Numerical Simulation of Butt Curl in the Semi-DC Casting of Aluminum Slabs

Numerical Simulation of Butt Curl in the Semi-DC Casting of
Aluminum Slabs
by Nobuhito Ishikawa *Butt curl which occurs in the semi-direct chill (DC) casting of aluminum slabs cancause metal bleeding and hot cracking accompanied by coincident bowing that
leads to poor yields in slab preparation. To understand the mechanism of butt
curl, the author has proprietarily developed a solidification stress model based on the elastoplastic incremental strain theory involving solidification. The analysis using the model shows thatbutt curl grows immediately after secondary cooling water begins to impinge on the slab bottom,
but its growth rate decreases as the bottom block descends and the slab bottom is cooled
increasing in rigidity. It is also shown that the driving force for butt curl growth is the torquemoment around the center of the slab bottom, which is caused by the tensile stress generated in
the mushy zone along the sump profile.

ABSTRACT1.

INTRODUCTION

Butt curl, which occurs in the semi-DC casting of aluminum resulting in an upward curling of slab bottoms asshown in Figure 1, can cause defects such as metal
bleeding at the short side of slabs, hot cracking of slab
bottoms, and slab bending due to the asymmetricalshape of slab bottoms. When it is serious, anyone ofthese defects can result in a total discard of a slab, thus
leading to poor casting yields. Moreover, formation of
concave shapes on the short side of slab bottoms referred
to as bow requires that the slab has to be severed at thebow position to assure a product width. Accordingly,
there is a need for countermeasures that can suppress
butt curl to improve casting yields.
Butt curl suppression methods widely used heretofore
include the CO2 method that reduces the efficiency of
secondary cooling, the pulse water method, the air turbo
method, together with the recent methods of using a moldprovided with a secondary cooling water system with two
different spray angles, and of using a deep bottom block.
However, taking the CO 2 method as an example, it isnoted that, because the concentration of CO2 gas is influenced by ion concentrations in the cooling water, when
the water quality is unstable an excessively slow coolingtakes place potentially resulting in melting and crackingof the slab bottom. Thus although a set of suitable conditions has to be established in applying the countermeasure technologies mentioned above, it is difficult to generalize these technologies because they belong to technicalknow-how of each company due to slight differences intheir casting facility specifications.
* Technical Research Div., Furukawa-Sky Aluminum Corp.

Molten metal
Mold
Primary cooling
Air gap cooling

Liquid region

Secondary cooling
Mushy zone
Solid region
Width direction
Bow
Butt curl
Bottom block

Withdrawal

Figure 1

Schematic illustration of aluminum semi-DC casting.

In the study of the mechanism for butt curl generation,
Doroste 1) and Tsunekawa 2) made a quantitative measurement of butt curl growth using position sensors cast in
slab bottoms, in which they reported that butt curl rapidly
grew immediately after secondary cooling water impinged
on the slab bottom. Whereas their reports capture thephenomenological essentials of butt curl growth mechanism, they seem to be insufficient in terms of explanation
for the solidification stress. Accordingly, the author has
developed a solidification stress model based on theelasto-plastic incremental strain theory, in which solidification strains are handled to be definitely different from thermal strains in calculating the process of butt curl growth,

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Numerical Simulation of Butt Curl in the Semi-DC Casting of Aluminum Slabs

to make comparative evaluations with phenomenologicalresults. In the analysis, the casting process was traced
over a withdrawal length of up to 1500 mm from the
beginning of casting until the end of butt curl growth,whereby the amount of butt curl was calculated using thedata on coordinate variations with respect to the initial(molten) slab shape. In particular, attention was paid tothe cooling conditions and temperatures at the initialstage of casting where butt curl rapidly grows, the solidification conditions, and the stress conditions working on
the sump profile, thereby making efforts to understandthe driving mechanism that govern the process of butt
curl growth.

2.

The solidification stress model developed here combines
the temperature model and the stress model of castingtaking the temperatures, strains, and stresses during casting into consideration, whereby each model is alternately
solved at every calculation time step to hand over the calculated results to the other model. The computational
scheme is such that the computational object is a virtual
system of molten metal with solid slab in a quarter domain
as shown in Figure 2 —which takes into account the symmetry of cast slabs, and that the boundary cooling condiz

Temperatures located above meniscus
level are fixed at pouring temperature.

Primary cooling
Air gap
Impingement point of
secondary coolant

Secondary coolingTransfer direction ofboundary conditions

Meniscus leveloBottom cooling

Figure 2

2.1 Thermal ModelIn the calculation of temperatures inside a slab, the temperature recovery method was used taking latent heat
into consideration, in which the non-stationary heat conduction equation (Equation 1) is solved excluding thelatent heat, and the result is used, after compensated forby a temperature addition corresponding to the latentheat, to redefine the intermediate liquid phase temperature as shown in Equation 2. The increment of solid phasefraction during the course is calculated by Equation 3.

xComputational quarter domain in symmetry andboundary conditions.

Nomenclature
B: strain-displacement matrix, C: specific heat, De: elastic
stress-strain matrix, Dp: plastic stress-strain matrix,
dS: surface element, dV: volume element, f: subsequent
yield function, fs: solid phase fraction, G: modulus oftransverse elasticity, h: heat transfer coefficient. H' : strain
hardening coefficient, L: latent heat, T: temperature,
T : liquidus line, Ts: solidus line, T∞: boundary temperature∂T= κ ∇ 2T

(1)

TLI = TL − (TL − TS ) f S(2)

C (TLI − T )
L

(3)

ρC

THEORYytions transfer opposite to the casting direction at the casting speed.

∂t∆ fS =On the other hand, the surface temperatures of slabs
were calculated using the heat transfer equation of
Equation 4, in which the heat transfer coefficients for the
mold-cooling (primary-cooling) and air-gap cooling
regions were given by Equation 5, which enables calculating these coefficients reversely using the measured
temperature data on the slab and mold, defining them tobe dependent on the air gap. In addition, the heat transfer
coefficients for the secondary cooling region were given
as a function of the slab surface temperature as shown in
Figure 3, which was obtained from temperature measurements of actual slab surfaces and from cooling experiments on high-temperature bottom blocks.
κ ∇ T = − h( T − T∞ )

 b


h = hm  gap + b 

(4)

c

(5)

2.2 Stress ModelIn the formula development of stress model, constitutive
equations 3), 4) of the model were derived from the elastoplastic theory based on the incremental strain theory. In
actual calculations, however, the surface force resulting
from the head height of molten metal on the sump profile
Greek letters
α : linear expansion coefficient, β : solidification shrinkage
ratio, ∆ t: time increment, ε e: elastic strain, ε p: plastic strain,
ε s: solidification strain, ε T: thermal strain, ε p: equivalent plasticstrain, κ : heat conductivity, Λ : coefficient of normality rule ofincremental plastic strain, ρ : density, σ : stress, σ : equivalentstress, σ o: flow stress, σ' : deviatoric stress, τ : shear stress,
φ : shape function of positional coordinate and temperature,ψ : shape function of displacement increment
Greek suffixes denote elements of matrix or vector, andduplicated suffixes in matrix calculation signify summation.

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Numerical Simulation of Butt Curl in the Semi-DC Casting of Aluminum Slabs

Heat transfer coefficient (Wm-2K-1)

25000

to complete solid phase is ignored in Equation 9.
By transforming Equation 9 together with Hooke's lawof elastic strain, Prager’s consistency condition in plastic
state, normality rule of incremental plastic strain, and a
relational expression between plastic strain and equivalent plastic strain, we can ultimately derive Equation 14,
the constitutive equation of the model.

20000

15000

10000

e

∆f =

5000

0

e

∆ σα = Dαβ ∆ ε β

0

100

200

300

400

500

600

700

∂f

p

Slab surface temperature (°C)

Figure 3

e

p

T

S

(6)

It was assumed that the thermal and solidification
strains were effective only in the solid phase region andthe mushy zone, respectively, and that they were isotropic. In particular, the solidification strain expressed by
Equation 8 is very important for representing stress concentration 5) in the mushy zone where butt curl deformation and hot cracking originate from, so that it is thought
inadequate to use a simplified formulation where solidification strains are involved with thermal strains.
T∆ ε T = [α ∆ T α ∆ T α ∆ T 0 0 0 ] × f S(7)∆ ε S = [β ∆ f S β ∆ f S β ∆ f S 0 0 0 ] × ( 1 − f S )(8)T

Next, in order to determine the plastic deformationthreshold of a slab, a function type was employed as thesubsequent yield function f, which is subject to von Mises
yield condition and isotropic hardening rule, using theequivalent plastic strain as a hardening parameter.
f ( σα , ε p , T ) = σ − σ 0 ( ε p , T )(9)In this connection, since physical properties in themodel are assumed to be constant for the sake of simplicity, the dependence on phase transition from liquid phase

∂f

∆ε p+

∂T

∆ T = 0

(11)

∂f

(12)

∂ σα
1

(13)

∆ σα = ( Dαβ + Dαβ )(∆ εβ − ∆ ε β − ∆ ε β )
e

−

1
S

p

e

Dαβ

∂f

T

∂f

∂ σβ ∂ T

S

(14)

∆T

Here, the stress-strain matrix Dp is a term becoming
effective in the plastic state, and can be represented as
deviatoric stress shown in Equation 15.
p
Dαβ
=−

1 e ∂f ∂f e
Dαµ
Dνβ
S
∂σµ ∂σνσ ′x  σ ′x σ ′  σ ′  y  y
σ ′z  σ ′z −1= 2
  
σ H ′ σ 2 τ xy  τ xy 
2 +3 G τ yz  τ yz 
9G  
τ zx  τ zx 

2.2.1. Constitutive Equation
Based on the incremental strain theory, the total strain
increment is defined as a summation of increments ofelastic, plastic, thermal, and solidification strains.
∆ε α = ∆ε α + ∆ε α + ∆ε α + ∆ε α

∂f
∂ε p

2
2
p
p
∆ ε p =  ∆ εα ∆ εα 3Heat transfer coefficients of secondary cooling.

was ignored due to the fact that the sump is rather shallow in the semi-DC casting of aluminum, together with thevolumetric force due to gravity because of its small absolute value in comparison to internal stresses. In the liquid
phase region, whereas stress is generated as describedlater due to the temperature dependency of flow stress, itnearly equals zero since the Young’s modulus of the liquid phase appearing in the related formulas is quite small.
It should be noted here that this model excludes boththe effect of metal feeding into dendrites and the concept
of coherence temperatures 5)~7) of stresses actually generated.

∆ σα +∂ σα∆ εα = Λ

800

(10)

T

(15)

It should be pointed out here that even in cases a quadratic form is used for the subsequent yield function, thestress-strain matrix Dp thus derived assumes the same
formula as Equation 15.
2.2.2. Loading-Unloading Determination
Loading-unloading determination is carried out according
to the state of the incremental plastic strain Λ standing on
the surface of subsequent yield function as shown below.
In case of f =0 and Λ≥0, then the state of loading:neutralIn case of f =0 and Λ<0, then the state of unloading(16)
Let us note that in the case of subsequent yield function
shown in Equation 9, the coefficient Λ equals to the equivalent incremental plastic strain.

3.

FINITE ELEMENT FORMULATIONIn the finite element formulation of this solidification stressmodel, isoparametric elements (hexahedron, eight nodal
points) are used to represent the position, temperature,and displacement increments in terms of a linear combination of nodal point data and a shape function.

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Numerical Simulation of Butt Curl in the Semi-DC Casting of Aluminum Slabs

X = φα xα(17)

Table 1T = φα Tα(18)

Density (kg/m3)

2500∆ Uα = ϕαβ ∆ dβ

(19)Heat capacitance (Jkg-1K-1)

1146

Liquidus line (°C)

648

3.1 Finite Element Formulation of Thermal Model
Finite element formulation of the thermal model is carriedout by applying the Galerkin method to Equations 1 and 4
to obtain a set of simultaneous equations for every nodetemperature.
Cαβ

∂ Tβ
∂t

+(

1
2
K αβ
+ K αβ) Tβ = FαSolidus line (°C)
Heat conductivity (Wm K )

(20)

(21)
(22)

2
K αβ
= h ∫ φ α φβ dS(23)

Fα = hT∞ ∫ φ α dS

(24)

In terms of time, furthermore, the Crank-Nicolson method is used for discretization to ultimately obtain a finite
element formula for the thermal model.
1
1

1
2
 2 ( K αβ + K αβ ) + ∆ t Cαβ  Tβ ( t + ∆ t ) 1
1
2) + ∆1t Cαβ  Tβ ( t ) + Fα
=  − ( K αβ
+ K αβ 2Latent heat (J/kg)

3.9×105

Thermal expansion coef. (1/°C)

2.5×10-5

Solidification shrinkage ratio

0.07

Slab thickness (m)0.6Slab width (m)1.65

Pouring temperature (°C)

700

Casting speed (mm/min)

60

Secondary coolant flow rate (lcm-1min-1)

3

Node : 1056, Element : 750
250
25°C
200

(25)

+ ∆ f αTp + ∆ f αSe + ∆ f αSp + ∆ f αY + ∆ f αR

(26)

The right-hand side comprises the load vectors relatedwith the surface force, volume force, thermal strain, solidification strain, and temperature dependence of flow
stress, and the residual term.
e/p
e/p
K αβ
= ∫ Bµα D µλ
B λβ dV(27)∆ fαS = ∫ ϕ βα ∆ FβS dS(28)∆ fαV = ∫ ϕ βα ∆ FβV dV(29)∆ fαTe/p =∫e/pBµα D µλ∆ ε λT dV(30)∆ fαSe/p =∫ Bµα D µλ ∆ ε λ dV

(31)e
∆ fαY = ∫ Bµα Dµλ

e/pS

3σ ′λ  ∂σ 0 − ∆TdV
2σ S  ∂ T ∆ fαR = ∫ ϕ µα FµS dS + ∫ ϕ µα FµV dV − ∫ Bµα σ µ dV

(32)
(33)

200°C
300°C
400°C

100

500°C
50

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Plastic strain

Figure 44.

( K αβe + K αβp ) ∆ dβ = ∆ fαS + ∆ fαV + ∆ fαTe

100°C

150

0

3.2 Finite Element Formulation of Stress Model
Finite element formulation of the stress model is carriedout through the principle of virtual work to ultimately
obtain simultaneous linear equations in terms of nodal
displacement increments, i.e. rigidity equations.

218

-1

Heat transfer coefficient in mold region
hm=1400 Wm-2K-1, b=0.4, c=0.5
Heat transfer coefficient of secondary cooling
Correlation from hot block quenching test

Flow stress (MPa) ∂φ ∂φ β ∂φα ∂φ β ∂φα ∂φ β 
1
 dV
K αβ
= κ ∫  α
+
+
∂y ∂y
∂ z ∂ z  ∂x ∂x635-1

where,
Cαβ = ρ C ∫ φ α φ β d V

Casting conditions and physical properties.

Stress-strain curves of AA3004 aluminum alloy
obtained by hot tensile tests.

RESULTS OF NUMERICALCALCULATIONAs for the reference conditions for calculating butt curl,
casting conditions for an aluminum alloy AA3004 shownin Table 1 were adopted. The initial shape of slab bottom,
i.e. the shape of bottom block, was assumed to havedouble curvatures. The temperature dependence of theflow stress was determined from hot tensile tests in compliance with JIS G0567 as shown in Figure 4, and the flow
stress curve was incorporated into the model using thefollowing equation.
σ 0 ( T ) = a ( T ) ε pn ( T ) + σ y ( T )(34)

4.1 Process of Butt Curl Growth
In this report, the amount of butt curl is defined as thecoordinate variation, due to shape changes, of the shortside center at the slab bottom from its initial position.
Figure 5 shows the growth process of butt curl under thereference conditions together with temperature changes
during the process at four points on the slab bottom. It

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Numerical Simulation of Butt Curl in the Semi-DC Casting of Aluminum Slabs

Temperature (°C)

35

Liquidus line

700
600

Solidus line

D

500

30

A

400

C

300

Butt curl

B

200

800

25
20
15
10

700
600
500
400

Butt curl (mm)

800

700°C

5

100

0

0

-5
0 100 200 300 400 500 600 700 800 900 1000 1100 1200

TL
z

700°C

600°C
z
x
y

x
y
450 mm (inner view)

Withdrawal length (mm)Figure 5

300
200
100
0
°C

450 mm (outer view)Calculated temperatures at selected points on theslab bottom and butt curl growth. (A: long side,
B: short side, C: corner, D: center)can be seen from Figure 5 that, since the withdrawal
length on the horizontal axis has a reference point at thecenter of the slab bottom, impingement of secondary
cooling water begins on the short side center at a withdrawal length of 180 mm, and that the water wets theentire periphery at a withdrawal length of 300 mm. It isalso seen that butt curl begins to grow rapidly at a 350mm position where the center portion of the slab bottom
starts solidification, gradually decreases in its growth rate
as the slab bottom temperature falls, and comes nearly toan end at a withdrawal length of 1000 mm ultimately forming a butt curl of 30 mm.
Figures 6 and 7 show the three-dimensional temperature distributions at the rapid and saturated periods ofbutt curl growth, and the distributions of vertical stress inthe slab width direction (the x-axis direction) that isassumed to be a main source of driving force, respectively. It can be seen that, after the entire periphery of the slab
is cooled by the secondary cooling water, the short sideof the slab bottom curls up with respect to the initial
shape (virtual melt slab) indicated by the frame line, andthat bowing occurs simultaneously. In terms of internal
stress, a distribution of tensile stress is seen near thesump profile, i.e. mushy zone and high-temperature solid
phase region, while compressive stress is generated in
the solid phase region around the periphery. The generation of such a stress state is attributable to the feature of
the solidification model used here, where the solidification
strain is handled to be definitely different from the thermal
strain. It would be impossible to obtain the tensile stress
distribution clearly shown here along the sump profile if
other models are used where the solidification strain istreated as involved with the thermal strain. In this connection, the widespread distribution of tensile stress over theslab bottom appearing at the later stages of descentresults from the decreased temperatures in the solid
phase region, and it makes little contributions to butt curl
growth itself.
The tensile stress distributed near the sump profile isgenerated by the solidified shell around the periphery
where its solidification contraction or thermal contraction
being impeded. Conversely, it can be said that the tensilestress near the sump profile pulls the solidified shell

700°C

800

TL

300
200
100
0
°C

TS

x

z

tion
irec
th d
d
i
y W

1150 mm (inner view)

Figure 6

Widt

300°C
h dir
z
ectio
n x
y

1150 mm (outer view)Calculated temperature distributions at the rapid andsaturated periods of butt curl growth.

zxy
450 mm (inner view)

x

700°C

700
600
500
400

z

on
irectiy Width d1150 mm (inner view)

Figure 7

42
26
10
-5
-21
-37
-53
-69
-84
-100
-116
MPa
x

z

y

450 mm (outer view)

53
36
10
-17
-43
-70
-97
-123
-150
-176
-203
MPa

z
y
tionx
1150 mm (outer view)

Width

direc

Calculated vertical stress distributions at the rapid
and saturated periods of butt curl growth.

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Numerical Simulation of Butt Curl in the Semi-DC Casting of Aluminum Slabs

Table 2
Before growing period
Torque moment is weak becauseof shallow sump profile.
withdrawal
Rapid growing period
Torque moment is strong enoughto cause butt curl motion.

Mushy zone
Solid region

1750

50

700

35

600

1750

50

700

40

1xxx

600

1280

50

700

22

1xxx

600

1600

63

700

32

3xxx

600

1140

48

690

40

3xxx

600

1140

48

690

35

3xxx

600

1340

60

700

20

3xxx

600

1650

60

700

32

5xxx

600

1920

50

700

30

50
45

Butt curl

Bottom block

Figure 8

600

1xxx

Proposed mechanism of butt curl development:
torque moment due to tensile stresses distributed
along sump profile bends the solidified bottom
shell at the early stage of casting process.

around the periphery toward the inside of the slab. Sucha phenomenon may be simulated with several persons
forming a circle hand in hand with each other; when theypull their hands all together, they will move toward thecenter of the circle. Figure 8 illustrates this situation interms of a torque moment standing on the sump profile,in which it is assumed that this torque moment bends theslab bottom to generate a butt curl. Accordingly, it isthought that while the torque moment is small at the earlystage of casting when sump is shallow, it increases as theslab descends leading to the most suitable situation forbutt growth where the sump has an appropriate depth
and the slab bottom is sufficiently hot yet. When the withdrawal length reaches around 1000 mm, however, theslab bottom presumably increases in size and in rigidity
with a decrease in temperature, and it constitutes an
obstacle to the torque moment thereby suppressing andterminating butt curl growth.
4.2 Comparison with Butt Curl Measurements
Table 2 shows the casting conditions and butt curl measurements for actual slabs. The samples were selected tohave as much a wide variety as possible of casting conditions such as slab width, descent speed, and pouring
temperature. Figure 9 shows the results of comparison
between the calculated and measured values for butt curl.
It is seen that the two values are in good agreement withan accuracy of ±20 %, confirming that the prediction
accuracy is superior. In this connection, the temperaturedependence of stress-strain curves for each alloy
obtained by high-temperature tensile tests is taken into
account in this calculation.
4.3 Relationship between Butt Curl and Slab Width
Figure 10 shows the calculated relationship between butt
curl and slab width. A linear relationship can be observed

Calculated butt curl (mm)Torque moment

Saturation period
Butt curl motion is suppressedby hardening of bottom shell.

Thickness Width Lowering speed Pouring
Measured(mm)(mm)(mm/min)temp. (°C) butt curl (mm)

1xxx

±20%
Tolerance

40
35
30
25
20
15
10
5
0

0

5

10

15

20

25

30

35

40

45

50

Measured butt curl (mm)Figure 9Comparison between calculated and measured values for butt curl.

40
35
Calculated butt curl (mm)Liquid region

AlloysCasting conditions and butt curl measurements.

y=0.0248x -9.6437
R2=0.6168

30
25
20
15
10
5
0
1000

1200

1400

1600

1800

2000

Slab width (mm)Figure 10 Relationship between butt curl and slab width.

despite a relatively large deviation, and it can be seen thatthe smaller the aspect ratio (slab width/slab thickness) the
smaller the butt curl. The reason for this tendency is presumably that, whereas in general each of the short andlong sides of a slab curls up, the internal stress acts tosuppress the curl on one side over that on the other side
when the latter surpasses the former —just in the case of
saddle shape formation in plane bending, so that thesmaller the aspect ratio the more these two stresses cancel each other thereby reducing butt curl.

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Numerical Simulation of Butt Curl in the Semi-DC Casting of Aluminum Slabs
25

5.
y=0.3759x + 4.5214

Calculated bow (mm)20R2=0.493

15

10

5

0

0

5

10

15

20

25

30

35

40

Calculated butt curl (mm)Figure 11 Relationship between butt curl and bow.

4.4 Relationship between Butt Curl and Bow
Figure 11 shows the calculated relationship between butt
curl and bow. Here also, a linear relationship can beobserved despite a relatively large deviation, and it canbe seen that the smaller the butt curl the smaller the bow.
It is conceptually understood that the initial rise of a solidified shell on the short side in the form of an integrated Lshaped body naturally leads to bow formation as the shellcurls upward, and this mechanism has been adopted by
Tsunekawa et al. to explain their experimental results inlaboratory. While excessive bowing is known to cause theproblem of metal bleeding at the beginning of casting, it
is considered that butt curl suppression constitutes thefundamental countermeasures for the problem.

CONCLUSIONS

An elasto-plastic solidification stress model has beendeveloped based on the incremental strain theory to analyze the process of butt curl growth. The following conclusions may be drawn from the results:
1) The solidification stress model has been confirmed,
through comparison with butt curl measurements, tohave an accuracy of prediction of ±20 %, ample performance.
2) In the growth process of butt curl, the torque moment
due to the tensile stress acting on the sump profile ofthe mushy zone plays an important role, and butt curl
grows rapidly immediately after the secondary cooling water wets the entire periphery of a slab bottom,
and the growth rate decreases to come to an end as
the slab bottom decreases in temperature andincreases in rigidity.
3) The relationships between butt curl and slab widthand between butt curl and slab bow have a tendency
similar to that obtained by actual casting.

REFERENCES
1) W. Droste, W. Schneider: Light Metals (1991) 945.
2) M. Tsunekawa, N. Hayashi, T. Uno: Sumitomo Light Metal
Technical Reports, Vol.37 (1996) 50.
3) Yagawa and Miyazaki: Analysis of Thermal Stress, Creep and Heat
Transfer by Finite Element Method, Science Publishing (1991). (inJapanese)
4) Inoue et al.: Analysis of Solid Physics and Phase Transformation,
Okawa Publishing (1995). (in Japanese)5) Hallvard G. Fjaer, Asbjorn Mo: Metallurgical Transactions B,
Vol.21B (1990) 1049.
6) Bruno Hannart, Frederic Cialti, Ruben Van Schalkwijk: Light
Metals (1994) 879.
7) Jung-Eui Lee, Tae-Jung Yeo, Kyu Hwan Oh, Jong-Kyu Yoon, U-Sok
Yoon: Metallurgical and Materials Transactions A, Vol.31A (2000)
225.

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