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8nd International Conference on Physical and Numerical Simulation of Materials Processing, ICPNS’16
Seattle Marriott Waterfront, Seattle, Washington, USA, October 14-17, 2016
Simulation of the influence of preheating on stress distribution
during multi-pass repair welding of cast steel
Wen Wang, Yajun Yin, Jianxin Zhou*, Min Wang, and Yun Ling
State Key Laboratory of Materials Processing and Die & Mould Technology, Huazhong
University of Science and Technology (HUST), Wuhan 430074, China
ABSTRACT
Preheating is an important process for multi-pass repair welding of cast steel to prevent bulking, or even crack
defects because of stress concentration. In order to obtain the heating parameters, it is important to calculate the
stress distribution under various preheating conditions. In this study, a thermal-mechanical computational
procedure based on thermal elastic-plasticity theory was developed to understand the evolution of thermal and
constraint stress. In the thermal analysis, both temperature dependent property parameters and latent heat of
material due to melting and solidification are taken into account; the thermal boundary is a mixture of convection
and radiation boundary conditions; a Gaussian volumetric heat source model is adopted to treat the heat put for
laser welding; and the multi-pass addition of the material is treated as quiet element method. For the mechanical
analysis, a simplified double linear constitutive model is used to reflect the elastic-plasticity behaviors of the base
and the filler; and also mechanical parameters are varied with temperature. Based on the program, firstly the
thermal and mechanical characterizes in the heating and heat affected zones are studied, and the influence of
preheating temperature and holding time on the final stress distribution during multi-pass repair welding are
simulated and analyzed. Besides, the effects of heating locations are also simply explored. The present study
could do help for increase the effectiveness and lifetime of damaged cast steel treating with repair welding.
Keywords: Multi-pass repair welding; Preheating treatment; Thermo-mechanical model; Numerical simulation
1. INTRODUCTION
Because of kinds of reasons, defects, like crack,
sand inclusion, pore and so on, often occurs during
the productive of cast steel [1, 2]. This will worsen
the properties of the products, even destroy it.
Application of repair welding have been used to
repair the defective cast steel in common [3, 4].
Appropriate method could not only save the cost, but
also achieve the standard of the properties. During
the repair welding process, because of the
concentration of heat input, the rate of heating and
cooling is very high, thus the steel is easy to crack
because of thermal stress and phase stress. As a
result, in practice, preheating, slow cooling,
controlling of inter-pass temperature are required to
ensure the effectiveness of repair welding [5]. During
the process of repair welding, residual stress is one
of the most important reasons for the defects of the
weld; it would deteriorate the strength, fatigue life of
the structure and accelerate the propagation of the
crack. Meanwhile, the inner physics of the transport
of heat and force process is very complex, traditional
methods based on experience and experimental test
is inefficiency and high scrap rate, the adoption of
numeric simulation is not only efficiency and low
scrap rate, but also could gain some important data
which could not be got by experiments. So carrying
out the simulation of residual stress of repair welding
of cast steel, and studying the influence of
preheating, slow cooling, controlling of inter-pass
temperature on residual stress is very important.
As early as 1940s, Rosenthal, et al. were the
first to gain the analytical solutions of temperature
field based on spot/line heat source model, but
because of too many simplify in heat source model,
the simulated temperature in welding zone has big
difference with experimental results [6]; then, the
approval of distributed face [7] and volumetric heat
source [8] has greatly improved the precise of the
simulated temperature field. along with the
development of computer software and hardware
and finite element theory, great improvement have
been achieved in stress simulation during welding
process, lots of reports on general finite element
simulation software ABAQUS [9, 10], ANSYS [11,
12] and specific finite element simulation software
SYSWELD [13, 14] on laser welding were consisted
with experimental results well, these findings were
2
helpful for guiding for production practice. Dean
Deng, et al. investigated the effects of solid-state
phase transformation on residual stress in low
carbon and medium carbon steels welds by TIG arc
welding process, results indicated that the residual
stresses were significantly affected by low
temperature phase transformation [9].Fu. GM, et al.
estimate the influences of the effects of preheat and
inter-pass temperatures on residual stresses in
welded structures representatives of ships and
offshore platforms [5]. However, because of process
particularity of repair welding: high degree of
constraints of the base on the welds, complexity of
local heat treatment, related reports is rarely and
needs to go further. Thus the present research on
the influence of preheating on stress distribution
during multi-pass repair welding of cast steel is
necessary.
In the present research, a three dimensional
transient heat-mechanical combined model are
proposed for the repair welding of ZG45 steel. Based
on the process characteristics, Gaussian volumetric
heat source model are adopted as the heat input,
convection and radiation heat transfer boundary
conditions are considered; Mises yield criterion is
used to judge the elasticity or plasticity state of the
material, double linear constitutive model are
adopted. What is more, based on the simulation
results, the characteristics of distribution and
magnitude of residual stress, as well as influence of
different preheating parameters on evolution of
residual stress during multi-pass repair welding
process are analyzed.
2. MATHEMATIC MODEL
The present numeric simulation is based on
finite element method. The thermal analysis and the
mechanical analysis were uncoupled and conducted
in sequence in order to reduce calculation time, as
well as guarantee calculation precise. As shown in
Fig. 1, heat transfer, mass transfer, temperature
dependant material parameters, evolution of
mechanical properties, heat source models are
considered in the present physical model. While
flows of the weld pool, phase transformation are
ignored.
Heat transfer
Heat input
Material
properties
Deformation
in solid
Fig. 1 Main physical model for simulation.
2.1. Temperature Field
The conduction of heat in the workpiece follows
the law of Fourier heat conduction, as described in
Eq. (1):
T   T    T 
  kx

   ky
t x  x  y  y 
  T 
&
 kz
  Q
z  z 
cp
(1)
 , c p and k is the density, specific heat
and thermal conductivity of the material; T is the
temperature field in the workpiece; Q& is the density
where
of the generated heat. Convection and radiation heat
transfer boundary conditions are adopted to describe
the heat interaction between the workpiece and the
environment, as shown in Eq. (2):
kn
T
 q  h T  T0    T 4  T04   0
n
(2)
where h is the convection coefficient, gained by
experiment;  is the Boltzmann constant;  is the
emissivity of the material, for ZG 45, 0.25 could be
adopted.
According to the process characteristics, the
present research used the Gaussian volumetric
model to describe the heat input of arc, as shown in
Figure 2. The density of the heat source of different
locations in the workpiece in Cartesian coordinate
system are shown in Eq. (3):
3
Linear isotropic reinforce model are adopted to
describe the plastic behavior of the material. The
influence of the phase transformation is ignored, the
total strain could be calculated as the sum of
elasticity strain, plasticity stain and thermal strain, as
shown in Eq. (7):
 ij   ije   ijp   ij
(7)
 ij could
where thermal strain
be calculated as Eq.
(8):
Fig. 2 Gaussian heat source model
q ( x, y, z )  q (0, 0, 0) exp[
where
heat
which
3Cs
( x 2  y 2 )]
H
log( )
z
(3)
2.3. Addition of material
could
be
calculated
as Cs  3 R : q (0, 0, 0) is the density of the heat
2
source at the original location, as calculated with Eq.
(4):
q (0, 0, 0) 
Quiet element method was used to deal with the
addition of the material. That is: the whole element
was included in the calculation model before the
start of the simulation, but unfilled elements are
multiplied with a very small factor, 1.0e-6. The factor
of the elements are dynamically dismissed when the
material were filled on the workpiece.
(4)
3Cs Q
 H (1 
(8)
T
Cs is a parameter related to the shape of the
source,
  = T  T0  1 1 1 0 0 0
3. SIMULATION PARAMETERS AND
FINITE CALCULATION MODEL
1
)
e3
where H is the depth of the heat source, Q is the
power density. The actual parameters of heat source
model could be adjusted as the actual profile of the
welds. The heat enthalpy method is adopted to
conduct the latent heat of fusion and solidification.
The heat enthalpy is the sum of sensible heat
capacity and latent heat, could be described as Eq.
(5):
H  C (T  Tm );
T  Tm
H  C (T  Tm )  H ;
T  Tm
H  0  H ;
T  Tm
The material of the work piece and fill material
are both ZG 45. The dimensions of the base are 300
mm, 300 mm and 30 mm in longitudinal, width and
height directions respectively. All three passes are
weld using TIG welding method, the welding current,
voltage, and travel speed are 160 A, 30 V and 2.5
mm/s. The length of each pass is 100 mm. Chemical
composition of ZG 45 is listed in Table I, and
simulation physical parameters are listed in Table II.
Table I Chemical composition of ZG 45.
(5)
Element
C
Si
Mn
S
P
Ni
Cr
Cu
Content
（%）
0.50
0.6
0.9
0.04
0.04
0.30
0.35
0.3
2.2. Stress Field
Table II Physical parameters used in the simulation.
Mises yield criterion is used to judge the
elasticity or plasticity state of the material, as shown
in Eq. (6):
Physical parameters
 =0.5  11   22   0.5  22   33  
2
2
2
0.5  33   11   6 12  6 23  6
2
where
2
 is the equal stress.
2
2
31
Symbol
Value
Density (kgm )

7850
Specific Heat (Jkg-1K-1)
Cp
480
Thermal conduct (Wm-1K-1)
k
50.2
Solidus temperature (K)
Ts
1708
Liquidus temperature (K)
Tl
1738
-3
(6)
4
Latent heat (Jkg-1)
Tm
1.02×105
Thermal emissivity

0.25
Young modulus (GPa)
E
210
Poisson ratio

0.31
Yield strength 0.2%(MPa)
s
310
Thermal expansion rate (10-6/K)

17.0
The calculation mesh model is shown in Figure
3. Element type is tetrahedron element, Sum of the
nodes and elements are 38165 and 198240. To
consider the real repair welding constrain conditions,
x-, x+, y-, y+, z- are assumed as strong spring
boundary conditions; z+ are free boundary.
(a) 20.0 s
Fig. 3. Finite element calculation model.
4. RESULTS AND DISCUSSION
4.1. The temperature field
As shown in Fig. 4, during the 1st weld pass,
after the very first unsteady period, isotherm of the
temperature become nearly unchanged, and move
along the welding direction with welding speed.
Evolution rule of temperature field during the 2nd
and 3rd weld pass is the same with the 1st weld
pass, and the peak value is almost the same (Fig. 5).
But the area of the high temperature zone is
enlarged because of the preheating effect of the
previous pass.
(b) 40.0 s
Fig. 4 Temperature field of the 1st weld pass.
(a) 60.0 s
5
(a) 20.0 s
(b) 100.0 s
Fig. 5 Temperature field of the 2nd and 3rd weld pass.
4.2. The stress field.
Fig. 6 shows the front and top views of the
longitudinal stress field during 1st weld pass. Along
the welding direction, the interaction weld zone of
beam and work piece shows compressive stress due
to the expansion of heating. But the weld zone which
has efficiently cooled presents tensile stress. This is
because that, shrinkage of the weld pool cooled
would be blocked with the effect of the cooled nearly
zone. The peak value of the tensile stress is about
150 MPa. Along the thickness direction, below the
tensile stress zone, there exists a large compress
stress zone with the peak value of 200 Mpa. Along
the transverses direction, away of the weld mental
and heat affected zone presents compress stress
with the peak value of 200 Mpa. But the size is
smaller than the compress zone in the thickness
direction. The distribution of longitudinal stress field
after the 2nd and 3rd weld passes is similar to the
1st one, but the area of both tensile and compress
zone is enlarged (Figure 7). This indicated that,
under the influence of hear input of the next weld
pass, the stress of the previous pass has been
effetely reset.
(b) 40.0 s
Fig. 6 Longitudinal stress field of the 1st weld pass.
(a) 80.0 s
6
(b) 120.0 s
Fig. 7 Longitudinal stress field of the 2nd and 3rd weld pass.
Fig. 8 illustrates the distribution of residual
longitudinal stress field after full cooled. Along the
thickness direction, the surface zone of the arc
interaction zone presents tensile stress with peak
value of about 250Mpa, below is compress zone,
which is highest in the start and end location the
weld passes. The magnitude of the start location is
300 Mpa, and that of the end location is 150 Mpa.
Along the transverses direction, the tensile stress
becomes gradually bigger away of the weld center;
outside of the tensile stress zone is compress zone
with small value of about 100 Mpa; and the rest of
the workpiece presents nearly no stress, which
indicate that there exists no plastic deformation.
cooled presents tensile stress with peak value of
about 150 MPa. Different from longitudinal stress,
the front direction of the compress stress zone
presents tensile stress with value of about 200 Mpa.
This indicates constraint conditions of workpiece are
strong during repair welding. Along the thickness
direction, similar with longitudinal stress below the
tensile stress zone, there exists a large compress
stress zone with the peak value of 300 Mpa.
However, different from longitudinal stress, below
the compress stress zone, presents tensile stress
with value of about 300 Mpa which further illustrates
that the workpiece is strongly constricted during
repair welding practice. The distribution of
longitudinal stress field after the 2nd and 3rd weld
passes is similar to the 1st one (Figure 10). But the
tensile zone arising from constraint conditions
becomes weaken due to the preheating effect of the
previous weld pass.
(a) 20.0 s
Fig. 8 Residual longitudinal stress field.
Fig. 9 shows the front and top views of the
transverse stress field during 1st weld pass. Along
the welding direction, similar with longitudinal stress,
the interaction weld zone of beam and work piece
shows compressive stress due to the expansion of
heating; and the weld zone which has efficiently
(b) 40.0 s
Fig. 9 Transverse stress field of the 1st weld pass.
7
Fig. 11 Residual transverse stress field.
(a) 80.0 s
4.3. Influence of preheating temperature
As shown in Fig. 12, after local preheating with
different temperatures, the temperature is uniform in
welding and heat affected zones. The maximum
temperature difference is no more than 20℃. Fig. 13
shows the simulation results of temperature field with
different preheating temperatures. As increasing of
preheating temperatures, the temperature gravity of
the frontier of the welding zones is therefore smaller.
This indicates that temperature distribution is
apparently relaxed with preheating process.
(b) 120.0 s
Fig. 10 Transverse stress field of the 2nd and 3rd weld pass.
Fig. 11 illustrates the distribution of residual
transverse stress field after full cooled. Along the
thickness direction, the surface zone of the arc
interaction zone presents tensile stress with peak
value of about 150Mpa, below is compress zone,
which is highest in the start and end location the
weld passes. The magnitude of the start location is
300 Mpa, and that of the end location is 200 Mpa.
Along the transverses direction, the weld start and
end zones presents weak compress stress, with
value of 100 Mpa. Away of the weld center, the
tensile stress is firstly become bigger, than get
smaller with peak value of about 150 Mpa.
(a) no preheating
(b) 100℃
8
(c) 200℃
conditions after 1st welding pass. Comparison
results present that, although the peak value of
stress is almost the same, the range of compress
stress has been enlarged apparently with increasing
of preheating temperatures. That is to say that the
stress gravity gets smaller with preheating process.
Therefore, preheating could be used to decrease the
potential of crack defects during repair welding of
cast steel.
(d) 400℃
Fig. 12 Temperature field after preheating.
(a) no preheating
(a) no preheating
(b) 100℃
(b) 100℃
(c) 200℃
(c) 200℃
(d) 400℃
Fig. 14 Longitudinal stress field at 40.0 s with different preheating
temperatures.
(d) 400℃
Fig. 13 Temperature field at 20.0 s with different preheating
temperatures.
Fig. 14 and 15 illustrate top view of longitudinal
and transverse stress fields after different preheating
(a) no preheating
9
(b) 100℃
(c) 200℃
(c) 200℃
(d) 400℃
Fig. 16 Residual longitudinal stress field with different preheating
temperatures.
(d) 400℃
Fig. 15 Transverse stress field at 40.0 s with different preheating
temperatures.
(a) no preheating
As illustrated in Fig. 16 and 17, the distribution
of longitudinal and transverse stresses make nearly
on difference after full cooled with preheating
process. The range of longitudinal tensile stress is
enlarged in small extent. Hence simulation results
indicated that preheating process have small
influence on distribution of residual stresses with the
present welding assumptions.
(b) 100℃
(a) no preheating
(c) 200℃
(b) 100℃
(d) 400℃
10
Fig. 17 Residual transverse stress field with different preheating
temperatures.
5. CONCLUSIONS
(1) As the increase of welding passes, temperature
gravity gets smaller on the influence of previous
welding pass; the peak value and evolution rules
are almost the same in different welding passes.
(2) During repair welding, as the increase of welding
passes, both the area of longitudinal tensile and
compress zone is enlarged; the transverse
tensile zone arising from constraint conditions
becomes weaken due to preheating effect of
previous weld pass. The maximum value of
residual longitudinal tensile and compress stress
is 250 and 300 Mpa; while that of residual
transverse tensile and compress stress is 150
and 300 Mpa.
(3) During repair welding, as the increase of welding
passes, the range of compress stress has been
enlarged
apparently with
increasing
of
preheating temperatures, while changes of
residual stresses is small under the present
welding assumptions.
[6]
[7]
[8]
[9]
[10]
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