142.0 0.330 15.75 25.5 1269.72
1373 7393.85 142.0 0.330 15.75 25.5 1344.96
1423 7365.62 142.0 0.330 15.75 25.5 1423.58
1473 7336.88 142.0 0.330 15.75 25.5 1505.57
55
Thermal stress analysis is performed specifying the temperature
distribution, temperature dependent mechanical properties and symmetry
boundary conditions to obtain the transient and residual stress fields. In
thermal analysis the heat flux is specified in 3172 time steps. It takes 6029
seconds to cool down from the maximum temperature to ambient (room)
temperature. Since load steps are too many, Ansys Parametric Design
Language (APDL) has been adopted to perform both thermal and structural
analyses.
Figure 5.3 shows the contour plot and Figures 5.4 and 5.5 shows
the graphical plot of temperature variation from the weld center line to the
edge of the plate along Y-direction (that is along the length of the plate). The
results indicate that the plate is undergoing significant temperature variation.
At the beginning, the temperature reduction in the area close to the weld axis
shows the quenching effect. Figure 5.6 shows the contour plot and Figure 5.7
shows a comparison of the residual stress ( x ) distribution perpendicular to
the weld of 2.25Cr1Mo steel plate obtained from the present 2D plane stress
analysis and 3D finite element analysis (Tahami and Sorkhabi 2009). The 2D
analysis result varies from 257 MPa (tensile) to -181 MPa (compressive) and
reaches to zero is in good agreement with those obtained from 3D FEA
results. Figures 5.8 and 5.9 give the stresses and strains at mid section
perpendicular to the weld.
56
Figure 5.3 Contour plot of temperature distribution of butt-welded
2.25Cr1Mo steel plate at t =12 sec
Figure 5.4 Variation of temperature from weld center line to the edge
of the 2.25Cr1Mo steel plate along its length direction
(at t=25, 35 & 55 secs)
250
300
350
400
450
500
550
600
650
700
0 25 50 75 100 125 150
Tem
per
atu
re(K
)
Distance from weld (mm)
at 25 sec
at 35 sec
at 55 sec
57
Figure 5.5 Variation of temperature from weld center line to the edge
of the 2.25Cr1Mo steel plate along its length direction
(at t=100 & 500 secs)
Figure 5.6 Residual stress ( x ) N/m2 distribution of 2.25Cr1Mo steel plate
250
300
350
400
450
500
0 25 50 75 100 125 150
Tem
per
atu
re(K
)
Distance from weld (mm)
at 100 sec
at 500 sec
58
Figure 5.7 Residual stress, ( x )distribution from the weld centre line to
the edge of the 2.25Cr1Mo steel plate along its length
direction
Figure 5.8 Residual stresses at mid section perpendicular to the weld of
the 2.25Cr1Mo steel plate
-200
-150
-100
-50
0
50
100
150
200
250
300
0 15 30 45 60 75 90 105 120 135 150
Res
idu
al
stre
ss(M
Pa
)
Distance from weld (mm)
2D FEA
3D FEA (Tahami and Sorkhabi 2009)
59
Figure 5.9 Residual strains at mid section perpendicular to the weld of
the 2.25Cr1Mo steel plate
5.3 2D ANALYSIS OF BUTT-WELDED JOINT OF ASTM 36
STEEL PLATES
Stamenkovic and Vasovic (2009) were performed a 3D residual
stress analysis of butt-weld joint of ASTM 36 steel plates (100 x 100 x 3mm)
with arc efficiency, =0.85; arc voltage, V = 24 V; and the current, I = 180A,
br = 3 mm and welding speed = 5 mm/sec. In this work 2D analysis is
performed by using the same geometry and parameters of Stamenkovic and
Vasovic (2009).Table 5.2 gives the temperature dependent properties of
ASTM 36 steel.
60
Table 5.2 Temperature dependant properties of ASTM 36 steel
(Stamenkovic and Vasovic 2009)
Temp
(K)
Density
(kg/m3)
Elastic
modulus
(GPa)
Poisson’s
ratio
Thermal
expansion
coefficient
(K-1
)X10-5
Thermal
conductivity
W/(m-K)
Specific
heat
(J/(kg-K))
Yield
stress
(MPa)
298 7880 210 0.3 1.15 60 480 380
373 7880 200 0.3 1.2 50 500 340
473 7800 200 0.3 1.3 45 520 315
673 7760 170 0.3 1.42 38 650 230
873 7600 80 0.3 1.45 30 750 110
1073 7520 35 0.3 1.45 25 1000 30
1273 7390 20 0.3 1.45 26 1200 25
1473 7300 15 0.3 1.45 28 1400 20
1673 7250 10 0.3 1.45 37 1600 18
1773 7180 10 0.3 1.45 37 1700 15
Figure 5.10 gives the contour plot of temperature distribution of
butt-welded plate at time t =10 sec. Figures 5.11 and 5.12 shows the
temperature distribution at mid section perpendicular to the weld. Figure
5.13 shows the contour plot of residual stress ( x ) distribution. Figure 5.14
shows a comparison of the residual stress ( x ) distribution perpendicular to
the weld obtained from the present 2D plane stress analysis and 3D finite
element analysis and test results (Stamenkovic and Vasovic 2009). It can be
seen from Figure 5.14, tensile stresses were developed in the weld zone.
These tensile stresses gradually decrease in the transverse direction away
from the weld center line and become compressive towards the edge of the
plate. The peak tensile residual stress estimates from the present 2D FEA is in
good agreement with those obtained from 3D FEA and experimental results
61
(Stamenkovic and Vasovic 2009). Figures 5.15 and 5.16 give the stresses and
strains at mid section perpendicular to the weld.
Figure 5.10 Contour plot of temperature distribution of butt-welded
ASTM 36 steel plate at t = 10 sec
Figure 5.11 Variation of temperature from weld center line to the edge
of the ASTM 36 steel plate along its length direction
(at t = 10, 15 & 20 secs)
0
500
1000
1500
2000
0 20 40 60 80 100
Tem
per
atu
re(K
)
Distance from weld (mm)
at 10 sec
at 15 sec
at 20 sec
62
Figure 5.12 Variation of temperature from weld center line to the edge
of the ASTM 36 steel plate along its length direction
(at t = 50 & 100 secs)
Figure 5.13 Residual stresses - x (N/m2) distribution of ASTM 36 steel plate
250
300
350
400
450
500
550
600
0 20 40 60 80 100
Tem
per
atu
re(K
)
Distance from weld (mm)
at 50 sec
at 100 sec
63
Figure 5.14 Comparison of residual stress ( x ) distribution from the
weld centre line to the edge of the ASTM 36 steel plate along
its length direction
Figure 5.15 Residual stresses at mid section perpendicular to weld of the
ASTM 36 steel plate
-300
-200
-100
0
100
200
300
400
0 20 40 60 80 100
Res
idu
al
stre
ss(M
Pa)
Distance from weld (mm)
2D-FEA
3D-FEA (Stamenkovic and Vasovic 2009)
Test (Stamenkovic and Vasovic 2009)
64
Figure 5.16 Residual strains at mid section perpendicular to weld of the
ASTM 36 steel plate
5.4 2D ANALYSIS OF BUTT-WELDED JOINT OF IN718
SUPER ALLOY PLATES
Deshpande et al (2011) performed a 3D analysis in a butt-welded
plate of IN718 super alloy (100 x 50 x 2mm) with the overall input of heat
flux QS = 350 Watts and br = 3 mm, welding speed = 1.59 mm/sec. In this
work a 2D analysis is performed with same geometry and parameters used in
Deshpande et al (2011). Table 5.3 gives the chemical composition (%wt) of
the material. Figure 5.17 shows the contour plot of temperature distribution at
the time of heat source reaching center of the plate. Figure 5.18 shows the
temperature variation from the weld center line to the edge of the plate along
transverse direction (along the length of the plate). The results indicate that
the plate is undergoing significant temperature variation. At the beginning, the
temperature reduction in the area close to the weld axis shows
65
the quenching effect. Figure 5.19 shows the comparison of thermal history at
the node at weld center line of mid plate for 2D and 3D analysis. Figure 5.20
shows the contour plot of residual stress component ( x ). Figure 5.21 shows
the comparison of 2D and 3D analysis of the longitudinal residual stress ( x )
from the weld center line to the edge of the plate along transverse direction,
which varies from 346 MPa (tensile) to -195 MPa (compressive) in 2D while
400 MPa (tensile) to -195 MPa (compressive) in 3D analysis. Figure 5.22
shows the comparison of 2D and 3D analysis of the transverse residual stress
( y ) from the weld center line to the edge of the plate along transverse
direction, which varies from 200 MPa (tensile) to -50 MPa (compressive) in
2D while 170 MPa (tensile) to -50 MPa (compressive) in 3D analysis. Figure
5.23 shows the comparison of 2D and 3D analysis of the longitudinal residual
stress ( x ) along the weld line along longitudinal direction, which varies from
350 MPa (tensile) to 0 MPa in 2D and 350 MPa (tensile) to 0 MPa in 3D
analysis. Figure 5.24 shows the comparison of 2D and 3D analysis of the
transverse residual stress ( y ) along the weld line along longitudinal
direction, which varies from 225 MPa (tensile) to -300 MPa (compressive) in
2D and 160 MPa (tensile) to -370 MPa in 3D analysis. Figure 5.24 shows that
the tensile stresses were developed in the weld zone. These tensile stresses
gradually decrease in the transverse direction away from the weld center line
and become compressive towards the edge of the plate. The peak tensile
residual stress estimates from the present 2D FEA is in good agreement with
those obtained from 3D FEA results (Deshpande et al 2011).
66
Table 5.3 Temperature dependent material properties of Inconel 718
(Deshpande et al 2011)
Chemical Composition (%wt)
Ni Co Cr Mo Fe Si Mn C Al Ti Cu P B S Nb+Tb
52.5 1.0 19.0 3.05 17 0.35 0.35 0.08 0.6 0.9 0.3 0.015 0.006 0.015 5.125
Temp
(0C)
Thermal
conductivity
W/(m-0C)
Specific
heat
(J/(kg-0C))
Heat
transfer
coefficient
W/(m2-
0C)
Elastic
modulus
(GPa)
Thermal
expansion
coefficient
(0C
-1)X10
-6
Yield
stress
(MPa)
0 10 400 25.0 200 12.5 300
100 13 420 25.1 200 13.0 300
200 15 440 25.4 200 13.5 300
300 17 460 26.3 200 14.0 300
400 18 480 28.1 200 14.5 300
500 19 490 30.9 200 15.0 295
600 21 510 35.2 195 15.5 290
700 23 550 41.1 190 16.0 275
800 24 600 48.9 175 16.5 250
900 25 610 58.9 125 17.0 175
1000 26 620 71.4 110 17.5 95
1100 28 625 86.7 100 18.0 50
1200 30 625 104.9 90 18.2 35
1300 30.5 625 126.5 90 17.5 30
1400 30.7 625 151.5 90 16.0 30
1500 31 625 180.5 90 14.5 30
67
Figure 5.17 Contour plot of temperature distribution at time t = 31. 44 sec
Figure 5.18 Graphical plot of temperature distribution at time t = 31.44 sec
0
200
400
600
800
1000
1200
1400
1600
0 10 20 30 40 50
Tem
p(
0C
)
Transverse Distance (mm)
at 31.44 sec
68
Figure 5.19 Comparison of temperature distribution of 2D and 3D from
the weld center line to the edge of the plate along its length
direction
Figure 5.20 Contour plot of residual stress x (N/m2)
0
200
400
600
800
1000
1200
1400
1600
0 20 40 60 80 100
Tem
per
atu
re-
0C
Time(sec)
3D (Deshpande et al 2011)
2D
69
Figure 5.21 Comparison of residual stress, x from the weld center line
to the edge of the plate along its transverse direction
Figure 5.22 Comparison of residual stress, y from the weld center line
to the edge of the plate along its transverse direction
-250
-150
-50
50
150
250
350
450
0 10 20 30 40 50Str
ess
(x
)M
Pa
Transverse Distance from weld (mm)
2D
3D (Deshpande et al 2011)
0
50
100
150
200
250
0 10 20 30 40 50
Str
ess
(y)
MP
a
Transverse Distance from weld (mm)
2D
3D (Deshpande et al 2011)
70
Figure 5.23 Comparison of residual stress, x along weld in longitudinal
direction
Figure 5.24 Comparison of residual stress, y along weld in longitudinal
direction
-50
0
50
100
150
200
250
300
350
400
0 20 40 60 80 100
Str
ess
(x
)M
Pa
Longitudinal Distance (mm)
2D
3D (Deshpande et al 2011)
-400
-300
-200
-100
0
100
200
300
0 20 40 60 80 100
Str
ess
(y)
MP
a
Longitudinal Distance (mm)
2D
3D (Deshpande et al 2011)
71
5.5 3D ANALYSIS OF BUTT-WELDED JOINT OF ASTM A36
STEEL PLATE
A thermo-mechanical 3D finite element analysis has been
performed to assess the residual stresses in the butt-weld joints of ASTM 36
steel plates (100 x 100 x 3mm) utilizing the commercial software package
ANSYS with arc efficiency, = 0.85; arc voltage, V = 24V; and the current,
I = 180A. The welding speed was 5 mm/sec. In the present analysis, br is set
to 3 mm. The spherical volume-specific density heat source distribution is
considered with a radius br . For thermal analysis, 3D element SOLID70 is
used. The element has eight nodes with a single degree of freedom,
temperature, at each node. The FE model contains 25755 nodes and 20000
elements. . In thermal analysis the heat source is specified in 3208 time steps.
It takes 6012 seconds to cool down from the maximum temperature to
ambient (room) temperature. For structural analysis 3D element SOLID45 is
used.
Figure 5.25 shows the contour plot and Figure 5.26 shows the
comparison of temperature distribution at 10 sec from the weld center line to
the edge of the plate along Y-direction (that is along the length of the plate).
The peak temperature reaches up to 1973K for the present analysis and 2112K
in 2D FEA, are in good agreement. The results indicate that the plate is
undergoing significant temperature variation. At the beginning, the
temperature reduction in the area close to the weld axis shows the quenching
effect. Figure 5.27 shows the residual stress contour plot )( x for 3D
analysis. Figure 5.28 shows the residual stress ( x ) distribution along top,
middle and bottom surfaces perpendicular to the weld obtained from the
present analysis, and it is compared with experiment result (Stamenkovic and
Vasovic 2009) and 2D finite element analysis. The analysis result varies from
383 MPa (tensile) to -78 MPa (compressive) and reaches to zero at top
72
surface, while it varies from 380.8 MPa (tensile) to -77.5 MPa (compressive)
and reaches to zero at middle surface, also varies from 388.4 MPa (tensile) to
-99 MPa (compressive) and reaches to zero at bottom surface, while it varies
from 380.5 MPa (tensile) to -190 MPa (compressive) and reaches to zero in
experiment and from 389 MPa (tensile) to -132 MPa (compressive) and
reaches to zero in 2D FEA results, is in good agreement. Figure 5.29 shows
the residual stress ( x ) distribution along top, middle and bottom surfaces
along the weld line obtained from the present analysis, and is compared with
2D finite element analysis results. The analysis result varies from 386 MPa
(tensile) to -272 MPa (compressive) at top surface, while it varies from 394
MPa (tensile) to -132 MPa (compressive) at middle surface, also varies from
385.6 MPa (tensile) to -131.4 MPa (compressive) at bottom surface while it
varies from 387 MPa (tensile) to -1 MPa (compressive) in 2D FEA results.
Figure 5.30 shows the residual stress ( y ) distribution for top, middle and
bottom surfaces along the weld line obtained from the present analysis and is
compared with 2D finite element analysis results. The analysis result varies
from 80 MPa (tensile) to -543 MPa (compressive), while it varies from 108
MPa (tensile) to -497 MPa (compressive) at middle surface, also varies from
83.5 MPa (tensile) to -434 MPa (compressive) at bottom surface, while it
varies from 161 MPa (tensile) to -343 MPa (compressive) in 2D FEA results,
is in good agreement. Figure 5.31 shows the residual stress ( x ) distribution
through thickness at weld center line. The result varies from 388 MPa to 384
MPa (tensile). Figure 5.32 shows the residual stress ( y ) distribution
through thickness at weld center line. The result varies from 72.5 MPa to 50.8
MPa (tensile).
73
Figure 5.25 3D contour plot of temperature distribution at 10 sec
Figure 5.26 Comparison of temperature distribution at 10 sec
0
250
500
750
1000
1250
1500
1750
2000
2250
0 20 40 60 80 100
Tem
per
atu
re,
0K
Distance from weld (mm)
2D
3D
74
Figure 5.27 Residual stress contour plot )( x N/m2
for 3D analysis
Figure 5.28 Comparison of residual stress, x from the weld center line
to the edge of the plate along its transverse direction
-300
-200
-100
0
100
200
300
400
500
0 20 40 60 80 100Str
ess
(x),
MP
a
Distance from weld (mm)
3D Top
3D Middle
3D Bottom
2D
Test (Stamenkovic and Vasovic 2009)
75
Figure 5.29 Comparison of residual stress, x along weld line
Figure 5.30 Comparison of residual stress, y along weld line
-300
-200
-100
0
100
200
300
400
0 20 40 60 80 100
Str
ess
(x),
MP
a
Distance from weld (mm)
3D Top
3D Middle
3D Bottom
2D
-600
-500
-400
-300
-200
-100
0
100
200
0 20 40 60 80 100
Str
ess
(y),
MP
a
Distance along weld (mm)
3D Top
3D Middle
3D Bottom
2D
76
Figure 5.31 Through thickness distribution of residual stress x at weld
center line
Figure 5.32 Through thickness distribution of residual stress, y at weld
center line
378
380
382
384
386
388
390
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Str
ess
(x),
MP
a
Distance from top surface to bottom (mm)
40
45
50
55
60
65
70
75
80
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Str
ess
(y),
MP
a
Distance from top surface to bottom (mm)
77
5.6 CONCLUDING REMARKS
From the above finite element analysis of welding simulation of 2D
and 3D analysis and its comparison with 3D and experimental results, it is
evident that the 2D welding simulations are found to reduce the complexity of
the problem and adequate for several design purposes in providing the
information regarding the criticality of residual stress in weld joints. Next
chapter provides the details on the thermo-mechanical analysis of welded
pipes.
