2008 karalis papazoglou pantelis

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: [email protected], [email protected]

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.


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 – –


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]


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.


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


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)


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


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].


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


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


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.


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].


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.


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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