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Journal of Materials Processing Technology 161 (2005) 497503

FEM simulation on microstructure of DC flash butt weldingfor an ultra-fine grain steel

Weibin Wanga, Yaowu Shia,, Yongping Leia, Zhiling Tianb

a School of Materials Science and Engineering, Beijing University of Technology, Beijing 100022, PR Chinab Central Iron and Steel Research Institute, Beijing 100081, PR China

Received 25 September 2003; received in revised form 22 July 2004; accepted 22 July 2004

Abstract

Finite element method (FEM) was used to simulate the process of a direct current (DC) flash butt welding (FBW) processing. In the

simulation thermalelectrical coupling and flash process are considered. Element live-death method was adopted to simulate metal melting

and metal loss during the flash process. Then, the temperature field of the welded joint was computed. In addition, a Monte Carlo (MC)

simulation technology was utilized to investigate the Austenite grain growth in the heat affected zone (HAZ) of the FBW for the ultra-fine

grain steel. On the basis of the result of the temperature field, an experimental data-based (EDB) model proposed by Gao was used to establish

the relation between the MC simulation time and real time in the grain growth kinetics simulation. Moreover, thermal pinning was considered

due to the effect of temperature gradient on HAZ grain growth of welded joint. The simulations give out the grain size distribution in HAZ

of the FBW welded joint for the ultra-fine grain steel and effect of grain growth due to temperature gradient.

2004 Elsevier B.V. All rights reserved.

Keywords: Ultra-fine grain steel; DC flash butt welding; Monte Carlo method; Microstructure simulation

1. Introduction

Ultra-fine grain steel is a newly steel developed from

TMCP(thermo-mechanical control process) technology. Fer-

rite grain size with micrometer or sub-micrometer was pro-

duced by the controlled thermo-mechanical process. The

steel is with super finegrainsize andsuperpurity. That greatly

improves its strength and toughness. Grain size is a key pa-

rameter dependent on the properties of materials. Due to the

grain size of the ultra-fine grain steel is very fine, the coarse

grain in the HAZ may deteriorate toughness of the HAZ[1].

In 1997, Japanese scientists started a project of super

steel [2,3]. In the same year, a project of 21st century struc-

ture steel began in Korea [4]. Later, a great fundamental

study of a new-generation steel named as Projects 973 be-

gan in China in 1999. In the project welding consumables

Corresponding author.

E-mail address: [email protected] (Y. Shi).

and welding technology were also studied in order to make

the welded joint have over 90% properties of the parent metal

[5,6].

In the present, the researches on the adaptability of

laser welding, MAG welding technology to the ultra-fine

grain steel have been widely conducted now. The FBW

technology is a high efficient joining process, and widely

used in train manufactory, long transportation pipeline

construction, architecture construction and other engineer-

ing field. Being a solid state joining process, the FBW

process is different from the common fusion welding.So, the research on the welding technology and its ef-

fect on the microstructure of the ultra-fine grain steel is

needed.

As there exist several controllable welding parameters in

the FBW, the choice of the welding technology is complex.

Thus, numerical simulation is useful tool for studying the

joining process of FBW.

In this work, FEM is used to simulate the welding process

of the FBW for the weld HAZ for the ultra-fine grain steel.

0924-0136/$ see front matter 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.jmatprotec.2004.07.098

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498 W. Wang et al. / Journal of Materials Processing Technology 161 (2005) 497503

Table 1

Chemical composition (wt.%) and tensile strength of 400MPa ultra-fine

grain reinforcement steel bar

C 0.18

Si 0.19

Mn 0.60

P 0.015

S 0.009Cr, Ni 0.3

Cu 0.17

b (MPa) 526.4

Fig. 1. Microstructure of 400MPa ultra-fine grain reinforcement steel bar.

The simulation includes the instantaneous temperature field,

stressstrain field. On the basis of the computed temperature

field, Monte Carlo method is used to analyze the Austenite

grain growth in the HAZ. However, discussion on the weld

stressstrain and weld formation will appear in other publi-

cation.

2. Materials and experiment

2.1. Test materials

An ultra-fine grain steel SS400 made by fining grain pro-

cess based on low carbon steel A36 is used in the test. The

reinforcement steel bar used in architecture is with diameter

Fig. 2. Morphology and microstructure of the FBW joint.

Table 2

Main parameters used in the FBW process

Mode Uniform accelerating

Flash length (mm) 12

Forging length (mm) 2.5

Flash velocity (mm/s2) 0.5

Stretch length (mm) 38

Output voltage (V) 7.2

of 20 mm and the average grain size is less than 10m. Its

microstructure consists of ferrite and pearlite. Table 1 shows

the chemical composition and mechanical properties of the

400 MPa ultra-fine grain reinforcement steel bar. Fig. 1 is the

microstructure of the base steel bar.

2.2. FBW experiments

A cam-controlled welder with power of 150 kW was used

in the flash butt welding. The main parameters used in pro-ducing the welded joints are given in Table 2.

During the welding process NiCr/NiSi thermal couples

were welded in the bottom of small holes drilled in the dif-

ferent position away from the interface of the butt-welded

joints. Metallographical examination was made from lon-

gitudinal section of the welded bar after welding. The

specimen was etched by 3% nitric acid ethanol solution.

Fig. 2(a) shows the morphology of the welded joint. The

coarsened microstructure at the weld interface is shown in

Fig. 2(b).

Vickers diamond hardness was investigated along the lon-

gitudinal section of the welded joint, and the results along

the length direction are shown in Fig. 3. The solid pointsindicate the hardness located in the inside of the joint, and

the hollow points indicate the hardness located in the outside

edge of the joint. It is clear that the hardness in the outside

edge is higher than that in the inside of the welded bar, as

much higher cooling rate exists in edge of the bar. In addi-

tion, the hardness in the HAZ is higher than that in the base

metal.

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W. Wang et al. / Journal of Materials Processing Technology 161 (2005) 497503 499

Fig. 3. Hardness distribution of the FBW joint.

3. FE simulation of temperature field

3.1. Basic equations

In the numerical computation of the DC FBW process,

thermalelectrical coupling was described by the electrical

potential equation and heat transfer equation. The electrical

potential equation gave out the distribution of electrical volt-

age in the bar, and the heat transfer equation gave out the heat

generation, heat transfer and temperature distribution.

Based on the electromagnetic theory, the electrical volt-

age distribution in the body meets the Laplace equation for

given electrical current. For axial symmetrical problem, the

following differential equation can be used to describe elec-trical voltage distribution of body:

r

1

E

U

r

+

1

r

U

r+

z

1

E

U

z

= 0 (1)

where rand z are the radial and axial coordinates, separately.

Uis the potential and E the resistivity of materials. With the

increase of the welding time, the resistivity is increased. For

contacted face, there is equation ofJ= U/c, where J is the

current density.

As theFBW process is an instantaneous heat transfer prob-

lem with interior heat source, the differential equation for

axial symmetrical heat transfer is as follows:

cT

t=

r

k

T

r

+

k

r

T

r+

z

k

T

z

+ qv (2)

where T is the temperature, c the mass capacity of materi-

als, the density, k the heat transfer coefficient and qv the

heat source intensity. The values ofqv for each element will

be obtained from electrical potential field via finite element

analysis.

qv =(U/r)2 + (U/z)2

e(3)

Fig. 4. Computational model.

where e is the electrical resistivity. The instantaneous heat

generation at the welded end is described by

Qc =(U)2

Rc+ qv (4)

where Rc is the surface contact resistance and Uthe poten-

tial drop at contacted interface.

3.2. Computational model

As the geometry of the test bar was symmetrical,

2D axial symmetry finite element model was utilized. 4-

Node even-parameter element was used in the analysis.

Smaller meshes were used at the zone of strong variation

of temperatures and deformations. For the simulated bar

with diameter of 20 mm, the model consisted of nodes of

57,864 and elements of 36,720, in which cooling jig was

included.

Fig. 4 shows the computational model in the

thermalelectrical coupling computation. In the model,

(1) is the axial symmetrical boundary; (2) is the contacted

surface or flash face; (3), (5) and (7) are the outer surface of

electrode and bar; (4) is the boundary of water-cooled copper

jig; (6) is the terminal of welded bar. In the computation,a commercial software ANSYS is used with compiled

program.

3.3. Materials properties

Electrical resistivity of materials will directly affect the

heating during the FBW process. For the test steel, electrical

resistivity is strongly related to temperature. In the compu-

tation, the resistivity is indicated by the following relations,

where the resistivitye is in m, and temperature Tis inC

[7].

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e = 8.56e 13T2 + 4.9e 10T+ 1.54e 7

(T < 800 C),

e = 2.875e 10(T 800)+ 1.094e 6 (T 800C)

The heat transfer coefficient kof the steel is indicated by

the following relations, where the heat transfer coefficient is

in W/(m C).

k = 3.49e 5T2 1.05e 2T+ 52.46 (T 400 C),

k = 3.14e 5T2 4.186e 3T+ 49.39

(400 C < T 800 C),

k = 27.21 (T > 800 C)

The specific heat c and densitym are described by

c = 1.29e 4T2 + 3.218e 101T+ 451.7

(T 400 C),

c = 7.77e 4T2 + 476.5 (400 C < T 600 C)

c = 3.08T 1092.4 (600 C < T 750 C),

c = 5.46T+ 5315.0 (750 C < T 850 C),

c = 672.3 (T > 850 C), m = 7860

where the specific heat and density of the steel are in J/(kg C)

and kg/m3, respectively. Then, the enthalpy of the steel at dif-

ferent temperature is computed from the following equation:

H=

c(T) dT (5)

The heat exchange coefficients at the surface of the steel

bar and copper jig are shown in Fig. 5. The heat exchange co-

Fig. 5. Heat exchange coefficient at boundaries with temperature.

efficient at water-cooling boundary is assumed to be constant

of 3800 W/m2 C.

3.4. Contact resistance

The heating of FBW is derived from the co-effect of self-

body resistance and contact resistance. In the entire process-ing of flash welding, contact resistance exists from the pro-

cess beginning to the end. The heat generated from contact

resistance makes the proportion of 8590% of the whole heat

output. Heat sources are concentrated at the butt region of the

work pieces.

In the simulation, heat flow density was used in the inter-

face of the butt joint. Live-death element method and flash

velocity are matched each other to simulate the metal melt-

ing and flash process. So-called live-death element method is

that first the time sections was divided by whole demanded

flashing time; second, the elements used in this section was

killed after the flash simulation is finished in this time sec-

tion and the simulation results were accumulated to the nextincrement step. Then, repeat this process till the end of the

whole computation time or flash process. In a computation,

for example, each layer is 1 mm and the meshes are with 10

layers, if flash length was 10mm. Flash time is 10s under the

condition of uniform flash process. In the simulation com-

putation the time of 1 s corresponds to 1 mm. When having

finished the first 1 s computation, the first layer of 1 mm is

killed. Then the results are added to the next computation, but

the first layer is not included in the next step computation.

The coupling step length is dependent to the relation between

the real flash distance and time.

Contact resistance is dependent on the number of liquidbridges andthe current line shrinkagein thebutt interface. It is

related to flash velocity and weld section. Contact resistance

was deduced by the following formula [8],

Rc =9500K7

S2/3vf1/3j 106 (6)

where K7 is a factor of steel property, and K7 = 1 for low

carbon steel. S is the welded cross-section, cm2, vf the flash

velocity, cm/s2, j the current density, A/mm2.

4. Monte Carlo simulation of microstructure

4.1. MC simulation of grain growth

The MC methodology to simulate the grain growth has

been described in detail in the literature [9,10]. Only the es-

sential of MC model is addressed here. First, a grain struc-

ture is mapped onto a discrete lattice. Each of the lattice sites

is assigned a random orientation number between 1 and N,

where Nis the total number of grain orientations. Each grain

is then represented by a collection of lattice. Grain boundary

segment is defined to lie between two sites of unlike orien-

tation. The local interaction energy, E, is calculated by the

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Hamiltonian:

E = J

nj=1

(SiSj 1) (7)

whereJis a positive constant which sets the scale of the grain

boundary energy, the Kroneckers delta function:

SiSj = 1 (Si = Sj)

SiSj = 0 (Si = Sj)(8)

where Si is the orientation at a randomly selected site i and

Sj are the orientations of its nearest neighbors and n the total

number of the nearest neighbor sites.

The kinetics of grain boundary migration are simulated by

selecting a site randomly and changing its orientation to one

of the nearest neighbor orientations based on energy change

due to the attempted orientation change. The probability of

orientation change is defined as

p = 1, E 0 (9)

p = exp

E

kBT

, E > 0 (10)

where E is the change of energy due to the change of ori-

entation, kB the Boltzman constant and T the temperature.

Successful transitions at the grain boundaries to orientations

of nearest neighbor grains thus correspond to boundary mi-

gration. Ewas introduced by the following formula:

E = J

ni=1

(SiS0 SiSn ) = J(n1 n2) (11)

where S0 is orientation before original orientation change. Snis orientation after original orientation change. n1 and n2 are

the number of neighbor grains which have different orienta-

tion change, respectively.

Successful orientation change on the grain boundary

means grainboundary migration. The velocity vi of boundary

migration is defined as

vi = C

1 exp

Ei

kBT

(12)

where Ei is the local chemical potential on grain boundary

and Cthe grain boundary migration rate.

In Monte Carlo model, time was defined as Monte Carlo

Step (MCS) or MC simulation time (tMCS). We assumed this

model to have Ngrid points. One MCS means attempt of N

orientation changes. Relationship between simulated grain

size and simulated time is defined as follows:

log

L

= log(K1)+ n1 log(tMCS) (13)

where L is the simulated grain size measured by mean grain

intercepts, the discrete grid point spacing in the MC simula-

tion, tMCS the MC simulation time or MC simulation iteration

steps, K1 and n1 are the model constants, which are obtained

by regression analysis of the data generated from MC sim-

ulation. The MC simulation time, tMCS, is a dimensionless

quantity.

4.2. Relation between MC simulation time and actual

time

In the MC model, the grain size variation with tMCS is

largely independent of material properties and actual-time

grain growth kinetics and is only dependent on the grid sys-

tem. To get the MC model for welds, we must build the re-

lationship between MC simulated time, actual time and tem-

peratures.

The experimental data-based (EDB) model proposed by

Gao [11] was adopted to relate tMCS and actual time in this

simulation. Under non-isothermal condition it must be inte-

grated over the entire thermal cycle by summing the grain

growth in short time intervals at different temperature. In or-

der to describe a course of heating and cooling, we divide

actual time into a series isothermal element. The total valueoftMCS can be described as follows:

(tMCS)nn1 =

L0

K1

n+

K

(K1)n

exp

Q

RTi

ti

(14)

where K is a constant and Q the activation energy, both K,

and Q are obtained from experimental data. Ti the mean tem-

perature in a time interval, ti.

Since the thermal cycle in the welded joint is a function of

the distance from the welded interface, the tMCS calculated

from Eq. (14) is varied at different site. In addition the tMCS

cannot be directly applied in the MC algorithm, because thechoice of grid point for updating orientation number is ran-

dom in the MC technique. Thus the probability to select each

grid point is the same in traditional MC calculations. How-

ever, grains must grow at higher rates in regions of higher

temperature in the welded joint, where a steep temperature

gradient exists. To solve this problem, a concept of site selec-

tion probability is introduced. Site selection probability p(r)

is defined as:

p(r) =tMCS

tmaxMCS(15)

where tMCS is the MC simulation time at any site in

the region and tmaxMCS is the maximum value of MC sim-

ulation time in the domain. Both tMCS and tmaxMCS can be

calculated from Eq. (14). The tMCS variation can thus

be transformed into the variation of site selection prob-

ability and applied in MC model. Thus the spatial vari-

ation of thermal cycle is included in the site selection

probability.

4.3. Effect of hot pin on austenite grain growth

By early research, we know that maximum Austenite

grain size of actual HAZ in the welded joint is smaller

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Fig. 6. Comparisons of temperature distribution between simulation and

experiment.

than physical simulated one. That is because the growth of

large grain in the HAZ is blocked by its neighbor small

grains. This effect is related to temperature gradient, and

is so-called hot pin effect. The larger the temperature gra-

dient is, the severely blocked grain growth is in the HAZ.

That is, the thermal pinning effect tends to restrict the

grain growth within the region with a sharp temperature

gradient.

Monte Carlo method is an effective way to take research

on hot pin effect in HAZ. Grain boundary transfer rate

varies greatly in the large temperature gradient, and this

variation may occur in boundary of only one grain. By theMonte Carlo method, the difference of grain boundary trans-

fer rate in the different position is considered by the trans-

fer from t to tMCS simulation relation and the site selection

probability.

Fig. 7. Thermal cycle with distance to the interface of welded joint.

Fig. 8. Comparison of simulated grain growth in and without consideration

of heat pinning.

Table 3

Grain size of simulatedand experimental microstructure at HAZnear fusion

lineSS400 bar (grain size, m)

Simulation 110

Experiment 111

Error (%) 0.9

5. Simulation results

5.1. Distribution of temperature field

Fig. 6 shows the comparisons between temperature dis-

tribution of simulation and experiment. Even the measured

values show some dispersion, the measured and simulated

results are basically in agreement. Fig. 7 shows temperature

history of measured and simulated results in the welded joint

for the ultra-fine grain steel bar.

5.2. HAZ microstructure

Fig. 8 shows the comparison of simulated grain structure

in HAZ and bulk metal heating. From the figure, we can see

the effect of hot pin on grain growth clearly. The grain growth

due to heat pinning is smaller than that of bulk metal heating.

In addition, the grain growth in former condition is slower

than the latter one.

To view the simulationresults quantitatively, the grain size

was measured near the fusion boundary of welded joints.

The mean lineal intercept processing is used to measure the

Austenite grainsize for both simulatedand practically welded

microstructures. Table 3 shows the comparison of simulated

grain size and experimental grain size near the fusion line.

6. Conclusion

(1) Model for simulating a DC FBW processing was built

by considering the electricalthermal coupling. Then, on

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this basis the structure of welded joint can be simulated

using a Monte Carlo method.

(2) In the simulation of weld temperature field, contact re-

sistance was in consideration. Element live-death tech-

nology was adopted to simulate metal melting and metal

loss during the flash process.

(3) It is proved that the Monte Carlo method can be success-fully used in the simulation of grain growth in the welds

for the flash butt welding processing.

(4) In the Monte Carlo simulation of welds, the hot pinning

effect must to be considered. The grain size due to hot

pinning effect is smaller than that of bulk metal uniform

heating.

Acknowledgements

The authors would like to express the heartfelt thanks for

the financial support from the National 973 Key Fundamental

Research Project (No. G1998061500).

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