validating the accuracy of heat source model

International Journal of Engineering & Technology IJET-IJENS Vol: 11 No: 05 9

111505-6868 IJET-IJENS @ October 2011 IJENS I J E N S

Abstract— Welding process generally is modeled as a moving

heat source over a solid. This paper used Goldak’s ellipsoidal

moving heat source model. Goldak has proposed a volumetric

heat source model according to the mathematical expressions:

2

2

2

2

2

2333

'''

),,(

36zyx rr

y

r

x

zyx

yx eeerrr

qq

. For a known heat

input value, crucial parameters of the Goldak’s heat source model

are rx, ry and rz. Using rx, ry and rz equal to 5mm, 2mm and 3mm

respectively; a well match temperature histories with

experimental result at observed positions and weld pool shape can

be obtained.

Index Term— Goldak’s heat source models, temperature

history, temperature field

I. INTRODUCTION

MANY benefits can be achieved through welding simulation.

Production cost can be reduced by limiting try and error of

experimental welding. Using simulation, welding risk can be

minimized in the earliest stage of the product development

cycle. Welding simulation can also ascertain the level and

distribution of residual stresses [1]. Welding simulation can be

used as a tool for study such as material behaviors under

welding phenomenon [2], the effects of weld metal yield

strength to residual stress [3] and the roles of phase

transformation in the residual stress development [4]. Welding

simulation is proposed to be used as assessment tool [5], and it

is expected welding simulation to be used as a complement of

experiment procedure in determining Welding Procedure

Standard (WPS) [6].

Welding process is modeled as a moving heat source over a

solid. Heat source can be modeled as a point heat source [7,8].

Point heat source is heat load with value equal to generated

heat q (J/s) over a nodal at a solid. Heat source may be

modeled as a surface heat source "q (J/m2s) [4,9,10]. Surface

heat source is heat flux that is heat generated over certain area.

The heat flux can be uniformly distributed or distributed

according to Gaussian distribution. Heat source can also be

represented as a volumetric heat source '''q (J/m3s) [11,12].

Volumetric heat source is a body heat load applies for certain

Djarot B. Darmadi is a Brawijaya University - Indonesia lecturer, he is

studying at University of Wollongong – Australia (e-mail :

[email protected] or [email protected] )

volume. As in surface heat source, volumetric heat source can

be uniformly distributed or distributed according to certain

pattern.

The welding process involves many different phenomenon

namely thermal, mechanical and metallurgical phenomenons.

In thermal model heat input from heat source is used to heat

and melt the welded metal. The heat is conducted away from

the heat source into base metal and the heat is lost to the

environment by convection and radiation and also by

conduction to contacting bodies. In thermal model temperature

history of certain node and temperature field for certain time

can be observed.

Analysis of welding process is often considered as a coupled

problem. When thermal model is coupled by mechanical

model, the analysis is usually called as Thermo-Mechanical

analysis (TM). Most analysis is performed in two steps:

thermal analysis followed by mechanical analysis. In TM

analysis temperature distribution in thermal analysis is used as

thermal load. Strain and stress as a function of time because of

the thermal load can be observed. Usually the effect of

mechanical model to thermal model is neglected. For certain

material, solid state phase transformation exists when heated to

such high temperature as in welding process. Since phase

transformation affects thermal and mechanical properties of

the welded material, it should be included in the analysis. If

the analysis includes phase transformation considerations, the

analysis is called as Thermo-Mechanical-Metallurgical (TMM)

analysis.

No matter until what extend the analysis will be carried out,

thermal analysis as a basic of welding phenomenon should be

correct. The most important thing in the thermal analysis is the

heat source model. The defects on the heat source model

mislead the next analysis. In this paper the accurate model of

heat source of bead-on-plate welding is proposed. The

validation is done by observing temperature histories of

measured nodes and comparing the predicted and measured

weld-pool shape.

II. GAUSSIAN SURFACE HEAT SOURCE MODEL

Since heat torch transmits heat over a surface, surface heat

source (heat flux) is closer to the real condition than point heat

source. Instead of uniformly distributed, many researchers

have used distributed surface disc heat source model according

Validating the Accuracy of Heat Source Model

via Temperature Histories and Temperature

Field in Bead-on-plate Welding

Djarot B. Darmadi

mailto:[email protected]

mailto:[email protected]



to Gauss distribution. For Gaussian distributed heat source,

heat at certain distance (ri) from heat source centre has value

according to equation 1.

2/"

0

" oi rrC

i eqq

(1)

where "

0q is heat flux generated at the center of heat source

model, ro is the outer disc radius and C is an arbitrarily

constants. It is generally assumed that the heat value at the

outer radius is 5% of the maximum heat at the center of heat

source. Using this assumption, the constant C is closed to 3

and equation (1) can be represented as in equation 2.

2/3"

0

" oi rr

i eqq

(2)

In Cartesian x-y coordinate system, equation (2) can be

expressed as in equation (3).

2

2

2

2 33

"

0

" oo r

y

r

x

i eeqq

(3)

III. GOLDAK VOLUMETRIC HEAT SOURCE MODEL

The volumetric moving heat source model is pioneered by

Goldak et.al. [13]. The existence of digging and stirring of arc

welding such as distributed pressure, surface tension and

buoyancy forces have been known in practical welding. Since

all of those phenomenons are distributed throughout a volume

of material, Goldak introduced volumetric heat source. The

relation between welding physics and volumetric heat source

model is well described by Gilles et.al. [14] as shown at figure

1.

If the welding process moves parallel to the z axis, and

represents a moving abscissa parallel to the z axis, the heat

load at a certain small increment volume inside an ellipsoid

can be expressed by distributed volumetric heat load as

expressed by equation (4). 222'''

0),,('''

CByAx

yx eqq (4)

A, B and C are constants; '''

0q is volumetric heat source

generated at heat source center. For simplification, Goldak

assumed weld plate as an infinite solid. Considering energy

conservation and that welding applied on a plate, i.e. semi

infinite solid, equation (5) is obtained.

0 0 0

'''

0

222

822 dxdydeqVIq CByAx (5)

where is welding efficiency, V is voltage (volt) and I is

electrical current (amp).

It is known mathematically that )(.2

12

terfdtet , and

at the limits 2

1

0

2

dte t . As a result equation (5) can be

written as in (6).

ABC

qq

'''02 (6)

Analog to Gaussian distributed surface heat source model,

the ratio between the minimum heat flux at the center of

ellipsoid and maximum heat flux at the ellipsoid center is

taken as 5%. Hence for elements at (rx,0,0), (0,ry,0) and

(0,0,rz) '''

0

"

),,( %5 qq yx

; and using equation (4) and (6),

equation (7) can be obtained for the Goldak heat source

model.

2

2

2

2

2

2333

'''

),,(

36zyx rr

y

r

x

zyx

yx eeerrr

qq

(7)

The maximum value of equation (7) is

zyx rrr

qq

36'''

0 at

position (0,0,0). Considering this condition and substituting

2

2

2

2

2

22 333

zyx

err

y

r

xr

, equation (7) can be simplified to

equation (8).

2

'''

0

'''

),,(er

yx eqq

(8)

IV. EXPERIMENT PROCEDURE BY NET

A major issue in modeling is accuracy and validity. To this

end the European Network on Neutron Techniques

Standardization for Structural Integrity (NeT) has published

experimental data and procedures which can be accessed at

https://odin.jrc.ec.europa.eu [15,16]. Experimental work was

carried out using bead-on-plate (bop) welding. Nine

thermocouples were attached at different measured points. The

welding procedures are summarized in table 1. Four identical

plate specimens (called as A11, A12, A21 and A22) are

https://odin.jrc.ec.europa.eu/



produced. A sketch diagram for the welding set up and

thermocouple positions are presented in figure 2 and figure 3

respectively. It should be noted that the origin of coordinate

system is at the weld stop end. The positions of the

thermocouples based on the chosen coordinate system are

tabulated in table 2.

Four sets of temperature histories for four specimens were

obtained from nine thermocouples. As the thermocouple Tc8

was not pushed far enough into the hole and there is no clear

reference to where the data was recorded, the Tc8

thermocouple was not considered. For thermocouple Tc9, the

data from specimen A21 were also excluded since they showed

a lower temperature and inconsistent with data from other

specimens [17].

The temperature dependent properties of the base metal and

welding filler were obtained from NeT [16]. The material

properties for the base metal and the weld metal are shown at

Table 3. The density and Poisson‟s ratio for both materials are

7966 kg/m3 and 0.294 respectively. In figure 4 are shown

thermal properties for both metals graphically.

V. FEM MODELING

In this paper, finite element model and simulation have been

carried out using ANSYS Parametric Design Language

(APDL) mode due to its flexibility over the Graphics User

Interface (GUI) mode. To obtain a good model of the heat

source, a very fine mesh should be provided in the area where

the heat source will pass through. Equation (7) can be used to

judge how fine the meshes need to be, which depends on rx, ry

and rz values; the higher these values the coarser the mesh

needs to be. Brick elements of 0.3mm brick mesh have been

used. The adequacy of the mesh size is analyzed after rx, ry and

rz values are determined.



A one-half model was used due to symmetry. The model is

comprised of 43,639 nodes and 71,128 elements of solid 70

elements. Denser meshes close to the weld line are needed due

to high temperature gradient at this position. Very fine meshes

in the weld area are needed to match closely the moving heat

source. Dense meshes are also applied at positions surrounding

a thermocouple to locate thermocouple positions accurately.

The final FEM mesh design is shown in figure 5.

Firstly the welding efficiency should be found. Since there

are no experiment data provided by NeT, welding efficiency

was determined by fitting the peak temperature at Tc9. The

thermocouple was chosen since it is least influenced by factors

such as heat source model, and heat from arc radiation. Only

global heat input affects it significantly. Moreover the

thermocouple indicates the temperature at the quasi steady

state and it is easy to locate accurately in FEM mesh. Normally

the welding efficiency of TIG ranges between 65% and 88%

[18]. Estimation of the welding efficiency was made based on

a simple model to save computer time. The finite element

mesh of the simplified model is shown at figure 6. A stepped

mesh was used to decrease the number of elements. The heat

rate intensity q (J/s) can be calculated from the product of the

heat input and welding speed. The heat rate intensity is applied

as point heat load. Data of the heat input and welding speed

are obtained from NeT. Observing peak temperature at Tc9 of



the simulation result on simplified model, the welding

efficiency was found to be 76%. Convection coefficient and

emissivity are assumed to be 5 W/m2.K and 0.5 respectively.

Ambient temperature is assumed as 25C based on the

averages of thermocouple measurements. Heat source

parameters (rx, ry, rz) are varied as (3mm, 3mm, 3mm), (5mm,

3mm, 3mm), (5mm, 2mm, 3mm) and (5mm, 2mm, 2mm).

Temperature histories and temperature field are evaluated

again experiment data provided by NeT.

Brick mesh sizes along the heat source trajectory are

0.3mm. The body heat source values depend on the distance

from the centroid of the elements to the center of the heat

source. Since the brick mesh sizes are 0.3mm and applying to

equation (7), comparison between '''

0

'''

),,( / qq yx

for each heat

source model is presented at table 4. The least value is 97.90

for [5,2,2] model which means the maximum body heat will be

represented by 97.90% of its value, and it can be assumed that

the mesh size along the weld path is sufficiently fine.

The welding simulation used element birth-and-death

technique approach. In the element birth and death technique,

the metal bead is growing with the moving heat source. First,

all of weld bead elements are “omitted” using EKILL

command in ANSYS-APDL and the growth is modeled using

EALIVE command. Born elements are elements of the weld

bead which are already left behind the moving heat source.

When the elements are born, their temperature should be at the

melting embedded filler metal temperature which is

superheated at 2400C [19]. Instead of applying temperature

node load, the body heat load rate ( '''q ) at elements was

applied. The body heat load value is such that it can produce a

temperature of 2400C at the growing weld bead. The heat

needed to elevated the weld pool from the initial temperature

of 25C to 2400C was evaluated using q = mcT. It should

be noted that the specific heat c, is temperature-dependent as

expressed in Table 3b. The specific heat at a certain

temperature range was taken as the mean value between these

ranges. The heat rate can be obtained using

v

STmcq

expression. Finally, the body heat load which should be

applied at the born weld bead can be obtained using equation

(9).

v

STcq ''' (9)

VI. RESULTS AND DISCUSSIONS

Temperature histories for varied heat source model are

compared as shown in figure 7. Figure 7a, 7b and 7c describe

temperature histories for thermocouple at the top surface. In

figure 7a are compared temperature histories at weld start

point, Tc1 for the closer thermocouple and Tc4 for the farther

one. Tc1 peak temperature are 245.127C, 257.742C,

254.748C and 251.251.183C for [3, 3, 3], [5, 3, 3], [5, 2, 3]

and [5, 2, 2] respectively. All of those peak temperatures are

achieved when t = 6.495s except for [3, 3, 3] heat source

model which, is obtained when t = 7.024s. Tc4 peak

temperature are 142.980C, 146.441C, 145.543C and

144.111C when time equal to 11.783s, 11.254s, 11.254s and

11.254s for those [3, 3, 3], [5, 3, 3], [5, 2, 3] and [5, 2, 2]

respectively.

Three important notes can be underlined here, first is that

the model with rx = 3mm showed split results with others in

term of peak temperature and when (time) the peak

temperature is achieved. Variation in the other heat source

model (ry and rz) does not show significant difference.

Regarding the coordinate system shown at figures 2 and 3, rx is

the size of ellipsoidal heat source model in the transversal

direction parallel to the surface of the base metal. Tc1 and Tc4

are the positions at surface those perpendicular to the weld

line. It may be the reason why rx affects the temperature

histories of the thermocouple in the coincide direction.

Evaluating standard deviation for Tc1 and Tc4, those are

5.420 and 1.531 respectively. This means Tc1 is more

susceptible to heat source model than Tc4; it is the second

notes that the closer position is more affected by the heat

source model than the farther one. The last but not the least

note is that using lower rx produces lagging time of the peak

temperature. Since the thermocouple is farther from heat

source model for the lower rx the longer time is needed for the

heat from the heat source model to reach the observed

position. Using rx = 3mm the peak temperature for Tc1 is

achieved at 7.024s whilst for rx = 5mm is at 6.495s that

lagging by 0.529s. Evaluating temperature histories for Tc4,

peak temperature for rx = 3mm is at 11.783 whilst for rx =

5mm is at 11.254s. Again the peak temperature with rx = 3mm

is lagging by 0.529s. The other insight which may also

precious is when evaluation is done for the same heat source

model but for different position (Tc1 and Tc4). Evaluating rx =

3mm peak temperatures are at 7.024s and at 11.783s for Tc1

and Tc4 respectively. Longer time for peak temperature of Tc4

is caused by the farther position than Tc1. The time for peak

temperatures differ by 4.759s. Using rx = 5mm peak

temperature for Tc1 and Tc4 are at 6.495s and 11.254 which

also differ by 4.759s with time lagging for Tc4 due to it farther

position to the heat source center.



Figure 7b describes temperature histories for position in the

middle of weld bead, Tc2 and Tc5 for closer and farther

position respectively. In figure 7c are shown temperature

histories for thermocouple at the weld end point, for the closer

(Tc3) and farther (Tc6) one. The peak temperatures and the

times when the peak temperatures is produced for varied heat

source model and for different position are summarized at

table 5. The same conclusions with thermocouple on the start

point for middle and end point thermocouples can be derived.

Peak temperatures at the middle position show higher values

than the start point thermocouples for the same heat source

model. That higher temperature as a result of the facts that the

middle position has been preheated by the heat source center

before the heat source center derived middle thermocouples z

coordinates.

The lower peak temperatures (compare to the middle

thermocouple) are exhibited by the thermocouple at the weld

end. Although the end point thermocouple are also preheated,

but the weld torch is extinguished instantaneously when the

weld torch center arrives at the end point. This sudden

extinction causes the lower peak temperature.

Next evaluation is done for thermocouple inside the base

metal (Tc7) and bottom-surface thermocouple (Tc9). Peak

temperature and time for the peak temperature for [3, 3, 3], [5,

3, 3], [5, 2, 3] and [5, 2, 2] heat source models at Tc7 are

256.639C, 254.720C, 252.970C and 252.289C

respectively which all achieved at 30.043s. The standard

deviation for the peak temperatures is 1.947. The low standard

deviation means no significant affect is observed because of

the heat source model variation. For the Tc9 the peak

temperatures are 200.593C, 200.577C, 199.298C and

198.351C at 33s. The standard deviation is even lower than

the standard deviation for Tc7 (1.087).

Temperature field at the mid-plate cross section are shown

at figure 8 for varied heat source model. The picture describes

temperature fields when heat source exactly at the middle of

the plate, thus it shows the maximum temperature at the cross

section position. It should be noted that the melting

temperature of the base metal is 1400C which means

isothermal line for 1400C also shows weld pool shape.

Observing figure 8, arrives to conclusion that heat source

model with rx, ry and rz equal to 5mm, 2mm and 3mm

respectively gives better weld pool shape than the others. With

the heat source model, the 1400C isothermal lines have the

width equal to the weld-bead.

The next comparison is made between experimental result

with thermal model of [5,2,3] heat source. In figure 9 is shown

comparison between weld-pool shape from [5,2,3] heat source

model and from experimental results. It can be said that the

FEM model of weld pool shape shown good agreement with

the experimental result. Not only has the width of the weld-

pool matched the experimental cross section but also the depth

of the weld pool.

In figure 10 temperature history from [5,2,3] heat source

model is compared to the experimental results. Four sets of

experimental temperature histories are obtained from four

specimens (A11, A12, A21 and A22). From these figures it

can be concluded that FEM simulation has shown a good

agreement with experimental results. Apart from showing the

general trend, the transient temperature values generally also

match the experimental data. For the close field

thermocouples, the FEM model predicts a lower temperature

than the measured peak temperature. The lower prediction may

be caused by the radiation of torch arc which was not modeled.

The „below bead‟ thermocouple (Tc7) from FEM model shows

a higher value than that measured by the thermocouple. The



„below bead‟ thermocouple was inserted 6.5mm deep in a hole

with diameter of 1.2mm. The possibility that the thermocouple

is not fully located at the tip of the hole is high. Incomplete

insertion could result in a larger distance from the heat source

and a lower measured peak temperature. If the measured point

is only 0.5mm farther from the heat source, simulation using

the ANSYS model showed that the peak temperature will fit

with the measured peak temperature.

VII. CONCLUSION

Varied heat source model has no significant difference for

temperature histories at observed positions, however small

different is shown at thermocouples close to the weld-bead.

Temperature field for close positions and weld pool shape are

significantly affected by heat source model. Observing

temperature histories and weld pool shape, heat source model

with rx, ry and rz equal to 5mm, 2mm and 3mm respectively

gives well match results with experimental data.

VIII. FUTURE WORKS

Practically, mechanical properties of resulted welding joint

are more preferable than thermal results (temperature history

or temperature field). The typical recent topic of interest of the

mechanical properties is residual stress. Discussion on residual

stress using the above validated thermal model will be a

precious work.

REFERENCES [1] ESI Group Released Notes (2006), The welding simulation solution,

p.4.

[2] Andrea Capriccioli, Paolo Frosi (2009), Multipurpose ANSYS FE

procedure for welding processes simulation, Fusion Engineering and

Design vol. 84 pp. 546 – 553.

[3] Dean Deng, Hidekazu Murakawa and Wei Liang (2008), Numerical and

experimental investigations on welding residual stress in multi-pass

butt-welded austenitic stainless steel pipe, Computational Material

Science, vol.42, pp.234-244.

[4] Deng Dean, Murakawa Hidekazu (2006), Prediction of welding

residual stress in multi-pass-butt-welded modified 9Cr-1Mo steel pipe

considering phase transformation effects, Computational Materials

Science, vol.37, pp. 209 – 219.

[5] Viorel Deaconu (2007), Finite element modeling of residual stress – a

powerful tool in the aid of structural integrity assessment of welded

structures, 5th Int. Conference Structural Integrity of Welded Structures,

pp.1 - 9, Romania.

[6] Lars-Erik Lindgren (2001), Finite element modeling and simulation of

welding part 1: increased complexity, Journal of Thermal Stresses, vol.

24, pp. 141 – 192.

[7] M. Van Elsen, M. Baelmans, P. Mercelis and J.P. Kurth (2007),

Solution for modeling moving heat source in a semi-infinite medium

and application to laser material processing, International Journal of

Heat and Mass Transfer, vol. 50, pp.4872 – 4882.

[8] S. Dragi and V. Ivana (2009), Finite element analysis of residual stress

in butt welding two similar plates, Scientific Technical Review, vol.59,

no.1, pp. 57 – 60.

[9] Z. Chai, H. Zhao and A. Lu (2003), Efficient finite element approach

for modeling of actual welded structures, Science and Technology of

Welding and Joining, vol.8, no.3, pp. 195 – 204.

[10] F. Lu, S. You and Y. Li (2004), Modeling and finite element analysis

on GTAW arc and weld pool, Computational Materials Science, Vol.29,

pp.371 -278.

[11] Lei Yu-cheng, Yu Wen-xia, Li Chai-hui and Cheng Xiao-nong (2006),

Simulation on temperature field of TIG welding of cooper without

preheating, Transaction of Nonferrous Metals Society of China, Vol.16,

pp.838 – 842.

[12] [12] X. Shan, C.M. Davies, T. Wangsdan, N.P.O‟Dowd and K.M.

Nikbin (2009), Thermo-mechanical modeling of a single-bead-on-plate



weld using the finite element method, International Journal of Pressure

Vessels and Piping, vol. 86, pp.110 – 121.

[13] John Goldak, Aditya Chakravarti and Malcolm Bibby (1984), A new

finite element model for heat sources, Metallurgical Transactions B,

vol. 15B, pp.299 – 305.

[14] Philippe Gilles, Walid El-Ahmar and Jean-Francois Jullien (2009),

Robustness analyses of numerical simulation of fusion welding NeT-

TG1 application : “Single weld-bead-on-plate”, International Journal

of Pressure Vessels and Piping, vol.86, pp.3 – 12.

[15] C.E. Truman and M.C. Smith (2009), The NeT residual stress

measurement and modeling round robin on a single weld bead-on-plate

specimen, International Journal of Pressure Vessels and Piping, vol. 84,

pp.1 – 2.

[16] Protocol for Phase 2 finite element simulation on the NeT single-bead-

on-plate test specimen, https://odin.jrc.ec.europa.eu

[17] M.C. Smith and A.C. Smith (2009), NeT bead-on-plate round robin:

Comparison of transient thermal prediction and measurements,

International Journal of Pressure Vessels and Piping, vol.86, pp.96 –

109.

[18] Kou, Sindo (2003), Welding metallurgy, John Willey & Sons Inc.

Publication.

[19] M.J. Painter and M.H. Davies (1994), Numerical modeling of the gas

metal arc welding process, Annual Report – CRC Project: 93.04.

https://odin.jrc.ec.europa.eu/

validating the accuracy of heat source model

Documents

point heat source

heat flux

volumetric heat source

volumetric heat source

heat q js

surface heat source

thermal model heat input

body heat load