INTRODUCTION
2.25Cr1Mo steels are widely used in both nuclear as well as conventional power
plants. Heavywall pressure vessels and pipes are often constructed from this
type of CrMo steel because of its excellent hightemperature strength. Therefore
welded joints of CrMo ferrite steels play very important role in the power
industry. Hence mechanical behaviors’ weld ability and Post Welding Heat
Treatment (PWHT) of CrMo steels have been extensively studied in recent decades.
The advantages of welding, as a joining process, include high joint efficiency,
simple set up, flexibility and low fabrication costs. Even though it has many
positive properties, fusion welding can alter the properties of the material
and may causes deflection, shrinkage and residual stresses in the joint (Richards
et al., 2008).
Thermal stresses are generated during welding due to the non uniform temperature
distribution around the joint. As the temperature of the base metal increases,
the yield strength decrease and the thermal stresses increase. It is well known
that resulting residual stresses have a strong influence on weld deformation,
fatigue, fracture, creep and buckling. Thus, it is important to analyze the
residual stresses due to welding. To determine the residual stresses around
a welded joint both nondestructive and destructive test methods can be used,
these methods include Xray diffraction, ultrasonic analysis, hole drilling
and sectioning. These methods are expensive or destructive, therefore numerical
methods are becoming a major tool to study the mechanical behaviour of the weldments.
These methods, which provide detailed analysis of the residual stresses due
to welding, have developed considerably during the last three decades due to
the improvements in computers and in the numerical techniques. These developments
are the work of Hibbitt and Marcal who developed numerical thermal mechanical
models using the finite element method (Hibbitt and Marcal,
1973). Lee and Chang (2007) have also developed a
3D FE model to calculate the residual stresses in welds. Murugan
et al. (2001) have proposed a numerical model for multipass welding
and a material database for toughness of buttwelded assemblies used in heavy
structures. Deng and Murakawa (2006) have produced the
simulation results which show that both volumetric and yield strength changes
have significant effects on welding residual stress in 2.25Cr1Mo steel pipes.
The effect of residual stresses on the fatigue strength in a weld toe for a
multipass fillet weld joint has been investigated by Messler
(2004).
In this study, the buttwelding of two 2.25Cr1Mo plates has been modeled
using FEM based software. To study the thickness effect on the residual
stresses in buttwelds, three cases with different plate thickness have
been analyzed. A 3D finite element model has been developed and the movement
of the electrode has been simulated using the death and birth of elements.
For this purpose a coupled thermomechanical solution method has been
used. The elastoplastic temperature dependent material behaviour has
also been taken into account. In this way, the alongweldjoint and through
thickness residual stresses and also effect of thickness on the residual
stress have been obtained.
WELD METALLURGY
Fusion welding involves the localized injection of intense heat and its dissipation
by conduction into the parent material. The weld microstructure at each location
is therefore closely related to the thermal history (Parmar,
1999). The different zones and their characteristics have been described
for a single pass weld by Mannan and Laha (1996) and
are shown in Fig. 1. Regardless of the primary solidification,
the fusion zone in low alloy steel transforms to austenite at a temperature
not far from its solidification point and then undergoes a solid state transformation
to a structure that will depend on both the harden ability of the alloy and
the cooling rate (Mannan and Laha, 1996).
Adjacent to the fusion zone is a Heat Affected Zone (HAZ); a region that is
not heated sufficiently to cause melting, but nevertheless has been altered
by the welding thermal cycle. As shown in Fig. 1, the HAZ
can be subdivided according to the extent to which grain growth and austenitisation
occur; into a coarse grained zone (CGHAZ), a fine grained zone (FGHAZ), an intercritical
zone (ICHAZ) and over tempered base metal. Fusion welding of thick walled components
necessarily involves many weld passes to fill up the joint. Weld beads covered
by other passes then experience multiple heat pulses and a further subdivision
of metallurgical zones (Kou, 2003).
RESIDUAL STRESS
When steel structures are welded, a localized fusion zone is generated
in the weld joint because of the high heat input from the arc and then
nonuniform temperature distribution is induced due to the heat conduction.
Therefore, nonuniform heat deformation and thermal stresses are included
in the aswelded parts. As a result, plastic deformation is retained within
the weldment and nonlinear plastic deformation and residual stresses exist
after cooling of the welded joint.
Different parameters determine the amount of the residual stresses and its
distribution pattern in welded joints. The major parameters are (Leggatt,
2008):
• 
The geometry of the parts being jointed 
• 
The material properties of the weld and parent materials, including
composition, microstructure, thermal properties and mechanical properties 
• 
Residual stresses which exist in the parts before welding, resulting
from the processes used to manufacture the components and fabrication
operations prior to welding 
• 
Residual stresses generated or relaxed by manufacturing operations
after welding or by thermal or mechanical loading during service life 

Fig. 1: 
Metallurgical zones in single pass weld, categorized according
to the maximum local temperature and micrographs, which, corresponds to
the weld in 2.25Cr1Mo steel ( Francis et al., 2007) 
FINITE ELEMENT MODELING
The analytical algorithm used in this study to calculate the residual
stresses due to the welding is shown in Fig. 2.
The commercial finite element code ANSYS has been used to carry out the
thermal and mechanical analysis. A sequentially coupled analysis of thermal
and mechanical analysis has been performed. In coupled thermomechanical
analysis, there are 4 degrees of freedom which one is the temperature.
This method will increase the accuracy of the model and also takes into
account the mutual effects of thermal strains and temperature. Also, a
bilinear elastoplastic model has been used to carry out the stress analysis.
The geometry of the model considered in this study is shown in Fig.
3.
Two semiinfinite plates of the joint are 4 mm thick and 72 mm width (along
the welding direction). In two other case studies, thicknesses of the plates
are 6 and 8 mm. The weldgroove angle is 60° and due to the symmetry, only
half of the weld and plates have been modeled.

Fig. 2: 
Flowchart of residual stress analysis 

Fig. 3: 
Joint configuration and FE boundary conditions for
two semiinfinite 2.25Cr1Mo lowalloyferritic steel plates 
The chemical composition of 2.25
Cr1Mo lowalloyferritic steel plates used in this study is shown in Table
1 (Kelly and Joseph, 1993).
Welding residual stresses are a consequence of interactions time, temperature,
deformation and microstructure. Physical and mechanical properties that
influence the development of welding residual stresses include thermal
conductivity, heat capacity, thermal expansion coefficient, elastic modulus
and Poisson’s ratio, yield strength, work hardening coefficient.
Yield magnitude residual stresses may occur if the thermal strain during
cooling after welding is greater than the yield strain, that is if:
α (T_{s} – T_{0})
≥σ_{Y}/E 
(1) 
where, α is the coefficient of thermal expansion, T_{s} is the
softening temperature, defined here as the temperature at which the yield strength
drops to 10% of its value at ambient temperature, T_{o} is the ambient
or uniform preheat temperature, E is the Young’s modulus, σ_{Y}
is the yield strength at ambient or preheat temperature (Leggatt,
2008).
The temperature dependent thermophysical and mechanical properties of the
2.25Cr1Mo steels are shown in Fig. 4, respectively (Deng
and Murakawa, 2008). The temperature of the melted filler material is set
to be 1510 °C. Since the plate can dissipate heat through convection, the
heat transfer coefficient on the plate surface is assumed to be 12 J/m^{2}/s/K.
Thermal model: During welding the governing partial differential
equation for 3D transient heat conduction, with heat generation rate Q,
heat flux rate and considering density ρ, thermal conductivity k
and specific heat c as functions of temperature only, is given by the
thermal equilibrium equation:
In all of the welding processes, a heat source provides the required energy
and causes localized high temperature spot. To simulate arc heating effects
during welding, the equivalent heat input can be assumed as the combination
of both surface and body heat flux components (Bang et
al., 2002). The total heat input can be given as follows:
Table 1: 
Chemical composition of the 2.25 Cr1Mo low alloy ferritic
steel (%) 

Q = Q_{s}+Q_{b}
= ηEI 
(3) 
where, Q_{s} and Q_{b} are the heat input due to surface
flux and body flux, respectively, η is the arc efficiency, E is voltage
and I is current. The ratio of Q_{b}/Q_{s} can be adjusted
to achieve an accurate representation of the fusion zone. In this study,
the total heat input was assumed to be 20% of surface flux and 80% of
body flux which are based on the experimental data and the calculated
size of the fusion zone. The arc efficiencies used in the analysis are
0.75 for SMAW and 0.40 for GTAW. The surface flux q_{s} and body
flux q_{b} are generally represented in the form of a Gaussian
distribution as follows:
where, a, b and c are the semicharacteristic arc dimensions in x, y and z direction.
This heat source model has often been used to approximate simple welding processes
carried out in the flat position, i.e., welding horizontally in a straight line
on a horizontal flat plate with the electrode perpendicular to the plate. A
characteristic of a lowhydrogen electrode is often a shallow penetration, which
suggests a heat distribution flatter and more evenly distributed than Gaussian.
Sabapathy et al. (2000) modified the Gaussian
heat source model by changing the exponential terms have used this model to
simulate inservice welding (Sabapathy et al., 2000).
In this study, the heat fluxes of Eq. 4 and 5
were modified by assuming the uniform distribution of heat fluxes in width and
thickness direction in order to simulate the shallow penetration of heat. The
surface and body fluxes can be given as follows:
where, A is the crosssectional area of the fusion zone. The values of
a and c were chosen as the half width of the fusion zone. The fixed zcoordinate
is related to the moving coordinate as follows:
where, v is the welding speed and τ is a lag factor to define the position
of the heat source at time t = 0 (Bang et al., 2002).
Mechanical model: Two basic sets of equations relating to the
mechanical model, the equilibrium equations and the constitutive equations
are considered as follows:
• 
Equations of equilibrium 
where, σ_{ij} is the stress tensor and b_{i} is
the body force.
• 
Constitutive equations for a thermal elastoplastic material 
The thermal elastoplastic material model, based on the Von Mises yield
criterion and the isotropic strain hardening rule, is considered. Stressstrain
relations is written as:
where, [D^{e}] is the elastic stiffness matrix, [D^{p}] is
the plastic stiffness matrix, [C^{th}] is the thermal stiffness matrix,
dσ is the stress increment, dε is the strain increment and dT is the
temperature increment (Chang and Teng, 2004).
Analysis model: The high temperature around the welding pool and
the existing heat dissipation through the plate and from the surface cause
a severe temperature gradient, which change the microstructure of the
metal next to the welded joint. Although, the Heat Affected Zone (HAZ)
itself is composed of different layers, but in this model, it has been
regarded as one layer and its physical properties are shown in Fig.
4. with temperature.
To model the movement of the welding electrode along the zaxis (Fig.
3), the weld has been divided into 3 parts and each part has 24 mm lengths
(Fig. 5). With the speed of 3 mm sec^{1} for the
movement of the welding electrode, each part will take 8 sec to finish which
will be called a step. These values have been adapted based on the Rosenthal’s
model and he has proved that in this way, the temperature in each part can be
assumed to be constant (Messler, 2004). In each step,
these parts have been added to the weldment (FE mesh) using Birth and Death
technique. The heat input has been applied to each part for 8 sec. After one
step, the elements of the second part have been introduced to the FE mesh (birth
of elements) and the heat source has been removed from the earlier part and
has been applied to the second part. By repeating this pattern, the third part
has been introduced until the welding has been completed.

Fig. 5: 
Three paths defined in welded plates to present the
results 
RESULTS AND DISCUSSION
The thermal analysis has shown that after cooling, the plate reaches
the steady state temperature distribution. Therefore, the residual stresses
at this stage have been presented here. Also, to capture the variation
of residual stress distribution (longitudinal stress) along the plate
as well as the plate thickness, three paths have been defined along the
xaxis and are shown in Fig. 5.
Comparisons of the results show the effect of the plate thickness on
the welding residual stresses.
It can be seen that along this path, by increasing the plate thickness,
the longitudinal residual stress in the weld axis increases significantly
from 165 MPa for 4 mm plate to 233 MPa for 8 mm plate (Fig.
6). Also the absolute amount of the compressive residual stress in
the parent material increases from 23.5 MPa for 4 mm plate to 54.5 MPa
for 8 mm plate. Figure 6 also shows that the distance
in which the longitudinal residual stress changes from maximum tensile
to minimum compressive level, increases from 0<x<11 mm for 4 mm
plate to 0<x<13 mm for 8 mm plate. It can be shown from Fig.
6, that the residual stresses reach almost zero level in x ≈
60 mm, however this distance is slightly larger for plate with larger
thickness.
Figure 7 shows that the plate thickness has a significant
effect on the weldaxis residual stresses. For plate with 4 mm thickness,
the accumulation of heat due to the welding of the earlier part, have
led to a significant reduction in stress level at the weldaxis: 5 MPa
for 4 mm plate comparing with 310 MPa for the plate with 6 mm thickness
and 660 MPa for the plate with 8 mm thickness.

Fig. 6: 
Distribution of the longitudinal residual stresses (σ_{z})
along path 1 on the plate surface 

Fig. 7: 
Distribution of the longitudinal residual stresses (σ_{z})
along path 2 on the plate surface 

Fig. 8: 
Distribution of the longitudinal residual stresses (σ_{z})
along path 3 on the plate surface 
This effect is becoming
more dominated along path 3 at Fig. 8. Figure
8 shows that the plate thickness has a significant effect on the weldaxis
residual stresses. For plate with 4 mm thickness, the accumulation of
heat due to the welding of the earlier part, have led to a significant
reduction in stress level at the weldaxis: 200 MPa for 4 mm plate comparing
with 60 MPa for the plate with 6 mm thickness and 300 MPa for the plate
with 8 mm thickness. As it can be seen in Fig. 8. the
weldaxis longitudinal residual stress level for both 4 and 6 mm plates
have been decreased. Also it shows that unlike plate with 8 mm thickness,
the location of the maximum tensile stress for 4 and 6 mm plates has been
shifted to the HAZ.
CONCLUSION
In this study, an FE based 3D model has been used to calculated the residual
stresses for a buttwelded joint. Also the effect of plate thickness on
the residual stresses has been studied.
The results show that:
• 
Using 3D model produce more accurate results. The different
patterns for residual stress distribution along three paths, confirms
that the use of 2D models will lead to erroneous results 
• 
Using element Birth and Death technique is a powerful tool to accommodate
the weld arc movement in a 3D FE model to carry out thermo mechanical
analysis 
• 
Due to the sever temperature gradient, the variation of physical
and mechanical parameters with temperature should be taken into account 
• 
By increasing plate thickness (from 4 to 8 mm), in the same condition,
the residual stresses increase by almost 70% 
• 
By increasing plate thickness, the residual stress affected zone
(distance with significant amount of residual stress) becomes larger 
• 
The longitudinal residual stress in weld axis, change from compressive
stress for 4 mm plate to tensile stress for 8 mm plate, along path
2 and 3 (Fig. 7, 8). This shows
that the pattern of residual stress distribution changes along the
electrode movement direction 