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The Accurate Prediction of the ThermalResponse of Welded Structures Basedon the Finite Element Method: Myth or Reality?
Dimitrios Karalis, Vasilios Papazoglou, and Dimitrios Pantelis
Abstract The thermal and metallurgical response of thin welded plates made of
Ck45 steel during shielded metal arc welding is investigated through numerical
results using the finite element method (FEM) and by in situ experimental mea-
surements.
The aim of this paper is to show that the typical and most common investi-
gation strategy followed for the solution of the heat transfer problem of welded
panels based on FEM investigations (prior to the commencement of real production
welding) does provide engineers with an efficient temperature – prediction tool if
autonomously used. The experimental welding verification is, however, deemed es-
sential for further analysis.
The paper places emphasis on the difficulties arising when attempting to deal
with the problem from the point of view of pure prediction. Detailed numerical ther-
mal modeling, including most of the thermal and metallurgical parameters that are
more or less involved in real welding, does not necessarily provide accurate results
as far as the transient temperature distribution is concerned due to the unknowns
involved. Typical unknown parameters such as the material model, the net heat in-
put and the amount of thermal energy released to the surroundings by convection
and/or radiation turn these numerical prediction tools into case sensitive and vari-
able systems that should be used very cautiously for direct accurate welding thermal
response predictions.
In the present paper the deviation between the predicted thermal results obtained
using detailed Finite Element Modeling and those obtained by means of experi-
mental measurements is clearly demonstrated. This fact implies the weakness of the
numerical FEM strategies to accurately predict the actual thermal response during
welding with respect to the modeling parameters that are unknown. An adapta-
tion procedure on the basis of the weld metal shape is thus proposed. The adapted
D. Karalis, V. Papazoglou (�), and D. PantelisShipbuilding Technology Laboratory, School of Naval Architecture and Marine Engineering,National Technical University of Athens, 9 Heroon Polytechniou Avenue, Zografou,Athens GR-157 73, Greecee-mail: papazog@deslab.ntua.gr, pantelis@central.ntua.gr
S. Pantelakis, C. Rodopoulos (eds.), Engineering Against Fracture: Proceedings 513of the 1st Conference,c© Springer Science+Business Media B.V. 2009
514 D. Karalis et al.
model is then used for a thorough investigation of the thermal response analysis.
These adapted thermal numerical results, later used for post-mechanical analysis,
are expected to more accurately address the problem of the transient and residual
stresses calculations, stresses which greatly affect the fracture behavior of a welded
structure.
Keywords SMAW · FEA thermal modeling · Experimental measurement · Ck45
steel · Metallurgical study
1 Introduction
The aim of welding simulations is to analyze the evolution of the manufacturing
process. Simulations are more significant if they aim at accurately predicting the
magnitudes of interest, such as temperatures or deformations, prior to the com-
mencement of the manufacturing process itself. This would provide an efficient tool
for the engineers during the design process of welded steel structures.
In general, interest has been focused on the transient and steady state thermal
and mechanical response of the welded system. If the numerical simulations are
carried out prior to the experimental or manufacturing process, the simulation mod-
els are treated as prediction models. They aim at calculating the thermo-mechanical
response without any real input from the exact fabrication process, with the excep-
tion of the welding parameters, welding setup, materials, initial clamps or tacks and
probably some very simple trial tests. In this case, accurate prediction in terms of
welding is a very complex and triggering task but its value is of great importance in
case of ship hull structural members, like stiffened panels, corrugated bulkheads or
stiffened curved side shells.
On the other hand, if the numerical simulations are carried out after the weld-
ing has been performed, the opportunity is provided for comparison of results and
model adaptation. Comparisons between numerical and experimental results can
lead to a process of numerical adaptation depending on the magnitude of results
deviation. This process aims at improving the response of the system that is been
modeled by the numerical simulations to follow. The drawback is that welding has
already been completed and its steady state response, like residual deformations or
final microstructure, if being of poor quality, has not been predicted on time by
the simulation. The corrections and modifications undertaken in numerical analysis
are included in the so called model-calibration or model-adaptation procedure. In
this case, simulations lose their pure prediction character and are turned into analy-
sis simulations, focusing on the thorough examination and optimization of the real
process.
The thermal and mechanical response of steel plates during welding has been
investigated by several authors during the last three decades. Most of the in-
vestigations are focused on either or both the thermal and the mechanical part
of the structural response through a combination of experimental and numerical
The Accurate Prediction of the Thermal Response of Welded Structures 515
simulations. The numerical part of the investigation still remains under high interest
due to its high complexity and due to the uncertainty in predicting the actual struc-
tural response prior the welding itself. An extensive review has been carried out by
Radaj [1] and more recently by Lindgren [2, 3].
As far as the thermal problem during welding is concerned, it consists of three
different stages: (a) the solution of the transient heat transfer problem based on
numerical simulation, (b) the experimental measurement of transient temperatures
or micro-structural characterization of the welded parts, and, if necessary, (c) the
adaptation of the initial simulation model in order to attain convergence between nu-
merical and experimental results. Adaptation aims at compensating for the unknown
parameters that are explicitly or implicitly involved during the numerical simulation.
For example, the arc efficiency, the heat losses to the surrounding environment (by
convection, radiation or metal to metal contacts), the analysis simplifications (e.g.
the two-dimensional heat flow consideration), the thermal material properties at el-
evated temperatures, and the experimental or in situ welding set-up are some typical
examples. In some cases, if the transient solid or liquid state transformations of the
material are also taken into account in the numerical investigation, the analysis is
turned into a micro-structural dependent analysis which may add to the uncertainty
of the modeling due to the increased complexity.
Further investigation can be carried out as soon as the transient temperature
distributions of the welded structure between numerical and experimental results
are in good agreement. The numerical models developed can be further used for
parametric analysis focusing on the optimization of the design process of the ma-
rine structure as far as the micro-structural evolution or maximum temperatures is
concerned, or they can alternatively be used for the calculation of the transient me-
chanical response of the welded system. In this case, the probability to correctly
calculate the steady state mechanical response of the steel structure is higher due to
exact thermal excitation.
The aim of this paper is to propose an investigation strategy to be followed for
the solution of the heat transfer problem of thin welded panels based on numerical
investigation and to emphasize the difficulties arising when trying to deal with the
problem from the point of view of pure prediction. The numerical solutions obtained
are then compared to the experimental results and adaptation modifications are car-
ried out in order to bring numerical and experimental results close to each other.
The adapted model is then used for a thorough investigation.
2 Experimental Set-Up
The aim of the experimental procedure, except for the welding itself, is to provide as
accurate as possible measurements of the transient thermal response of the welded
system. These would be later used in order to compare them with temperature results
obtained from the numerical analysis.
516 D. Karalis et al.
In general, measurements usually employed for this task are temperature and
micro-hardness measurements, combined with results from standard metallogra-
phy technique using optical microscopy. As far as the temperature measurements
is concerned, the maximum austenitization temperatures (Ta-max) reached as close
as possible to the weld metal and the cooling rate between 800◦C and 500◦C (Δt8/5)
in the heat affected zone are usually of great interest. The former accounts for
the austenite grain size and hardenability of steel and the latter for the solid state
transformations during cooling. The exact size of the weld pool and the final micro-
structural state of the material at the steady-state condition (that is when the material
has completely cooled down) is also to be taken into account.
The experimental setup consisted of thin plates made of Ck45 steel. The size of
each of the steel plates was 700×200×4mm3 as shown in Fig. 1. The plates were
free from initial curvatures and other imperfections, except that they were slightly
oxidized. The shielded metal arc welding technique and basic electrodes made by
ESAB, type OK55.00, E7018 class, according to AWS-A5.1 were employed for the
welding. The latter is a very low carbon electrode suitable for Ck45 steel welding.
The chemical composition of base and weld metal are listed in Table 1. The welding
parameters were tuned at V = 26V, I = 145A and v = 0.003m/s [4]. Prior to the
commencement of the experiments, the plates were tack welded at x = 0, 0.125,
0.250, 0.450, 0.575 and 0.7 m and the electrodes were dried at 350◦C for 2 h.
Temperature measurements were obtained using ANSI-. Chromel-Alumel ther-
mocouples of 0.002 m tip diameter, that were theoretically capable for measuring up
to 1370◦C. The exact location of the thermocouples, derived from local measure-
ment carried out after the completion of the experiments, is shown in Fig. 1. The
thermocouple positions listed in Table 1 were selected after extensive experimental
Thermocouple Position (m)No 1 x = +0.380, y = +0.004, z = +0.002 No 2 x = +0.360, y = +0.003, z = +0.002 No 3 x = +0.340, y = +0.005, z = +0.002 No 4 x = +0.360, y = +0.080, z = +0.002
Fig. 1 Plate dimensions and locations of thermocouples (No1 to No4)
Table 1 Chemical composition of Ck45 steel and weld metal
% w/w (C) (Si) (Mn) (S) (P)
Ck45 0.42–0.5 0.15–0.35 0.5–0.8 0.035 0.035
Weld Metal 0.06 0.5 1.5 – –
The Accurate Prediction of the Thermal Response of Welded Structures 517
investigation based on the following criterion: the temperatures measured at the
positions selected during all experiments should be higher than the transformation
temperature of steel (A1 = 723◦C). The aim of the extensive experimental investi-
gation was also to attain repeatability of the results due to the welding technique
employed (SMAW).
3 Numerical Modelling
For the numerical simulation of the transient heat transfer response the finite element
analysis method was used by developing numerical models using the commercial
finite element software ABAQUS [5]. A two-dimensional analysis was set up refer-
ring to the cross section of the welded plates. Due to symmetry, only one half of the
welded plate was modeled. Mesh density was tuned in order to attain convergence
of thermal response, thus 1,575 linear four nodded plane quadrilaterals were used.
Heat input was modeled based on the double ellipsoid distribution of arc heat, as
proposed by Goldak et al. [6–8]. This distribution is shown schematically in Fig. 2
and is described by Eqs. (1–5):
Q f (x,y,z, t) =6√
3r f Qahbhch fπ
√π
e− 3(x−vt)2
c2h f e
− 3y2
a2h e
− 3z2
b2h (1)
Qr(x,y,z, t) =6√
3rbQahbhchbπ
√π
e− 3(x−vt)2
c2hb e
− 3y2
a2h e
− 3z2
b2h (2)
Fig. 2 The double ellipsoid heat distribution [6–8]
518 D. Karalis et al.
r f =2ch f
ch f + chb(3)
rb =2chb
ch f + chb(4)
Q = ηV I (5)
in which v refers to the arc longitudinal velocity and η to the arc efficiency. For
the modeling procedure, all elements that were involved within the double ellipsoid
distribution were assigned an individual thermal load curve according to their co-
ordinates (y, z) in the two-dimensional plane. The heat applied was considered to
be distributed on the element surfaces [9], while the weld metal was activated at
the melting temperature [2, 3]. For the estimation of double ellipsoid dimensions
a simple “bead on plate” trial experiment was carried out with exactly the same
welding parameters used for the welding experiments. This procedure allows the
measurement of the double ellipsoid dimensions by simple means and without any
additional cost prior to the commencement of the real weld; otherwise these have
to be estimated according to the literature or based on semi-empirical methods.
Similar procedures have been adopted by other investigators [10–12] for the esti-
mation of the arc dimensions. The final values of the distribution dimension were
tuned at ah = 0.006m, bh = 0.004m, chf = 0.002m and chb = 0.005m. The arc
efficiency was taken equal to η = 0.75, based on the values proposed in the litera-
ture [1]. All material and boundary non-linearities were included in the thermal part
of the analysis. More specifically, temperature dependent thermal material proper-
ties [1–3,13] were assigned for the whole thermal analysis, taking into consideration
that the final material microstructure was free of martensite that exhibits different
thermal properties at room temperature compared to ferrite-pearlite which was the
initial micro-structural state of the steel. This assumption was later checked through
the cooling rates calculated by the software. The temperature and microstructural
dependent thermo-physical properties of Ck45 steel employed for the numerical
analysis are shown in Figs. 3–5. The value of heat conductivity above the liquidus
temperature was set to be equal to 230W/m◦C in order to account for molten metal
stir effects. Latent heat was also included in the analysis by specifying the solidus
and liquidus temperature of the base and weld metal. Its value was set equal to
260kJ/kgr. As far as the heat loss is concerned, radiation and heat convection to the
surroundings was taken into account. The model used for the calculation of the heat
loss was based on the equivalent convection model [14, 15] which is described by
Eq. (6):
h = 24.1×10−4 × ε×T1.61(W/m2 ·◦C) (6)
in which �h� refers to the convection coefficient, �T� refers to the current
surface temperature of the element and �ε� to the emissivity that was supposed
to be equal to 0.8, a typical value for slightly oxidized steel plates. Finally, the initial
temperature of the base metal was set to be 25◦C referring to the room temperature.
The Accurate Prediction of the Thermal Response of Welded Structures 519
Fig. 3 Mass density dependence on temperature [1–3, 13]
Fig. 4 Thermal conductivity dependence on temperature [1–3, 13]
4 Prediction Results and Discussion
A typical view of the cross section at x = 0.350m of the welded plates is shown
in Fig. 6 obtained my means of optical stereoscopy. In Fig. 7 the temperature dis-
tributions calculated using the finite element method are shown for the same cross
section. In this figure, all the sectioned area included within the grey temperature
isotherm refers to the melted zone (weld metal, dilution zone). The temperature
520 D. Karalis et al.
Fig. 5 Specific heat dependence on temperature [1–3, 13]
Fig. 6 Typical view of the weld cross section at x = 0.350 m (experimental results)
Fig. 7 Liquidus isotherm of the weld cross section, as predicted (units in K)
The Accurate Prediction of the Thermal Response of Welded Structures 521
0
200
400
600
800
1000
1200
1400
0 100 200 300 400 500 600
time (sec)
Tem
per
atu
re (C
)No1
No2
No3
No4
Fig. 8 Measured temperature distributions
results shown in Fig. 7 refer to the model developed before welding took place,
aimed at predicting the temperature distributions and cooling rates. As far as the
comparison between numerical and experimental results is concerned, a typical view
of the measured temperature profiles at the locations shown in Fig. 1 is provided in
Fig. 8. It is obvious that none of the thermocouples measured any temperature higher
than 1,300◦C. The overestimation of the liquidus isotherm is mainly focused at the
bottom side of the plates (z = 0.004m plane) in which the liquidus isotherm extends
to a great distance form the axis of symmetry (y = 0m) compared to the actual weld
metal size shown in Fig. 6. This observation is not valid for the top surface of the
plates (plane z = 0m), on which the weld metal extension has been better predicted.
On the other hand, the cooling rate Δt8/5 calculated by the simulation and measured
by experiment at the locations of thermocouples 1, 2, and 3 (see Fig. 1), was 21 and
22 s, respectively.
Prior to any further comparisons between measured and calculated temperatures,
it has already been observed that the melted zone is greater in size in Fig. 7 than
that of Fig. 6. This error may have been introduced due to several reasons such as
modeling assumptions or modeling simplifications. As soon as the heat input was
modeled as accurately as possible and time incrementation and meshing was consid-
ered to be of adequate density, any deviation between numerical and experimental
observations, apart from the uncertain material properties close to the liquidus tem-
perature, may be due to inaccurate estimation of the double ellipsoid dimensions,
especially in the longitudinal direction, overestimation of the arc efficiency or in-
accurate modeling of heat loss. The latter has also been discussed by Papazoglou
et al. [16]. Notice that the two dimensional analysis formulation that was employed
tends to over-predict temperature fields due to the fact that no heat flow is allowed
in the longitudinal direction. Furthermore, the size of the hump that is generated
on the upper surface of the weld metal during welding, as shown in Fig. 6, is not
taken into account in the finite element model. The latter affects the accuracy of
522 D. Karalis et al.
the calculated temperature distributions in both directions of the two-dimensional
plane. Moreover, temperature distributions like these shown in Fig. 7 can not hap-
pen in real practice since, due to the gravity loads, the molten weld metal flows
away, thus a large amount of thermal energy is removed. In this case, the welder
would consciously adjust the arc speed in order to avoid melt or burn-through, a
parameter that is considered to be constant during the simulation.
As a result, the unknown parameters involved in the analysis (e.g. heat input,
arc efficiency, material properties, double ellipsoid dimensions, heat loss, size of
the weld metal hump, variable welding speed) prevent the analyst to directly and
systematically predict with high accuracy the temperature distributions during nu-
merical welding simulation. The question that arises is whether the finite element
results shown in Fig. 7 are sufficient for any further processing.
In the case of a general heat transfer investigation and analysis, the prediction
of the temperature fields may be adequate regarding general thermal information.
Alternatively, and aiming at compensating for the governing unknown parameters,
further parametric analysis on the basis of these parameters may be carried out in
order to predict the minimum and maximum size of the weld shape and heat affected
zone. Thus it is expected that the results obtained during the pure prediction phase
should be presented in a parametric way with respect to the governing unknown
parameters. Typical results of this parametric analysis can look like these shown in
Fig. 9 regarding e.g. the arc efficiency. Thus, if dealing with the problem on the basis
of the aforementioned parametric analysis, the Finite Element Method is turned
into an efficient prediction tool that can be autonomously used, but the prediction
accuracy will obviously vary within a specific range, verified and confirmed by the
end of the actual manufacturing itself.
As a result, it is derived that due to the unknowns involved in the thermal part of
the numerical analysis, the systematic accurate prediction of the thermal response
prior to the commencement of the actual welding itself and prior to any kind of nu-
merical adaptations, tends to be more or less a myth since it is very difficult or even
impossible to exactly estimate the actual values of all the unknowns involved. On
the other hand the presentation of the thermal results on the basis of parametric anal-
ysis aiming at compensating for the unknowns is more than reasonable. However,
the main governing parameters selected by the user depend on the analysis.
5 The Adaptation Procedure, Results and Discussion
In case of further processing aiming at a thorough micro-structural characterization
of the heat affected zone and weld metal, the current model presented until now
is considered insufficient. It is also doubtful whether the calculated temperature
response is sufficient for further analysis of the mechanical response of the sys-
tem, since the weld metal shape and size and the temperature distribution within
the heat affected zone are considered as essential parameters for the mechanical re-
sponse of thin steel plates. This topic has been also discussed by Camilleri et al. [17],
Kuzminov [18], Vinokurov [19], and Radaj [1].
The Accurate Prediction of the Thermal Response of Welded Structures 523
Fig. 9 Typical results regarding the weld metal shape and size on the basis of parametric analysis(units in K)
For the above reasons, an adaptation procedure was followed. During this adap-
tation, the surface convective loads applied on the bottom side of the plate were
modified in order to account for the additional heat losses that were not taken into
account [20], such as heat diffusion due to plate contact with the welding table and
to compensate for the unknowns involved in the analysis. The value of the convec-
tion heat transfer coefficient was tuned until good agreement was attained between
numerical and experimental results regarding the shape of the weld metal only. This
procedure allows the adaptation of the numerical and experimental results but is
strictly case-dependent and aims at the utilization of the specific thermal model
for further investigation of similar welding set-ups only. It also allows the implicit
consideration of all heat losses that are not taken into account during the initial
524 D. Karalis et al.
Table 2 Maximum temperatures and cooling rates Ta-max (◦C)/Δt8/5 (s)
Measured FEA FEA
As predicted Adapted
Mid-plane position – y (m)0.003 1,280/22 1,500/21 1,338/18
0.004 1,140/22 1,402/21 1,264/18
0.005 941/22 1,292/21 1,156/18
0.080 83 107 87
Fig. 10 Liquidus isotherm of the weld metal cross section. The model has been adapted to realmeasurements (units in K)
modeling procedure. Similar adaptation methods are discussed by the authors for
non conventional welding techniques (solar welding) [21].
The temperature values of the initial and adapted finite element model, together
with the measured temperatures are shown in Table 2. The extension of the weld
metal at the same cross section (x = 0.350m) is shown in Fig. 10 for the adapted
model. In this case, both weld metal size and shape, cooling rates and maximum
temperatures are considered to be in better agreement with experimental results, but
still not exact. Notice, that the adapted numerical model can not perfectly match
the experimental results, which validates the assertion presented before, that the
accurate prediction prior to the commencement of the actual welding itself and prior
to any kind of numerical adaptations is unlikely to be realized on a scientific and
clearly documented basis.
The heat affected zone shown in Fig. 11 extends up to Δy = 0.0095m from the
axis of symmetry (y = 0m) and is considered to be in good agreement with the
experimental results which extension was Δy = 0.008m. The cooling rate calculated
at the far end of the heat affected zone (y = 0.0095m, z = 0.002m) was Δt8/5 =16.3s which is a bit less compared to areas of the heat affected zone close to the
weld metal, as shown in Table 2. This small difference of the cooling rate between
the two areas of the heat affected zone leads to the assumption that a constant mean
The Accurate Prediction of the Thermal Response of Welded Structures 525
Fig. 11 Isotherm of 1,053K(780◦C) for the heat affected zone (model has been adapted to realmeasurements)
WM HAZ BM
Fig. 12 Microstructure of the weld metal, heat affected zone and base metal
cooling rate value along the transverse axis would suffice for further micro-structural
or mechanical modeling of the heat affected zone for the adopted welding.
The micro-structural state of the weld metal, heat affected zone and base metal
are also shown in Fig. 12. The base metal consists of a mixture of ferrite and pearlite.
The heat affected zone consists of a mixture of bainite, ferrite and pearlite. The
weld metal consists of fine grained ferrite. Thorough investigation as far as the mi-
crostructure of low-alloy steel weld metals is concerned has been carried out by
Bhadeshia et al. [22]. In his study, mixture of allotriomorphic ferrite, Widmanstatten
ferrite side-plates, acicular ferrite and small quantities of microphases are mentioned
as typical microstructure constituents in similar low carbon weld metals. Martensite
was absent in the entire cross section of the weld, except for a few areas close to the
boundary zone between weld metal and heat affected zone. The amount of marten-
site investigated in this area was treated as negligible by the authors.
The measured cooling rate between 800–500◦C is plotted on the CCT diagram
[13] as shown in Fig. 13, while the micro-hardness distribution along the transverse
direction from the weld is shown in Fig. 14. From Fig. 13 it is derived, that the
final micro-structural state of the heat affected zone would be a mixture of fer-
rite, pearlite and bainite with a mean hardness value between 353 and 254 HV.
526 D. Karalis et al.
Fig. 13 Cooling curve plotted on the CCT diagram
Fig. 14 Micro-hardness distribution along the transverse direction at mid-plane
This mean hardness is also proved by the experimental micro-hardness distribu-
tion shown in Fig. 14, in which the weld metal, the heat affected zone and the base
metal have average hardness equal to 250, 300 and 220 HV, respectively. The maxi-
mum austenitization temperatures Ta-max calculated by the numerical analysis along
the heat affected zone from y = 0.007m to y = 0.0095m is shown in Fig. 15. The
maximum temperatures reached (shown in Fig. 15 and Table 2) together with a
mean value of cooling rate explain the micro-hardness profile within the heat af-
fected zone obtained by the experimental measurements shown in Fig. 14 [1–3,12].
The Accurate Prediction of the Thermal Response of Welded Structures 527
Time (s)
y=0.007m
y=0.0095m
0.00
0.50
x103
Ta-max (K)1.00
1.50
0.40 0.80 1.20 1.60 2.00
Fig. 15 Maximum austenitization temperature Ta-max (K) calculated in the heat affected zone,from y = 0.007m to y = 0.0095m, at mid-plane (step of 0.0005 m)
Maximum austenitization temperatures and the mean cooling rate presented above
can be further used for the exact description of the micro-structural dependence of
the mechanical properties of the heat affected zone in a post-mechanical simulation.
6 Conclusions
The aim of the finite element analysis, as far as welding is concerned, is to predict
the transient and steady state response of the welded system prior the welding itself.
It aims at solving for temperatures and deformations, thus predicting the final struc-
tural quality providing a significant tool for the design of marine structures and their
strength assessment.
Normally, a distinct deviation between numerical and experimental results is ex-
pected due to the unknowns involved and due to the increased complexity. Unknown
material properties, arc efficiency, micro-structural dependency and the total heat
loss are mentioned as typical common unknowns. A parametric analysis with re-
spect to the governing unknown parameter(s) selected by the user may help better
understand the range of this deviation. This distinct deviation generated during the
early prediction phase (which turns the systematic accurate pure prediction into a
myth) is not always clearly reported by investigators, since the numerical results
published may already contain a kind of calibration or adaptation. Furthermore, the
range of this deviation is treated as the decisive criterion for (a) further thorough
investigation using the same numerical model, or (b) numerical model adaptation.
The latter aims at adapting the numerical analysis to the real welding world, thus
compensating for the governing unknowns. Attention should be paid whether the
adaptation followed is general or case dependent. Thorough investigation of the
process and analysis using the adapted model is then suggested.
528 D. Karalis et al.
As far as the specific study is concerned, a distinct deviation between numerical
and experimental results was observed during the prediction phase as the weld metal
predicted by simulation was larger in size and shape than in real welding. A case-
dependent adaptation procedure on the basis of the weld metal shape and size was
proposed in order to adapt numerical and experimental results. The latter is a cost
effective adaptation procedure as it does not require any temperature measurements.
Furthermore the weld metal size can easily be measured in situ at least for the single
pass welds. The adapted model on the basis of the weld metal shape presented satis-
factory results compared to the magnitudes calculated by the numerical simulation.
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