VSEBINA – CONTENTS
PREGLEDNI ^LANKI – REVIEW ARTICLES
Finite-difference methods for simulating the solidification of castings
Simulacija strjevanja z metodo kon~nih razlik
V. Grozdani} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
IZVIRNI ZNANSTVENI ^LANKI – ORIGINAL SCIENTIFIC ARTICLES
Pressureless reactive sintering of TiAl-TiC and Ti3Al-TiC composites
Reakcijsko sintranje kompozitov TiAl-TiC in Ti3Al-TiC pri atmosferskem tlaku
V. Kevorkijan, S. D. [kapin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
An optical-emission-spectroscopy characterization of oxygen plasma during the oxidation of aluminium foils
Karakterizacija kisikove plazme med oksidacijo aluminijevih folij z opti~no emisijsko spektroskopijo
N. Krstulovi}, U. Cvelbar, A. Vesel, S. Milo{evi}, M. Mozeti~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
Effect of ageing a two-phase Fe-NiCrMo alloy on the strain hardening at room temperature and at 290 °C
Vpliv staranja dvofazne zlitine Fe-NiCrMo na deformacijsko utrjevanje pri sobni temperaturi in pri 290 °C
R. Celin, J. Vojvodi~ Tuma, B. Arzen{ek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Identification of material properties of quasi-unidirectional carbon-epoxy composite using modal analysis
Identifikacija materialnih lastnosti za kvazienosmerni kompozit ogljik-epoksi z modalno analizo
R. Zem~ík, R. Kottner, V. La{, T. Plundrich . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
Re-oxidation phenomena during the filtration of steel by means of ceramic filters
Reoksidacijski procesi med filtriranjem jekla s kerami~nimi filtri
K. Stránský, J. Ba`an, J. Dobrovská, A. Rek, D. Horáková . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
The use of response surface methodology for prediction and analysis of surface roughness of AISI 4140 steel
Uporaba metodologije odgovora povr{ine za napoved in analizo hrapavosti pri jeklu AISI 4140
F. Kahraman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
STROKOVNI ^LANKI – PROFESSIONAL ARTICLES
Determination of optimal ball burnishing parameters for surface hardness
Dolo~itev optimalnih parametrov krogli~nega glajenja za pove~anje trdote povr{ine
A. Sagbas, F. Kahraman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
17. MEDNARODNA KONFERENCA O MATERIALIH IN TEHNOLOGIJAH, 16. – 18. november, 2009, Portoro`, Slovenija
17th INTERNATIONAL CONFERENCE ON MATERIALS AND TECHNOLOGY, 16–18 November, 2009, Portoro`, Slovenia . . . . . 275
ISSN 1580-2949
UDK 669+666+678+53 MTAEC9, 43(5)231–274(2009)
MATER.
TEHNOL.
LETNIK
VOLUME 43
[TEV.
NO. 5
STR.
P. 231–274
LJUBLJANA
SLOVENIJA
SEP.–OCT.
2009

V. GROZDANI]: FINITE-DIFFERENCE METHODS FOR SIMULATING THE SOLIDIFICATION OF CASTINGS
FINITE-DIFFERENCE METHODS FOR SIMULATING
THE SOLIDIFICATION OF CASTINGS
SIMULACIJA STRJEVANJA Z METODO KON^NIH RAZLIK
Vladimir Grozdani}
University of Zagreb, Metallurgical Faculty, Aleja narodnih heroja 3, 44103 Sisak, Croatia
Prejem rokopisa – received: 2008-12-15; sprejem za objavo – accepted for publication: 2009-05-12
Mathematical models of casting solidification for different geometrical complexities have been developed and checked. Special
emphasis is given to the numerical finite-difference methods for solving the partial differential equations for heat conduction in
two- and three-dimensions, which are the basis for the simulation of solidification. In the case of three-dimensional
mathematical models, the methods of Douglas and Brian are especially efficient because they are unconditionally stable and of
the second order with regard to the approximation of time and space. Both methods have a two-dimensional variant and Brian´s
method is identical to the implicit alternating direction method. To obtain an algorithm for the solidification with the application
of implicit finite-difference methods, the system of the tri-diagonal matrix has to be solved, for which an efficient algorithm
exists. In addition to the implicit methods of solving Fourier´s partial differential equation of heat conduction, also the
unconditionally stable explicit finite-difference methods are used. These are the methods of partial steps, the classical method,
and Saulyev’s method. These methods also allow a first-order accuracy. On the basis of the quoted numerical methods for
solving the partial differential equation of heat conduction, the algorithms of casting solidification of different complexity have
been obtained and programmed in the computer languages ASCII FORTRAN and FORTRAN 77, and the simulation has been
performed with a SPERRY 1106 computer and personal computers.
Key words: casting solidification, heat conduction method of finite differences, computer simulation
Razviti in preverjeni so bili matemati~ni modeli za litje in strjevanje z razli~no geometri~no kompleksnostjo. Poseben poudarek
je na metodi kon~nih razlik za re{itev parcialnih diferencialnih ena~b za prevajanje toplote v dveh in treh dimenzijah, ki so
podlaga za simulacijo strjevanja. V tridimenzionalnem modelu sta posebno u~inkoviti metodi po Douglasu in Brianu, ker sta
nepogojno stabilni in drugega reda glede na aproksimacijo ~asa in prostora. Obe metodi imata tudi dvodimenzionalno varianto,
Brianova metoda pa je identi~na z metodo implicitne alternativne diference. Za razvoj algoritma za strjevanje z metodo
implicitne kon~ne razlike je treba re{iti problem tridiagonalne matrice, za katero obstaja u~inkovit algoritem. Kot dodatek
implicitne metode za re{itev Fourierove parcialne diferenecialne ena~be za prevajanje toplote se uporabljajo tudi nepogojno
stabilne metode kon~nih razlik. Med njimi so metoda delnih korakov, klasi~na metoda in Saulyjeva metoda, ki omogo~ajo, da se
dose`e natan~nost prvega reda. Na podlagi teh numeri~nih metod za re{itev parcialnih diferencialnih ena~b za prevajanje toplote
so bili razviti algoritmi za litje in strjevanje z razli~no kompleksnostjo, programirani v ra~unalni{kih jezikih ASCII FORTRAN
in FORTRAN 77, in izvr{ene simulacije z ra~unalnikom SPERRY 1106 in na osebnem ra~unalniku.
Klju~ne besede: livno strjevanje, prevajanje toplote, metoda kon~nih razlik, ra~unalni{ka simulacije
1 INTRODUCTION
Mathematical modelling is a scientific method that
provides solutions for most foundry problems that have
remained unsolved for a long time, e.g., the solidification
of castings. This was made possible by the rapid
development of computers and numerical methods for
solving partial differential equations.
The first step in establishing the mathematical
models of solidification is Fourier’s partial differential
equation of heat conduction. In the domain of casting the
equation has been solved by considering the mould
geometry and the initial and boundary conditions.
During the operationalization of the mathematical model
the appropriate numerical methods are used: the
finite-element method (FEM) 1–5 and the method of finite
differences (FDM) 6–8. The FEM is more complicated
than the FDM, and it is used for castings with a complex
geometry and also for curved surfaces. The FDM may be
explicit and implicit 9.
For the explicit FDM the space derivative is for-
mulated in terms of known values, whereas for the
implicit FDM the space derivative is in terms of values
that are yet to be computed. The explicit method allows
the new value of the dependent variable to be computed
essentially with repeated applications of a single
formula, whereas the implicit method requires the
solution of a system of simultaneous equations.
The "computational molecules" for the explicit and
implicit methods are illustrated in Figure 1. Circles are
Materiali in tehnologije / Materials and technology 43 (2009) 5, 233–237 233
UDK 669.186+669.14:519.68 ISSN 1580-2949
Pregledni ~lanek/Review article MTAEC9, 43(5)233(2009)
Figure 1: Computational molecules for the a) explicit and b) implicit
methods
Slika 1: Ra~unske molekule za a) eksplicitno in b) implicitno metodo
used to denote those temperatures used in formulating
the space derivatives, and the crosses for those employed
in the time derivative. The full circles denote values
already known and the empty circles those about to be
computed.
The explicit methods for solving the partial
differential equation of heat conduction are usually
dependent on the choice of space and time steps and are
not unconditionally stable and are preferred at the oper-
ationalization of the mathematical models. However,
there are some explicit methods that are unconditionally
stable as well. In this work a review of the numerical
methods to solve a partial differential equation of heat
conduction, which has been the most frequently used
during the simulation of casting solidification, is given.
2 MATHEMATICAL MODELS
The mathematical models of casting solidification
consist of the partial differential equation of heat
conduction with the appropriate initial and boundary
conditions. The partial differential equation of heat
conduction in the rectangular coordinate system has the
form 10–13:
∂
∂
∂
∂
∂
∂
∂
∂2
T
t
a
T
x
T
y
T
z
= + +⎛
⎝⎜
⎞
⎠⎟
2
2
2 2
2
(1)
In the cylindrical coordinate system 10–13:
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
T
t
a
T
r
T
r r
T
r
T
z
= + + +⎛
⎝⎜
⎞
⎠⎟
2
2 2
2
2Θ 2
(2)
And in the spherical coordinate system 10–13:
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
T
t
a
r r
r
T
r r
T= ⎛
⎝
⎜ ⎞
⎠
⎟ + ⋅ ⎛
⎝
⎜ ⎞
⎠
⎟
1 1
2
2
2 sin
sin
θ θ
θ
θ
+ ⋅⎡
⎣⎢
⎤
⎦⎥
1
2 2
2
2r
T
sin θ ϕ
∂
∂
(3)
The initial conditions were derived on the basis of the
system of thermal balance 14:
t = 0 T = TS
Ti =
ρ ρ ρ
ρ ρ
m pm L K pK s m f
m pm K pk
H
C
C T C T
C
+ +
+
∆
(4)
The analytical solution of the partial differential
equation of heat conduction for the case of the thermal
contact of two semi-infinite media is 15:
t = 0 T = TS
T T
T T
K
K
a
a
if s
L s
K
m
m
k
= +
−
+1
(5)
The boundary conditions are of the fourth kind and in
a real complex system the mould-casting core-chill may
be written as 15:
Km
∂
∂
T
n
m = KK
∂
∂
T
n
K (6)
Km
∂
∂
T
n
m = Kj
∂
∂
T
n
j
(7)
Km
∂
∂
T
n
m = Kh
∂
∂
T
n
h (8)
Kk
∂
∂
T
n
K = Kj
∂
∂
T
n
j
(9)
The thermo-technical properties of a material that
depend on the temperature 16–18 and the latent heat of
crystallization are incorporated into the equation for the
specific heat of the metal (the method of modified
specific heat) in the following way:
∆H c c T
T
T
f p
*
p( )d
s
1
= −∫ (10)
3 NUMERICAL METHODS
There are two finite-difference methods for solving
the three-dimensional differential equation of heat
conduction in a non-stationary state: the Douglas method
6 and Brian’s method 19. The first method is a
modification of the Crank-Nicolson method 6 that was
proposed by Douglas:
1
2
12 2 2∂ ) + ∂ ∂x i,j,k i,j,k
n
y i,j,k
n
z i,j,k
n
i,j
T T T T
a
( * + + =
,k,n
i,j,k i,j,k
nT T
t
* −
∆
(11)
1
2
2 2 2∂ ) + 1
2
∂ ) ∂x i,j,k i,j,k
n
y i,j,k i,j,k
n
zT T T T( (
* **+ + + T
a
T T
t
i,j,k
n
i,j,k,n
i,j,k i,j,k
n
=
−1 **
∆
(12)
1
2
1
2
1
2
2 2∂ ) + ∂ ) ∂x i,j,k i,j,k
n
y i,j,k i,j,k
nT T T T( (* **+ + + z i,j,k
n
i,j,k
n
i,j,k,n
i,j,k i,j,k
n
T T
a
T T
t
2 1 1( + + =
−
)
n+ 1
∆
(13)
The second method is a modification of the
Douglas-Racford method 20, and according to Brian it is
the most efficient method for the numerical integration
of a three-dimensional equation of heat conduction:
∂ ∂ ∂x i,j,k y i,j,k
n
z i,j,k
n
i,j,k,n
i,j,k
T T T
a
T
2 2 2 1* + + =
−* T
t/
i,j,k
n
∆ 2
(14)
∂ ∂ ∂x i,j,k y i,j,k z i,j,k
n
i,j,k,n
i,j,k
T T T
a
T
2 2 2 1* **+ + =
**
2
− T
t/
i,j,k
n
∆
(15)
∂ ∂ ∂x i,j,k y i,j,k z i,j,k
i,j,k,n
i,j,
T T T
a
T
2 2 2 1* ** ***+ + = k i,j,k
nT
t/
***
2
−
∆
(16)
∂ ∂ ∂x i,j,k y i,j,k z i,j,k
i,j,k,n
i,j,
T T T
a
T
2 2 2 1* ** ***+ + = k i,j,k
nT
t
n +1 −
∆
(17)
In practice, Brian recommended the simpler form:
∂ ∂ ∂x i,j,k y i,j,k
n
z i,j,k
n
i,j,k,n
i,j,k
T T T
a
T
2 2 2 1* + + =
−* T
t/
i,j,k
n
∆ 2
(18)
∂ ∂y i,j,k y i,j,k
n
i,j,k,n
i,j,k i,j,k
T T
a
T T
t
2 2 1**
*
+ =
−**
∆ / 2
(19)
∂ ∂z i,j,k
n
z i,j,k
n
i,j,k,n
i,j,k i,j,k
n
T T
a
T T
2 1 2 1+ + =
−n +1 − 2T
t/
i,j,k
**
∆ 2
(20)
V. GROZDANI]: FINITE-DIFFERENCE METHODS FOR SIMULATING THE SOLIDIFICATION OF CASTINGS
234 Materiali in tehnologije / Materials and technology 43 (2009) 5, 233–237
It was proved that Brian’s original method can have
the following form:
∂ ∂ ∂x i,j,k y i,j,k
n
z i,j,k
n
i,j,k,n
i,j,k
T T T
a
T
2 2 2 1* + + =
−* T
t/
i,j,k
n
∆ 2
(21)
∂ ∂ ∂x i,j,k y i,j,k z i,j,k
n
i,j,k,n
i,j,k
T T T
a
T
2 2 2 1* **+ + =
**
2
− T
t/
i,j,k
n
∆
(22)
∂ ∂ ∂x i,j,k y i,j,k
n
z i,j,k
n
i,j,k,n
i,j,k
T T T
a
T
2 2 2 1 1* + + =+
n +1
2
− T
t/
i,j,k
**
∆
(23)
The general solution of Brian’s modified method for
general points (i,j,k) and the points on the boundary
surface between the mould and the metal in a rectangular
coordinate system are given in Appendix A.
The methods of Douglas and Brian are uncondi-
tionally stable and converge with the discretization error
O(t)2 + (x)2 + (y)2 + (z)2
. Both methods have a
two-dimensional option, and Brian’s method is identical
to the implicit alternating direction (IAD) method.
The IAD method subdivides each t into two half-
time steps, each of duration of t/2. The space deriva-
tives are approximated implicitly in the x-direction and
explicitly in the y-direction over the first t/2; the
procedure is reversed over the second t/2 – explicitly in
the x-direction and implicitly in the y-direction. In the
rectangular coordinate system it may be written as 14:
∂ ∂x i,j
n
y i,j
n
i,j,n
i,j i,j
n
T T
a
T T
t/
2 1 2 2 1+ + =
−
/
n +1 /2
2∆
(24)
∂ ∂x i,j
n
y i,j
n
i,j,n
i,j i,j
n
T T
a
T T
t
2 1 2 2 1
1 2
1+ +
+
+ =
−
/
/n +1
∆ / 2
(25)
And in the case of the polar coordinate system as 15:
∂ + ∂r i,j
n i,j
n
i,j
n
j
z i,j
n
i,j,n
T
T T
r r
T
a
2 1 1 2 1 2
2
1+
−
=+ − +
∆
/
T T
t/
i,j i,j
nn + 1/ 2
2
−
∆
(26)
∂ + ∂r i,j
n i,j
n
i,j
n
j
z i,j
nT
T T
r r
T2 1 1
1
1
1
2 1 2
2
1+ +
+
−
+
++
−
=
∆
/
a
T T
t/i,j,n
i,j i,j
nn + 1
2
− + 1 2/
∆
(27)
The implicit alternating direction method is uncon-
ditionally stable and is of second order with regard to the
discretization of time and space. In parallel with the
implicit alternating direction methods, the uncondi-
tionally stable explicit methods have been developed: the
partial-steps method 7, the Saulyev explicit method
6,7,21–28 and the "classical" method 7. The partial-steps
method consists of two steps, which are written as:
T T
t
a T
i,j i,j
n
i,j,n x i,j
n
n +1 /2 −
= +
∆
∂ 2 1 2/ (28)
T T
t
a T
i,j i,j
n
i,j,n y i,j
n
n +1 −
=
+
+
1 2
2 1
/
∆
∂ (29)
This method is of the first order in terms of accuracy
and with the approximation error O(t)+(x)2+(y)2
.
The Saulyev method is another efficient finite-
difference procedure for approximating the solution of
the two-dimensional heat-conduction equation. It relies
on two explicit equations, to be used in turn over
successive time steps. Each equation by itself appears to
be "unbalanced", but is in fact the mirror image of the
other; thus the two equations may be regarded as
complementary to each other. The basic computational
molecules are illustrated in Figure 2.
From time-level n to time-level n+1 (Figure 2a), the
derivatives are approximated as follows:
∂
∂
T
t
T T
t
i,j n i,jn≈
−+, 1
∆
(30)
∂
∂ 2
2
1 1 1 1
2
T
x
T T T T
x
i ,j n i,j n i,j n i ,j n≈
− − +− + + +, , , ,
( )∆
(31)
∂
∂ 2
2
1 1 1 1
2
T
y
T T T T
y
i,j n i,j n i,j n i,j n≈
− − +− + + +, , , ,
( )∆
(32)
This method is also of the first order in terms of
accuracy. The last method for solving the two-dimen-
sional differential equation of heat conduction is the
"classical" method with the discretization error O(t) +
(x)2 + (y)2
, which may be written as:
T T
t
a T T
i,j
n
i,j
n
i,j,n x i,j
n
y i,j
n
–
)
1
2 2
−
+
∆
= (∂ ∂ (33)
T T
t
a T T
i,j
n
i,j
n
i,j,n x i,j
n
y i,j
n
+
+ +
−
+
1
2 1 2 1
∆
= (∂ ∂ ) (34)
Based on the quoted numerical methods for solving
the partial differential equation of heat conduction,
algorithms for the solidification of castings of different
complexity have been obtained, as shaped-steel castings
(L,T,H), as a low-carbon cast-steel gear blank, as gray
iron and a cast-steel flange, a cast-steel valve housing,
bars, cylinders, spheres, steel rail-wheel casting, etc.
14,15,29–46. The algorithms are programmed in the computer
languages ASCII FORTRAN and FORTRAN 77, and
Materiali in tehnologije / Materials and technology 43 (2009) 5, 233–237 235
V. GROZDANI]: FINITE-DIFFERENCE METHODS FOR SIMULATING THE SOLIDIFICATION OF CASTINGS
Figure 2: Computational molecules for the Saulyev method. The grid
points are marked with crosses, and the full circles and empty circles
are used for the time, the x-direction, and the y-direction derivatives,
respectively.
Slika 2: Ra~unske molekule za metodo po Saulyjevu. Mre`ne to~ke
ozna~ene s kri`ci, polnimi krogi in praznimi krogi so uporabljene za
~as ter x- in y-derivate.
the simulation is performed on a SPERRY 1106 com-
puter and on personal computers.
4 CONCLUSION
Mathematical models of the casting solidification of
different geometrical complexities, which are based on
Fourier’s differential equation of heat conduction, have
been developed and investigated in this paper. To obtain
satisfactory results this equation is solved by means of
numerical finite-difference methods. In the case of the
three-dimensional differential equation of heat con-
duction, two numerical methods are applied, Douglas’s
and Brian´s, which are unconditionally stable and are of
the second order with regard to the time and space
approximation. For solving the two-dimensional partial
differential equation of heat conduction there are espe-
cially efficient implicit alternating direction methods,
which are unconditionally stable, and the explicit
methods of finite differences: the partial-step method,
the "classical" method and the Saulyev method. In
contrast to the implicit alternating direction methods,
which are of second order with regard to the time and
space approximation, the explicit methods are of first
order in terms of accuracy.
List of symbols
a – thermal diffusivity
cp – specific heat
cp
* – specific heat in interval of solidification
Hf – latent heat of fusion
K – coefficient of heat conduction
n– normal
r – coordinate
t – time
T – temperature
T*, T**- successive approximations of T at the half time-step
x,y,z – coordinate
Index:
h – chill
i – coordinate
if – temperature on the boundary surface
j – coordinate; core
k – mould
l – pouring; liquidus
m – metal
n – time step
r – coordinate
s – sand
f – fusion
x,y,z – coordinate
5 REFERENCES
1 C. S. Krishnamoorthy, Finite Element Analysis, Theory and pro-
gramming, Tata McGraw-Hill, New Delhi, 1987
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Appendix A.
General solutions of Brian’s modified method in a
rectangular coordinate system.
When the partial differential equations of heat
conduction (1), representing the solidification and cool-
ing of steel casting in a sand mould, are approximated by
means of Brian’s method, the equations (21), (22) and
(23) are obtained. These equations are valid for the
general point (i,j,k) in the mould and casting. In
equations (21)–(23), ai,j,k,n is the temperature diffusivity
at the point (i,j,k) at temperature Ti j k
n
, , . The reciprocal
value of the Fourier number is:
Z
x
a ti j k n i j k n
, , ,
, , ,
( )= ∆
∆
2
(35)
In the case of the equidistant net (x = y = z),
equations (21), (22) and (23) may be written in the
following form:
− + + − =− +T Z T Ti j k i j k n i j k i j k1 12 1, ,
*
, , , , ,
*
, ,
*( )
= + + + +− + − +T T T T Zi j k
n
i j k
n
i j k
n
i j k
n
i j k, , , , , , , , , , ,(1 1 1 1 2 n i j k
nT− 2) , , (36)
− + + − =− −T Z T T Ti j k i j k n i j k i j k i j1 12 1, ,
**
, , , , ,
**
, ,
**
, ,( ) k i j kT
*
, ,
*− +2
+ + + + −+ − +T T T Z Ti j k i j k
n
i j k
n
i j k n i j k1 1 1 2 1, ,
*
, , , , , , , , ,( )
n (37)
− + + − =−
+ +
+
+T Z T T Ti j k
n
i j k n i j k
n
i j k
n
i1
1 1
1
12 1, , , , , , , , ,( ) − − +1 2, ,
*
, ,
*
j k i j kT
+ + + −+ − +T T Z T Ti j k i j k i j k n i j k i j1 1 12 1, ,
*
, ,
**
, , , , ,
**
, ,( ) k
** (38)
Equations (21)-(23) represent the approximation for
the net points in the homogeneous rectangle without
boundary conditions.
In the case of the boundary interface, a perfect
contact between the mould and the metal is assumed.
Figure 3 illustrates the vertical boundary surface YZ
between the mould (K) and the metal (M) for an
approximation of the value T* at the point (i,j,k).
By means of the Taylor series, the temperatures
Ti j k−1 , ,
* and Ti j k+1 , ,
* around Ti j k, ,
* on the vertical boundary
surface are obtained:
T T xT
x
Ti ,j k i,j k xk xxk− ≈ −1
2
2,
*
,
* * *( )
!
∆ ∆ (39)
T T xT
x
Ti ,j k i,j k xm xxm+ ≈ −1
2
2,
*
,
* * *( )
!
∆ ∆ (40)
Where Ti j k
n
, , represents the temperature derivation
∂ ∂T / x* for the mould (k) in the net point (i,j,k). From
equations (39) and (40), the derivation of the second
order is expressed:
T
x
T T xTxxk i ,j k i,j k xk
*
,
*
,
* *
( )
( )= − +−
2
2 1∆
∆ (41)
T
x
T T xTxxm i ,j k i,j k xm
*
,
*
,
* *
( )
( )= − ++
2
2 1∆
∆ (42)
By means of Brian’s method and assuming that on
the boundary interface there is a continuity of heat flow:
K T K Tk xk m xm
* *= (43)
We obtain:
[ ]2 2 1 1( ) ( ) ( ), ,
*
, ,
*
, ,
*
, ,
*
∆x
K T T K T Tk i j k i j k m i j k i j k− +− + − +
( ) ( ), , , ,K K T K K T
K
a
K
a
k m y i j k
n
k m z i j k
n k
k
m
m
+ + + = +⎛
⎝
⎜
⎞
⎠
∂ ∂2 2 ⎟
−T T
t/
i j k i j k
n
, ,
*
, ,
∆ 2
(4
4)
By dividing equation (44) with (Kk + Km)/(x)2 and
with
Z
x
t K K
K
a
K
ai j k n k m
k
k
m
m
, , ,
( )
( )
=
+
+⎛
⎝
⎜
⎞
⎠
⎟
∆
∆
2
(45)
We obtain:
2
2 1
2
1
K
K K
T Z Z
K
K K
Tk
k m
i j k i j k n i j k
m
k m
i+
+ + −
+− +, ,
*
, , , , ,
*( ) 1 , ,
*
j k =
= + + + +− + − +T T T T Zi j k
n
i j k
n
i j k
n
i j k
n
i j k, , , , , , , , , , ,(1 1 1 1 2 n i j k
nT− 2 ) , , (46)
By analogy, equations for the second intermediate
value T**(47) and the value Tn+1 for second t/2 (48) are
obtained:
− + + − =− +T Z T T
K
k
i j k i j k n i j k i j k
k
k
, ,
**
, , , , ,
**
, ,
**( )1 12 1
2
+
− +−
k
T T
m
i j k i j k1 2, ,
*
, ,
*
+
+
+ + + −+ − +
2
21 1 1
K
K K
T T T Zm
k m
i j k i j k
n
i j k
n
i j k n, ,
*
, , , , , , ,( 1) , ,Ti j k
n (47)
− + + − =−
+ +
+
+T Z T T
K
i j k
n
i j k n i j k
n
i j k
n
, , , , , , , , ,( )1
1 1
1
12 1
2 k
k m
i j k i j k
k k
T T
+
− +−1 2, ,
*
, ,
*
+
+
+ + −+ −
2
2 11 1
K
K K
T T Z Tm
k m
i j k i j k i j k n i j k, ,
*
, ,
**
, , , , ,
*( ) * , ,
**+ +Ti j k1 (48)
In the same way the approximations for temperatures
on the vertical XZ and the horizontal XY boundary
surfaces are derived.
V. GROZDANI]: FINITE-DIFFERENCE METHODS FOR SIMULATING THE SOLIDIFICATION OF CASTINGS
Materiali in tehnologije / Materials and technology 43 (2009) 5, 233–237 237
Figure 3: The vertical boundary surface YZ between the mould and
the metal (x = z).
Slika 3: Vertikalna lo~ilna povr{ina YZ med kokilo in kovino (x =
y)

V. KEVORKIJAN, S. D. [KAPIN: PRESSURELESS REACTIVE SINTERING OF TIAL-TIC ...
PRESSURELESS REACTIVE SINTERING OF TiAl-TiC
AND Ti3Al-TiC COMPOSITES
REAKCIJSKO SINTRANJE KOMPOZITOV TiAl-TiC IN Ti3Al-TiC
PRI ATMOSFERSKEM TLAKU
Varu`an Kevorkijan1, Sre~o Davor [kapin2
1Independent Researching plc, Betnavska cesta 6, 2000 Maribor, Slovenia
2Jo`ef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
varuzan.kevorkijansiol.si
Prejem rokopisa – received: 2009-03-26; sprejem za objavo – accepted for publication: 2009-06-20
TiAl and Ti3Al based composites reinforced with volume fractions 10–50 % of TiC particles were successfully prepared by
pressureless reaction sintering of reaction mixtures consisting of commercial titanium aluminide powders (TiAl with traces of
Ti3Al and the single phased Ti3Al) blended with the appropriate amount of ceramic reinforcement, 5–10 % of Al powder and, in
some cases, also 5 % of Ti powder added as sintering agents. The green compacts made from the blended powder mixture were
reaction sintered at 1300 °C for 2 h in an Ar + 4 % H2-rich environment using a vacuum furnace. The morphology of the
commercial powders and the microstructure of the as-sintered composites were studied by scanning electron microscopy and
X-ray diffraction analysis.
The pressureless sintering of as-received TiAl and Ti3Al powders resulted in samples with 10–15 % of the retained porosity. On
the other side, the addition of 10 % of TiC particles to the sintering mixture improved pressureless densification enabling
fabrication of composite samples with >95 % of theoretical density without addition of free aluminium. In these particular
cases, densification was promoted by chemical reactions between TiAl or Ti3Al and TiC leading to the formation of Al2Ti4C2
and Ti3AlC secondary bonding phases, respectively. However, as it was confirmed by sintering experiments, for successful (>95
% of theoretical density) pressureless densification of composite samples with more than 10 vol. of TiC, the addition of 5–10 %
of free aluminium and 5 % of titanium, depending on the actual amount of TiC reinforcement, was necessary. The addition of
Al and Ti promotes liquid reaction sintering and the formation of secondary Ti-Al-C bonding phases in an Al-Ti co-continuous
network.
The tensile properties and Vickers hardness of composite samples were measured at room temperature. The improvement in
tensile properties (except elongation) and Vickers hardness was found to correlate with the amount of TiC reinforcement in the
matrix.
Key words: TiAl-TiC and Ti3Al-TiC composites, pressureless reaction sintering, secondary bonding phases, microstructure,
room temperature tensile properties, Vickers hardness
Z reakcijskim sintranjem smo pripravili goste kompozitne materiale (z gostoto ve~jo od 95 % teoreti~ne gostote) na osnovi
spojin TiAl in Ti3Al, oja~anih z ustrezno koli~ino kerami~ne faze, z volumenskim dele`e, Al-prahu 5–10 % in, v dolo~enih
primerih, tudi z dodatkom 5 % Ti-prahu. Uporabljen komercialni TiAl prah je vseboval sledove Ti3Al, medtem ko je bil prah
Ti3Al enofazen. Dodatek prahov Al in Ti k izhodnim sestavam je omogo~al bolj{e sintranje. Izhodne homogenizirane sestave
smo enoosno stisnili v pelete in jih reakcijsko sintrali v vakuumski pe~i pri 1300 °C, 2 h v za{~itni atmosferi Ar + 4 % H2.
Morfologijo, sestavo in velikost delcev izhodnih prahov ter mikrostrukturo pripravljenih vzorcev smo analizirali z elektronskim
vrsti~nim mikroskopom in energijsko disperzijsko analizo ter z rentgensko pra{kovno difrakcijo.
Sintrani vzorci na osnovi spojin TiAl in Ti3Al izkazujejo od 10 % do 15% poroznosti. Pri dodatku 10 % TiC k tem spojinam pa
dobimo goste vzorce z gostoto ve~ kot 95 % teoreti~ne. V teh sistemih pote~ejo med segrevanjem reakcije med TiAl oziroma
Ti3Al in TiC, pri ~emer nastajajo vezne sekundarne faze Al2Ti4C2 in Ti3AlC. Ugotovili smo, da za pripravo gostih kompozitnih
materialov z reakcijskim sintranjem (>95 % teoreti~ne gostote) pri vi~jem dodatku kot 10 % TiC potrebujemo {e 5–10 % Al in 5
% Ti, kar je odvisno od koli~ine TiC. Dodana elementa Al in Ti omogo~ata reakcijsko sintranje v teko~i fazi in tvorbo
sekundarnih veznih faz na osnovi Ti-Al-C, dispergiranih ko-kontinuirni matriki Al-Ti.
Mehanske lastnosti (natezno trdnost in trdoto) smo merili pri sobni temperaturi. Izbolj{anje natezne trdnosti in Vickersova
trdota sta sorazmerni, ratezek pa obratno sorazmeren ve~anju vsebnosti TiC v kompozitih.
Klju~ne besede: TiAl-TiC in Ti3Al-TiC kompoziti, reakcijsko sintranje pri atmosferskem tlaku, sekundarne vezne faze,
mikrostruktura, mehanske lastnosti pri sobni temperaturi, trdota po Vickersu
1 INTRODUCTION
TiAl- and Ti3Al-based intermetallic-matrix compo-
sites (IMCs) reinforced with ceramic particles have
several advantages over conventional titanium alloys,
such as higher elastic modulus, lower density, better
mechanical properties at elevated temperatures, and
higher oxidation resistance 1,2. However, bringing these
attractive intermetallic composite matrices into commer-
cial use largely depends upon the availability of practical
and competitive processing routes. Due to difficulties in
production of IMCs by foundry methods and the high
cost of powder processing, the elemental powder
metallurgy (EPM) route has been gaining more and more
attention. According to the EPM processing route,
near-net shape IMC products can be fabricated by the
consolidation and forming of blended Ti and Al
elemental powders and ceramic reinforcement, followed
by a subsequent reactive synthesis and sintering process.
However, due to the large difference between the partial
diffusion coefficients of Ti and Al, the synthesis of
TiAl/Ti3Al alloys via reactive sintering follows a
Materiali in tehnologije / Materials and technology 43 (2009) 5, 239–244 239
UDK 669.715:620.18:621.762.5 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 43(5)239(2009)
mechanism in which Al atoms move into the Ti lattice,
thus leading to the formation of Kirkendall diffusion
pores 5. Although hot isostatic pressing (HIP) and other
pressure-assisted methods have been reported to be
effective in eliminating the porosity of reactively
sintered TiAl- and Ti3Al-based composite matrices 6–9,
their high cost and low production efficiency make them
unsuitable for commercial use.
In the present study the assumption was made that, if
sufficient reactivity in the system is provided, pressure-
less sintered TiAl- and Ti3Al-based IMCs with >95 % T.
D. may be successfully obtained, starting from TiAl and
Ti3Al powders mixed with suitable ceramic reinforce-
ment (such as TiC) and sintering additives (Al and Ti
powders). During high temperature presureless sintering,
TiC and Al react with the TiAl and Ti3Al matrix forming
different bonding phases. These promote further densifi-
cation and elimination of porosity in the system.
Thus, the aim of this study was to investigate the
potential of the pressureless sintering method in fabri-
cation of fully dense, high quality TiAl- and Ti3Al-based
IMCs by applying reaction mixtures consisting of
commercial titanium aluminide powders mixed with
various amounts (volume fractions from 10 % to 50 %)
of TiC ceramic particles, 5–10 % of Al and 5 % of Ti
sintering agent.
2 EXPERIMENTAL
Composites were prepared with blending commer-
cially available powders of either TiAl or Ti3Al with TiC
powder in appropriate amounts to create titanium
aluminide-based matrices with volume fractions (10, 20,
30, 40 and 50) % of TiC discontinuous reinforcement.
The powder blends were thoroughly mixed and sub-
sequently cold compacted. In all cases, the reaction
synthesis was conducted at 1300 °C for 2 h in an Ar + 4
% H2-rich environment using a vacuum furnace.
The as-synthesized composite samples were cut,
machined and polished in accordance with standard
procedures.
Microstructural characterization was performed by
scanning electron microscopy (SEM), whereas X-ray
diffraction (XRD) measurements were applied to the
samples to identify the phases and their crystal structure.
The specimens for optical microscope (OM) observa-
tion were electrolytically polished in a solution of 95 %
CH3COOH and 5 % HClO4, and then etched in a solution
of 5 % HNO3, 15 % HF, and 80 % H2O. The main grain
sizes were measured by the linear intercept method.
The specimens for XRD were abraded with SiC
paper and were then subjected to diffraction using CuKa
radiation.
Quantitative determination of the volume percentage
of the retained porosity was performed by analysing OM
and SEM micrographs of infiltrated composites using the
point counting method and image analysis and pro-
cessing software.
The tensile properties (tensile strength, 0.2 % tensile
yield strength and elongation) of the composite
specimens were determined in accordance with the
ASTM test method, E8M-96. The tensile tests were
conducted on drum shaped tension-test specimens 3.5
mm in diameter and 16 mm gauge length using an
automated servo-hydraulic tensile testing machine with a
crosshead speed of 0.254 mm/60 s.
The Vickers hardness (HV) measurements were
performed at room temperature on polished composite
samples as an average of 15 indentations. These
measurements were made on an automatic digital tester
using a pyramidal diamond indenter with a facing angle
of 136° A 0.025 kg indenting load, 50 µm/s load
applying speed, and a 15 s load holding time.
3 RESULTS AND DISCUSSION
3.1 Morphology of titanium aluminide powders applied
The as-received powders are non-agglomerated, with
well shaped individual particles having similar particles
V. KEVORKIJAN, S. D. [KAPIN: PRESSURELESS REACTIVE SINTERING OF TIAL-TIC ...
240 Materiali in tehnologije / Materials and technology 43 (2009) 5, 239–244
Figure 1: (a) SEM micrograph of as-received commercial TiAl
powder and (b) XRD spectra of the TiAl powder showing traces of
Ti3Al compound
Slika 1: (a) SEM-posnetek komercialnega prahu TiAl in (b) XRD-
spekter prahu TiAl s sledmi spojine Ti3Al
size (Figure 1 and 2). TiAl was with traces of Ti3Al
while Ti3Al powder was single phase.
3.2 Microstructure development in IMCs reinforced
with TiC
Generally, the microstructure of IMCs consists of an
intermetallic matrix (based on an ordered intermetallic
compound or a multiphase combination of intermetallic
compounds), the ceramic particulate reinforcement and
an interfacial region with the secondary phases formed
during reactive sintering.
Cost-effective, pressureless densification of TiAl and
Ti3Al powders, as well as of TiAl and Ti3Al powders
blended with ceramic particulates most often results in
V. KEVORKIJAN, S. D. [KAPIN: PRESSURELESS REACTIVE SINTERING OF TIAL-TIC ...
Materiali in tehnologije / Materials and technology 43 (2009) 5, 239–244 241
Figure 3: SEM micrograph of pressureless sintered non-reinforced
TiAl compact. Sintering conditions: 1300 °C, 2 h
Slika 3: SEM-posnetek vzorca TiAl, sintranega pri atmosferskem tla-
ku brez dodatkov kerami~ne oja~itve. Pogoji sintranja: 1300 °C, 2 h
Figure 2: (a) SEM micrograph of as-received commercial Ti3Al
powder and (b) XRD spectra of the Ti3Al powder
Slika 2: (a) SEM-posnetek komercialnega prahu Ti3Al in (b)
XRD-spekter prahu Ti3Al
Figure 4: SEM micrograph of pressureless sintered non-reinforced
Ti3Al compact. Sintering conditions: 1300 °C, 2 h
Slika 4: SEM-posnetek vzorca Ti3Al, sintranega pri atmosferskem tla-
ku brez dodatkov kerami~ne oja~itve. Pogoji sintranja: 1300 °C, 2 h
Figure 5: SEM micrograph of (a) Ti3Al reactively bonded with
Ti3AlC and (b) TiAl reactively bonded with Al2Ti4C2 phases
Slika 5: SEM posnetek (a) Ti3Al reakcijsko vezanega s Ti3AlC in (b)
TiAl reakcijsko vezanega s fazo Al2Ti4C2
material that is not free of porosity. Typical micro-
structures of pressureless sintered non-reinforced TiAl
and Ti3Al samples made from the commercial powders
used in this work are presented in Figures 3 and 4. The
samples obtained are porous (85–90 % T. D.).
However, based on the experimental results of
pressureless sintering of TiAl-TiC and Ti3Al-TiC
samples, it was recognized that addition of TiC improves
the densification of the system, enabling pressureless
fabrication of composites with more than 95 % of T. D.,
Table 1. Until the amount of TiC reinforcement in TiAl
and Ti3Al based composites not overcome 10 %, pressu-
reless sintering was completed without addition of any
sintering agents. Densification was promoted by chemi-
cal reactions between TiAl or Ti3Al and the formation of
Al2Ti4C2 and Ti3AlC secondary phases:
2TiAl + 2TiC = Al2Ti4C2 (1)
2Ti3Al + TiC = Ti3AlC + AlTi2 + 2Ti (2)
As evident in Figures 5 a,b, the in situ formed
Al2Ti4C2 and Ti3AlC phases are involved in bonding of
intermetallic grains and elimination of Kirkendall
diffusion pores resulting in samples with density about
98 % T. D., Table 1.
The resulting microstructures of the sintered
composite samples with 10 % of TiC particulate are
presented in Figure 6 a, b.
As evident in Figure 6 a,b, the sintered samples
possessed a near uniform distribution of equiaxial
intermetallic grains, secondary phases and retained
porosity. Larger pores were located mostly at the inter-
face region, while high magnification observation
revealed the presence of numerous fine pores uniformly
distributed through the secondary phase, Figure 7.
V. KEVORKIJAN, S. D. [KAPIN: PRESSURELESS REACTIVE SINTERING OF TIAL-TIC ...
242 Materiali in tehnologije / Materials and technology 43 (2009) 5, 239–244
Figure 6: SEM micrograph of samples with the starting composition:
(a) 90 % TiAl + 10 % TiC and (b) 90 % Ti3Al-10 % TiC sintered up to
95 % T. D. Sintering conditions: 1300 °C, 2 h, (c) XRD spectra of the
sample with the starting composition 90 % TiAl + 10 % TiC and (d)
XRD spectra of the sample with the starting composition 90 % Ti3Al
+ 10 % TiC
Slika 6: SEM-posnetek vzorcev z za~etno sestavo: (a) 90 % TiAl + 10
% TiC in (b) 90 % Ti3Al-10 % TiC sintranih nad 95 % T. G. Pogoji
sintranja: 1300 °C, 2 h, (c) XRD-spekter vzorca za~etne sestave 90 %
TiAl + 10 % TiC in (d) XRD-spekter vzorca za~etne sestave 90 %
Ti3Al + 10 % TiC
Figure 7: SEM micrograph of porous secondary phase between TiAl
grains. Numerous fine pores are nearly uniformly distributed, inclu-
ding some larger ones at the interface. The grey inclusions are
solidified aluminium.
Slika 7: SEM-posnetek porozne sekundarne faze med zrni TiAl.
[tevilne fine pore so skoraj enakomerno razporejene, vklju~no z
nekaterimi ve~jimi na fazni meji. Vklju~ki sive barve so iz strjenega
aluminija.
In samples with 20–50 % of TiC reinforcement,
successful pressureless densification was achieved only
by addition of 5–10 % of free aluminium as sintering
agent. The role of free aluminium was twofold: (i) it
reacted with TiC forming Al-Ti-C bonding phase and (2)
provided liquid Al-Ti phase necessary for liquid reaction
sintering and impregnation of pores.
The microstructure of the composites obtained,
Figure 8, is characterized by isolated TiAl and Ti3Al
V. KEVORKIJAN, S. D. [KAPIN: PRESSURELESS REACTIVE SINTERING OF TIAL-TIC ...
Materiali in tehnologije / Materials and technology 43 (2009) 5, 239–244 243
Table 1: Average room temperature tensile properties and Vickers hardness of various laboratory prepared composite samples
Tabela 1: Povpre~ne vrednosti mehanskih lastnosti, izmerjene pri sobni temperaturi in vrednosti trdote po Vickersu vzorcev kompozitov
Initial chemical
composition in volume
fractions (%)
Retained
porosity
(%)
E
(GPa)
Tensile
strength
(MPa)
0.2 % tensile
yield strength
(MPa)
Vickers
hardness
(GPa)
Elongation
in 50 mm
(%)
90Ti3Al + 10TiC 4.1 ± 0.4 118 ± 12 474 ± 47 323 ± 32 2.9 ± 0.3 0.5 ± 0.05
75Ti3Al + 20TiC+5Al 3.9 ± 0.4 158 ± 16 518 ± 52 389 ± 39 3.6 ± 0.4 0.3 ± 0.03
60Ti3Al + 30TiC+10Al 3.6 ± 0.4 194 ± 20 547 ± 55 419 ± 42 5.8 ± 0.6 0.2 ± 0.02
50Ti3Al + 40TiC+10Al 3.3 ± 0.3 222 ± 22 596 ± 60 448 ± 45 6.2 ± 0.6 0.1 ± 0.01
40Ti3Al + 50TiC+10Al 4.4 ± 0.4 253 ± 25 619 ± 62 490 ± 49 6.5 ± 0.7 0.1 ± 0.01
90TiAl + 10TiC 4.0 ± 0.4 196 ± 20 339 ± 34 273 ± 27 2.7 ± 0.3 0.5 ± 0.05
75TiAl + 20TiC+5Al 3.8 ± 0.4 215 ± 22 368 ± 37 289 ± 29 3.2 ± 0.3 0.3 ± 0.03
70TiAl + 20TiC+10Al 3.4 ± 0.3 226 ± 23 419 ± 42 322 ± 32 5.1 ± 0.5 0.2 ± 0.02
60TiAl + 30TiC+10Al 3.9 ± 0.4 244 ± 24 453 ± 45 346 ±35 5.6 ± 0.6 0.2 ± 0.02
50TiAl + 40TiC+10Al 4.0 ± 0.4 272 ± 27 493 ± 49 380 ± 38 6.0 ± 0.6 0.1 ± 0.01
40TiAl + 50TiC+10Al 4.2 ± 0.4 299 ± 30 516 ± 52 412 ± 41 6.4 ± 0.6 0.1 ± 0.01
Figure 8: SEM micrograph and XRD spectra of the sample with the
starting composition of TiAl-50 % TiC-5 % Al. The secondary formed
Al2Ti4C2 and AlTi2 phases are porous.
Slika 8: SEM-posnetek in XRD-spekter vzorca za~etne sestave
TiAl-50 % TiC-5 %Al. Sekundarno ustvarjene faze Al2Ti4C2 in AlTi2
so porozne.
Figure 9: SEM micrograph and XRD spectra of TiAl-50 % TiC-10 %
Al-5 % Ti composite sample with a secondary phases well infiltrated
with solidified Al-Ti alloy (dark continuous phase)
Figure 9: SEM posnetek in XRD-spekter vzorca za~etne sestave
TiAl-50 % TiC-10 % Al-5 % Ti s sekundarnimi fazami popolnoma
infiltriranimi z zlitino Al-Ti (temna zvezna faza)
grains well surrounded by a secondary bonding phases
and finely dispersed TiC particulates.
However, as evident in Figure 8, the secondary
phases formed during reactive sintering of specimens
with a high amount of TiC and 5 % of Al remain porous.
For a more complete densification of secondary phases,
the free aluminium content in the green compacts was
increased to 10 % and 5 % of Ti powder was also added.
The role of Ti was to promote the infiltration of an Al-Ti
alloy into the porous regions of the secondary phases and
the formation of TiAl and/or Ti3Al secondary inter-
metallics inside the pores leading to its closuring.
The microstructure of samples sintered with addition
of Al and Ti is shown in Figure 9.
3.3 Mechanical properties
The results of room temperature tensile tests on
composite samples are listed in Table 1. As a result of
matrix reinforcement, significant improvements in
Young’s modulus, tensile strength and ultimate tensile
strength as well as Vickers hardness of the fabricated
composites were observed, resulting in IMCs with
excellent mechanical properties. These mechanical
properties were found to be slightly better in composites
with Ti3Al-based matrix compared to the TiAl-based
matrix counterparts. Comparing the mechanical proper-
ties of composite samples with various volume fractions
of ceramic particles in the matrix, it was found that
Young’s modulus, tensile strength, ultimate tensile
strength and Vickers hardness increased while elon-
gation decreased with an increasing fraction of ceramic
reinforcement.
4 CONCLUSION
A study of the fabrication of TiAl- and Ti3Al-based
intermetallic matrix composites (IMCs) discontinuously
reinforced with 10 % to 50 % of TiC was conducted by
applying conventional pressureless reactive sintering of
single phase TiAl or Ti3Al powders and ceramic rein-
forcement. Following this cost-effective procedure, com-
posites till 10 % of TiC reinforcement were routinely
pressureless sintered to densities higher than 95 % of T.
D. by solid state sintering with no sintering agents. On
the contrary, in samples with more than 10 % of TiC
reinforcement, the prerequisite for complete densifica-
tion was the addition of small amount of Al powder or
the mixture of Al and Ti powders with slight excess of
Al over Ti-Al or 3Ti-Al stoichiometric composition. The
elemental aluminium and titanium were involved in the
formation of secondary bonding phases and liquid
reaction sintering while the excess of aluminium is
necessary for complete infiltration of pores in the
secondary phases formed during reactive sintering. In
this way, dense composite samples with 10 % to 50 % of
TiC reinforcement and a retained porosity less than 5 %
were successfully obtained, revealing the significant
industrial potential of this fabrication method.
Metallographic analysis of the as-densified micro-
structures confirmed that during densification TiAl and
Ti3Al react with TiC and Al forming various secondary
phases (Al2Ti4C2, Ti3AlC, AlTi2) responsible for simulta-
neous bonding of intermetallic grains and elimination of
pores. An un-identified, continuous Ti-Al-C phase was
also detected in samples sintered with addition of Al and
Ti.
Regarding the room temperature tensile properties,
the improvement of tensile strength, tensile yield
strength and modulus was found to correlate with the
amount of ceramic reinforcement in the matrix. How-
ever, quite the opposite behaviour was found regarding
elongation, where the introduction of ceramic particles
into the intermetallic matrix in all specimens led to a
significant reduction of elasticity.
The best tensile properties (except elongation) were
obtained in TiAl-TiC and Ti3Al-TiC samples with the
highest amount (50 %) of ceramic reinforcement.
Acknowledgment
This work was supported by funding from the Public
Agency for Research and Development of the Republic
of Slovenia, as well as the Impol Aluminium Company
from Slovenska Bistrica, Slovenia, under contract No.
1000-07-219308
5 REFERENCES
1 Bassics of Thermodynamics and phase transitions in complex
intermetallics, E. B. Ferre, ed.,World Scientific, Singapore, 2008, pp.
147
2 S. Djanarthany, J. C. Viala, J. Bouix: Mater. Chem. Phys., 72 (2001),
301
3 E. K. Y. Fu, R. D. Rawlings, H. B. McShane, J. Mater. Sci., 36
(2001), 5537
4 M. Sujata, S. Bhabgava, S. Sangal, J. Mater. Sci. Lett., 16 (1997),
1175
5 F. Wenbin, H. Lianxi, H. Wenxiong, W. Erde, L. Xiaoqing, Mater.
Sci. Eng., 403 (2005), 186.
6 R. Martin, S. L. Kampe, J. S. Marte, T. P. Pete, Metall. Mater. Trans.
A, 33 A (2002), 2747
7 Y. Yun-long, G, Yan-sheng, W. Hai-tao, W. Chuan-bin, Z.
Lian-meng, Journal of Wuhan University of Technology – Mater.
Sci. Ed., 19 (2004), 1
8 T. W. Lee, C. H. Lee, J. Mater. Sci. Lett., 18 (1999), 801
9 E. K. Y. Fu, R. D. Rawlings, H. B. McShane, J. Mater. Sci., 26
(2001), 5542
V. KEVORKIJAN, S. D. [KAPIN: PRESSURELESS REACTIVE SINTERING OF TIAL-TIC ...
244 Materiali in tehnologije / Materials and technology 43 (2009) 5, 239–244
N. KRSTULOVI] ET AL.: AN OPTICAL-EMISSION-SPECTROSCOPY CHARACTERIZATION ...
AN OPTICAL-EMISSION-SPECTROSCOPY
CHARACTERIZATION OF OXYGEN PLASMA DURING
THE OXIDATION OF ALUMINIUM FOILS
KARAKTERIZACIJA KISIKOVE PLAZME MED OKSIDACIJO
ALUMINIJEVIH FOLIJ Z OPTI^NO EMISIJSKO SPEKTROSKOPIJO
Nik{a Krstulovi}1, Uro{ Cvelbar2, Alenka Vesel2, Slobodan Milo{evi}1,
Miran Mozeti~2
1 Institute of Physics, Bijeni~ka 46, HR-10000 Zagreb, Croatia
2 Jozef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia
slobodanifs.hr
Prejem rokopisa – received: 2009-06-06; sprejem za objavo – accepted for publication: 2009-06-18
A highly reactive oxygen plasma was applied for the oxidation of aluminium foils. The plasma was created within a
radio-frequency discharge operating at a power of 300 W and a frequency of 27.12 MHz. Samples of Al foils with dimensions
of (20 × 40) mm were placed into the discharge chamber. During the treatment of the foils with oxygen plasma, the optical
spectra were measured simultaneously with an optical spectrometer. The predominant spectral features observed during the
treatment were atomic oxygen lines at 777.4 nm and 844.6 nm, atomic hydrogen lines and an OH band at 309 nm. As the
oxidation took place other spectral features appeared. The major lines were Na at 589.35 nm and K at 766.5 nm and 769.9 nm.
The time evolution of the Na and K peaks showed well-defined maxima after about a minute of plasma treatment. These
maxima depended on the pressure in the discharge chamber. At the lowest pressure of 30 Pa the maxima appeared after about
100 s, while at a pressure of 80 Pa the maxima appeared after about 50 s. At a pressure of 120 Pa these maxima appeared after
about 125 s. This behaviour was explained by the segregation of Na and K on the surface of the foil and the rapid desorption
into the gas phase.
Keywords: oxygen plasma, aluminium foils, oxidation, optical emission spectroscopy
Za oksidacijo aluminijevih folij smo uporabili visoko reaktivno kisikovo plazmo, ki smo jo ustvarili z radiofrekven~no
razelektritvijo pri frekvenci 27,12 MHz in mo~i 300 W. Vzorce Al-folij dimenzij 20 × 40 mm smo polo`ili v razelektritveno
posodo in obdelali s kisikovo plazmo. Med obdelavo smo isto~asno snemali opti~ni emisijski spekter z opti~nim
spektrometrom. Prevladujo~a spektralna posebnost obdelave so bili atomski kisikovi vrhovi pri valovnih dol`inah 777,4 nm in
844,6 nm, atomski vodikovi vrhovi ter molekulski pas OH pri 309 nm. Po za~etku oksidacije folij se je pojavila tudi emisija Na
pri 589,35 nm in K pri 766,5 nm ter 769,9 nm. ^asovni razvoj teh vrhov je pokazal na izrazit maksimum po eni minuti
obdelave. Izkazalo pa se je, da je ta maksimum odvisen od tlaka v razelektritveni posodi. Pri najni`jem tlaku 30 Pa se je
maksimum pojavil pri 100 s, medtem ko se je pri tlaku 80 Pa pri 125 s. Tako vedenje smo pojasnili s segregacijo Na in K na
povr{ino folij in njihovo hitro desorpcijo v plinsko fazo.
Klju~ne besede: kisikova plazma, aluminijeve folije, oksidacija, opti~na emisijska spektroskopija
1 INTRODUCTION
Commercially available aluminium foils are now-
adays widely used in different industries, including the
electronic and food industries. Aluminium is characte-
rized by good electrical and thermal conductivities, and
since the material is relatively inexpensive its application
is very broad. However, in some cases the surface of the
aluminium foil should be modified. In many cases, for
example, the material would perform better if a thin film
of oxide is formed on the surface. Anodic oxidation
ensures the formation of such an oxide film by a process
that requires special equipment which is not always
available. An alternative technique is the oxidation of
metals using an oxygen plasma 1–6. This technique
proved to work very well for several metals, including
stainless steel. Since the application of such a method is
interesting for the electronics industry we performed
research on a modification of aluminium foils with a
highly reactive oxygen plasma 7–10. It was found that a
thin film of the order of 10 nm is rapidly grown on such
foils. The technology should not cause any other
modification of the material. In order to see whether the
micro-elements are not affected by the plasma treatment
we performed a systematic study of the plasma charac-
terization during a treatment of aluminium foils.
Namely, the microelements that may be depleted from
the foils are presented in such a tiny concentration that
they are not visible with standard techniques for surface
and thin-film characterization. On the other hand,
metallic atoms have low excitation energies and are thus
visible by optical emission spectroscopy, even when
present in extremely low concentrations 11.
2 EXPERIMENTAL
The experiments were performed in a plasma reactor,
which is schematically shown in Figure 1. The reactor is
made from borosilicate glass with a low recombination
coefficient for the reaction O + O  O2. The diameter of
Materiali in tehnologije / Materials and technology 43 (2009) 5, 245–249 245
UDK 669.715:621.762.5 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 43(5)245(2009)
the glass tubes presented in Figure 1 is 40 mm.
Two-sided tubes serve for the plasma characterization.
One tube is terminated with a quartz window, while the
other one is used for mounting a catalytic probe 12–14. The
samples are fixed on a thermocouple probe and placed in
the centre of the discharge chamber, as shown in Figure
1. The RF coil is connected to the radiofrequency gene-
rator operating at a power of 300 W and a frequency of
27.12 MHz. On one side, the discharge chamber is
pumped with a two-stage rotary pump with a nominal
pumping speed of 16 m3/h, while on the other side
commercially available oxygen is continuously leaked.
The pressure in the experimental system is measured
with an absolute pressure gauge. The ultimate pressure
in the system is about 7 Pa. The residual atmosphere
consists of water vapour and traces of other gases 15. The
optical emission spectra are detected through an optical
fibre by an optical spectrometer (Ocean Optics HR 2000
CG-UV-NIR). The spectra were detected in the entire
range from 200 nm to 950 nm. The spectra were taken at
an integration time of 900 ms and a repetition time of
1 s. The spectral resolution of the spectrometer was
1 nm. The spectral sensitivity of the optical system was
measured with a reference light source (LS-1-CAL,
OceanOptics), and with a deuterium lamp for the range
below 400 nm. The spectral sensitivity is almost flat in
the region between 400 nm and 800 nm, but it drops
significantly towards the edges 15,16.
3 RESULTS
The samples were exposed to oxygen plasma at
different pressures between 30 Pa and 120 Pa. The
optical spectra were measured continuously during the
plasma treatment, as explained above. Typical optical
spectra are shown in Figure 2. Figure 2 represents three
characteristic spectra: after a) the first few seconds b)
after 50 s, c) after a prolonged treatment. The major
spectral features are oxygen atom lines in the red part of
the spectra and O2 molecular band at 760 nm (b1+g –
X3g– (0,0)) 17. Apart from these lines, additional lines of
the atomic hydrogen Balmer series and the impurity
molecular OH band at 309 nm 18, the N2 2nd positive
band, (C3u – B3g) around 315 nm 19, and the CO Ang-
strom band 450–600 nm 20 are present. As the oxidation
took place, other spectral features appeared. The major
lines were Na at 589.35 nm (unresolved D-lines) and K
at 766.5 nm and 769.9 nm. The time evolution of all
these peaks during the plasma treatment of the Al foil is
shown in Figure 3 for the O, Na and K transitions, and
in Figure 4 for the other peaks: H, CO, O2, OH. All
these experiments were performed at a pressure of 80 Pa.
Note that the oxygen line’s intensity exhibits a local
minimum, while the Na and K lines are of maximum
intensity. Another set of experiments was performed at
different pressures. The time at which the maximum in
the sodium peak was observed is plotted in Figure 5.
4 DISCUSSION
The spectrum presented in Figure 2 a) is rather
typical for oxygen plasma created in an experimental
chamber that is sealed with rubber gaskets and never
N. KRSTULOVI] ET AL.: AN OPTICAL-EMISSION-SPECTROSCOPY CHARACTERIZATION ...
246 Materiali in tehnologije / Materials and technology 43 (2009) 5, 245–249
Figure 2: Typical optical emission spectra of the plasma in a) the first
few s b) after 50 s, c) after a prolonged time (220 s). The oxygen gas
pressure was 80 Pa and the discharge power 300W
Slika 2: Zna~ilni opti~no emisijski spekter plazme v a) prvih nekaj
sekundah, b) po 50 s in c) po dalj{em ~asu (220 s) pri tlaku kisika 80
Pa in razelektritveni mo~i 300W
Figure 1: Schematics of discharge vessel
Slika 1: Shema rezelektritvene posode
backed 15,21,22. Apart from the oxygen lines we could
observe the OH band in the UV range as well as the
molecular nitrogen and CO bands. The relatively strong
emission from the hydrogen atoms is due to the
dissociation of water molecules in our plasma. The
nitrogen band probably comes from a small leakage of
the system, while the CO band is probably due to the
oxidation of traces of organic impurities. All these
spectral features decrease in intensity with an increasing
treatment time, as shown in Figure 4. Such a decrease is
explained by the continuous pumping of the vacuum
system and, also, the relatively good oxidation of the
organic impurities. More interesting is the appearance of
the Na and K peaks, as is clearly shown in Figure 2 b).
These elements do not come from the discharge chamber
because they are not observed for the case of an empty
chamber. The origin of these two metals is obviously the
aluminium foil. A strong maximum of these peaks is
observed versus the treatment time, as shown in Figure
3. Such maxima are explained by the heating of the
aluminium foils during the plasma treatment. Namely,
the aluminium foil interacts with the oxygen atoms that
are present in a large concentration in the oxygen
plasma. The interaction is both physical and chemical.
The major physical interaction is a heterogeneous
surface recombination. At the reaction O + O 
 O2 the
dissociation energy is released and observed as the
internal energy of the aluminium foil. The recombination
coefficient definitely depends on the surface properties
of the aluminium foil, as well as its temperature.
N. KRSTULOVI] ET AL.: AN OPTICAL-EMISSION-SPECTROSCOPY CHARACTERIZATION ...
Materiali in tehnologije / Materials and technology 43 (2009) 5, 245–249 247
Figure 5: The treatment time at which the maximum of the Sodium
589.35 nm peak was achieved is plotted versus pressure
Slika 5: ^as obdelave v odvisnosti od tlaka, pri katerem je dose`en
maksimum vrha natrija 589,35 nm
Figure 4: Time evolution for H (656,2 nm), CO (519,3 nm), O2
(760,5 nm), OH (309 nm) intensities during a plasma treatment in 80
Pa of oxygen pressure
Slika 4: ^asovna odvisnost intenzitet vrhov H (656,2 nm), CO
(519,3 nm), O2 (760,5 nm), OH (309 nm) pri obdelavi v kisikovi
plazmi s tlakom 80 Pa
Figure 3: Time evolution for Oxygen 777,4 nm, Sodium 589,35 nm
and Potassium 766,5 nm intensities during a plasma treatment at 80 Pa
of oxygen pressure
Slika 3: ^asovna odvisnost intenzitet vrhov kisika O 777,4 nm, natrija
Na 589,35 nm in kalija K 766,5 nm pri obdelavi v kisikovi plazmi s
tlakom 80 Pa
Although exact data are not available, it is generally
accepted that the recombination coefficient increases
with increasing temperature. This is the main heating
mechanism. Apart from the physical reactions there is
also a chemical reaction, e.g., the formation of a thin
oxide film. Let us now discuss an extremely pronounced
peak in the sodium and potassium lines versus the
plasma treatment time. At first the sample temperature is
low, so hardly any migration of Na and K from the bulk
toward the surface is observed. However, as soon as the
samples are heated to an elevated temperature, surface
aggregation occurs and thus the intensity of spectral line
increases with increasing temperature. After a certain
treatment time the temperature is so high that the
formation of an oxide film is accomplished. The oxide
film represents a diffusion barrier for the migrating Na
and K atoms so the concentration of these two metals in
the plasma keeps decreasing. The drop in the Na and K
lines is far from being sudden. This effect may be
explained either by inhomogeneous oxidation or by poor
pumping from the discharge region. Namely, both Na
and K may adsorb on the surface of the glass chamber
and desorb slowly during the continuous pumping. Let
us now explain the very well pronounced minimum in
the curve presented in Figure 5. At low pressure the
density of the oxygen atoms is relatively low, so the
heating by heterogeneous surface recombination is
relatively poor. That is why the maximum is observed
after about 100 s of plasma treatment. At high pressure,
the oxygen atom density is high, but the treatment time
is even longer. This effect can be explained either by
good cooling of the sample due to pretty large drift
velocity of the gas through our plasma reactor or by the
lack of energetic ions. Namely, the kinetic energy of the
ions reaching the surface of the aluminium foils depends
on both the Debye length and the mean free path 23,24. In
the case of a short Debye length and a long mean free
path the sheath around the sample is collision-less, so
oxygen ions do not lose their kinetic energy. At the other
extreme the ions suffer many collisions with neutrals in
the sheath and lose practically all their kinetic energy. In
our plasma the Debye length keeps increasing with the
increasing pressure and the mean free path keeps
decreasing with the increasing pressure. Obviously, the
samples exposed to plasma at 30 Pa are bombarded with
energetic oxygen ions, while this effect is missing at 120
Pa. In between these two extremes the ion energy is still
high enough and the oxygen atom density is reasonably
high to allow for rapid heating of the samples and thus
the oxidation is acheived after about 50 s.
5 CONCLUSIONS
Samples of commercially available aluminium foils
were exposed to a highly reactive oxygen plasma. The
plasma was characterized by optical emission spectro-
scopy. We observed a rapid decrease in the concen-
tration of the impurities originally present in the
discharge chamber. As the temperature of the samples
was increasing we observed a rapid desorption of
potassium and sodium from the samples. This desorption
was explained by the migration of these two micro-
elements from the bulk aluminium towards the surface.
As an oxide film was formed on the surface, the
diffusion was blocked and the intensity of Na and K
spectral lines was decreasing with the increasing
treatment time. Our results clearly show the applicability
of optical emission spectroscopy for studying the
migration of elements that are present in bulk aluminium
at concentrations that cannot be detected with standard
methods for the surface and thin-film characterization.
Acknowledgements
This research was performed within the Slovenian-
Croatian bilateral project BI-SLO-HR-01(2009-2010).
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N. KRSTULOVI] ET AL.: AN OPTICAL-EMISSION-SPECTROSCOPY CHARACTERIZATION ...
Materiali in tehnologije / Materials and technology 43 (2009) 5, 245–249 249

R. CELIN ET AL.: EFFECT OF AGEING A TWO-PHASE FE-NICRMO ALLOY ...
EFFECT OF AGEING A TWO-PHASE Fe-NiCrMo ALLOY
ON THE STRAIN HARDENING AT ROOM
TEMPERATURE AND AT 290 °C
VPLIV STARANJA DVOFAZNE ZLITINE Fe-NiCrMo NA
DEFORMACIJSKO UTRJEVANJE PRI SOBNI TEMPERATURI IN
PRI 290 °C
Roman Celin, Jelena Vojvodi~ Tuma, Boris Arzen{ek
Institute of Metals and Technology, 1000 Ljubljana, Lepi pot 11, Slovenia
roman.celinimt.si
Prejem rokopisa – received: 2009-03-26; sprejem za objavo – accepted for publication: 2009-05-26
Fe-NiCrMo alloys were aged in the temperature range 290 °C to 350 °C for the spinodal decomposition of the ferrite solid
solution. The tensile properties and the Charpy notch toughness were determined at room temperature and at 290 °C. The
stress-strain curves were examined and the strain-hardening exponent was determined. This exponent changed little during the
increase of the ferrite hardness and it is greater at 290 °C than at room temperature. This confirms the explanation proposed for
the different effect of the test temperature on the notch toughness and the tensile properties.
Key words: austenite-ferrite microstructure, mechanical properties, ferrite hardness increase, strain hardening
Zlitina Fe-NiCrMo je bila starane v razponu temperature od 290 °C do 350 °C za spinodalno razgradnjo trdne raztopine v feritu.
Dolo~ene so bile raztr`ne lastnosti in zarezna `ilavost pri sobni temperaturi in pri 290 °C. Analizirane so bile krivulje napetost –
deformacija in dolo~en eksponent deformacijske utrditve avstenita. Ta eksponent se malo spremeni zaradi pove~anja trdote
ferita in je ve~ji pri 290 °C kot pri sobni temperaturi. To potrjuje razlago, zakaj so pri vi{ji temperaturi raztr`ne lastnosti ni`je,
zarezna `ilavost pa ve~ja kot pri sobni temperaturi.
Klju~ne besede: mikrostruktura ferita in avstenita, mehanske lastnosti, pove~anje trdote ferita, deformacijska utrditev
1 AIM OF THE INVESTIGATION
During the ageing of Fe-NiCrMo alloys with a micro-
structure of austenite and ferrite the hardness of the
ferrite is increased because of the spinodal decompo-
sition of the solid solution in ferrite into two consti-
tuents: one enriched in chromium and the second
enriched in nickel. In both phases the initial -iron
lattice is preserved, while the lattice parameters are
modified. Both constituents accommodate with elastic
internal stresses that increase the hardness and brittleness
and, after magnetisation, result in alloys with a suitable
chemical composition and hard magnetic properties1,2.
The kinetics of the decomposition depends on the
diffusional transport of atoms in the substitutional solid
solution in the ferrite. The rate of diffusion depends
strongly on the temperature, and for this reason, the rate
of spinodal decomposition-ageing is very slow in the
temperature range in which alloys of this type are
operating in power plants. In the ageing process of
ferrite, the solid solution in austenite is stable; it may
only change with the precipitation of carbides if the
content of carbon is above the solubility limit. At higher
temperature, the spinodal decomposition is replaced by
the formation of 
-phases, which greatly diminishes the
ductility of the alloys3. With ageing, the properties of the
alloys with a two-phase microstructure of austenite and
ferrite are changed, depending on the volume share of
ferrite and the extent of its decomposition.
In investigations of this type of alloys4 it was
established that the change of properties was greater for
an alloy with 14.5 % of -ferrite than for an alloy with
8.5% of -ferrite when ageing in the temperature range
300 – 400 °C, while at higher temperatures the ageing
effect was smaller. These findings were confirmed5,
where it was found, also, that the content of -ferrite
determined from the Schaeffler diagram was unreliable
and that the distribution of ferrite in as-cast alloys was
inhomogeneous and could vary between 1.5 and 22.5 for
the same cast piece. The ageing effect on the Charpy
toughness was very strong in the temperature range 303
°C to 325 °C and the initial toughness was achieved
again after annealing at 550 °C. Of the several processes
that could affect the alloy’s properties, the main
embrittlement process is that of spinodal decomposition6.
A correlation was developed7 for the assessment of the
embrittlement and the prediction of changes in the
fracture and the Charpy and tensile properties of the
as-cast two-phase alloys. The use of small specimens for
the investigation of in-service-aged elbows gives reliable
values for the J-a results on the condition that strongly
deviating specimens are rejected8. The low-cycle fatigue
increases rapidly with the increase of the ageing time9.
In10,11 these findings were confirmed with the investi-
gations of alloys with a different volume share of ferrite.
Materiali in tehnologije / Materials and technology 43 (2009) 5, 251–255 251
UDK 669.14.018.298:620.178 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 43(5)251(2009)
It was found, also, that the tensile properties of the
unaged and aged alloys were lower and that the notch
toughness was higher when testing at 290 °C. The aim of
this work was to establish whether the difference was
related to the different strain-hardening behaviour of the
alloys at room temperature and at 290 °C.
In Figure 1 the effect of the ageing time and tempe-
rature on the ferrite and austenite microhardness are
shown10,11. The austenite micro-hardness is not affected
by the ageing, while the micro-hardness of the ferrite
starts to increase after an ageing time that is shorter with
higher temperature when the increase of the hardness is
faster and stronger.
In Figures 2 and 3 the tensile properties and the
notch toughness are given as a selection of data in10,11.
After ageing and a hardness increase of the ferrite from
HV 295 to about HV 650 units (an increase of the hard-
ness by 2.15 times), the elongation and the reduction of
area are decreased at both testing temperatures by about
30 %. For the average of the specimens aged for diffe-
rent times, the elongation and the reduction of area are
lower by about 25 % at 290 °C than at room temperature.
The yield stress is increased very slightly with the
increase of the ferrite hardness at both testing tempera-
tures, and it is only about 11 % greater for both testing
temperatures after the hardness of the ferrite was
increased to HV 650 units. For the tensile strength, the
effect of ageing time is greater, as at both testing tempe-
ratures it is increased by about 18 %. The effect of the
testing temperature is greater for the yield stress, as it is
decreased on average by 27 % at 290 °C, while the
tensile strength is decreased by about 19 %. The changes
are, in absolute values, larger with a large initial level
and are of 99 MPa for the yield stress and 140 MPa for
the tensile strength.
In Figure 4 the effect of ageing time at three
temperatures on the notch toughness is shown for testing
at room temperature and at 290 °C. When testing at
room temperature, the notch toughness starts to decrease
faster after ageing at 350 °C and 320 °C after the ferrite
hardness has increased to about 350 units. This shows
that the notch toughness is more sensitive to the effect of
the ferrite’s hardness increase. In11 an explanation was
proposed; that in the process of Charpy plastic defor-
mation and fracturing during a rapid toughness decrease,
the ferrite starts to fracture with a cleavage and that the
accelerated decrease of the notch toughness is related to
the cleavage of the ferrite inserts ahead of the tip of the
propagation fracture. By ageing at 350 °C at a ferrite
hardness of about 540 units a level of notch toughness is
achieved that is not changed during any further increase
of the hardness to 650 units. With a lower ageing tempe-
rature the final notch toughness level is achieved after
the longest ageing time. The explanation could be either
a difference in the extent of the spinodal decomposition
due to the difference in the ageing temperature or that
due to a level of hardness of about 450 units. It is mostly
those ferrite inserts fracture with cleavage that have a
favourable space orientation with regards to the plane of
the propagating crack.
For the non-aged alloy the notch toughness is higher
at 290 °C than at room temperature by about 20 J or 18
R. CELIN ET AL.: EFFECT OF AGEING A TWO-PHASE Fe-NiCrMo ALLOY ...
252 Materiali in tehnologije / Materials and technology 43 (2009) 5, 251–255
Figure 2: Effect of ageing time on the elongation and the reduction of
area at room temperature and at 290 °C
Slika 2: Vpliv trajanja staranja na razteznost in kontrakcijo pri sobni
temperaturi in pri 290 °C
Figure 3: Effect of ageing time on the yield stress and the tensile
strength at room temperature and at 290 °C
Slika 3: Vpliv trajanja staranja na mejo plasti~nosti in raztr`no trdnost
pri sobni temperaturi in pri 290 °C
Figure 1: Effect of ageing time at 290 °C, 320 °C and 350 °C on the
micro-hardness of the ferrite and austenite
Slika 1: Vpliv ~asa staranja pri 290 °C, 320 °C in 350 °C na mikro-
trdoto ferita in avstenita
%. After the longest ageing time the notch toughness at
room temperature is decreased by about 82 % and much
less, only by about 36 %, at a temperature of 290 °C.
Accordingly, at this stage of the decomposition of the
solid solution in ferrite, the difference in the notch
toughness at 290 °C and room temperature is increased
by about 3.5 times.
The tensile properties are lower and the notch
toughness is higher when testing at 290 °C, than at room
temperature. In11 it is assumed that the differences
between the properties at room temperature and 290 °C
are probably the difference in the deformation and the
fracturing behaviour of both kinds of tests due to the
presence of the notch on the toughness specimens and
the difference in test time, which cause a high local
heating due to the very fast deformation and fracturing
during the testing of the notched specimens12. A possible
effect of the different strain hardening at both testing
temperatures is surmised and this investigation is aimed
at its experimental verification. The ageing temperature
of 350 °C was selected because it results in the largest
and fastest changes of ferrite hardness and notch tough-
ness.
2 EXPERIMENTAL WORK
For this investigation the alloy and specimens in10,11
were used, although the details on the preparation,
ageing and testing of the alloys will also be summarised
here. The composition of the investigated alloy was: 0.06
C, 1.68 Si, 0.67 Mn, 0.03 P, 0.01S, 9.0 Ni, 20.8 Cr and
2.46 Mo. The microstructure of the alloy is shown in
Figure 5. The ageing temperatures were 290 °C, 320 °C
and 350 °C and the ageing time was up to 17.520 h. Only
specimens aged at 350 °C were used in this investigation
because of the highest increase of the ferrite hardness.
All the mechanical tests were performed at room tempe-
rature (22 °C) and at 290 °C. The micro-hardness was
determined only at room temperature. Additional measu-
rements of the ferrite micro-hardness were performed to
determine more accurately the hardness increase during
the ageing time of the start of the rapid decrease of the
notch toughness and the tensile tests were performed for
specimens aged for up to the longest ageing time.
Austenite does not fracture with a cleavage, and so for
this reason, and according to8, the exceedingly deviating
Charpy results were rejected as being due to the local,
greatly increased content of ferrite in the specimen with
a small section and the as-solidified microstructure.
The uniform plastic deformation was determined by
measuring the lengthening of the strain on the stress-
strain curves from the end of the elastic deformation to
the maximum stress of the strain curves. This part of the
true-stress, true-strain curve was digitalised, a linear
dependence was obtained in the log-log coordinates and
the approximate strain coefficient was deduced from its
slope for specimens aged for different times at 350 °C.
The shape of the recorded stress-strain curves in
Figures 6 and 7 shows that the tensile behaviour of the
alloy depends on the extent of the age hardening of the
ferrite and of the testing temperature. In Figures 8 and 9
the strain hardening part of the stress-strain curves
between the start of the plastic deformation and the
maximum tensile force are shown. The linear shape
confirms that the slope of the dependence can be used as
a reliable representation of the strain-hardening expo-
nent.
Theoretically, the effect of increasing the strain on
the deformation resistance is due to the increase in the
number of dislocations, and it is deduced as13



– 
0 =  G b 
1/2 (1)
where 
 is the deformation resistance at a deformation
of , 
0 is the deformation resistance at the start of the
plastic strain,  is the density of dislocations, G is the
shear modulus and b is the Burgers vector.
The equation is not used because of the experimental
complexity of determining the density of the dislo-
cations. The strain-hardening exponent is used instead of
R. CELIN ET AL.: EFFECT OF AGEING A TWO-PHASE Fe-NiCrMo ALLOY ...
Materiali in tehnologije / Materials and technology 43 (2009) 5, 251–255 253
Figure 5: Microstructure of the investigated alloy with 27 % of ferrite
Slika 5: Mikrostruktura raziskovane zlitine s 27 % ferita
Figure 4: Effect of ageing time at three temperatures on the notch
toughness at room temperature and at 290 °C
Slika 4: Vpliv ~asa staranja pri treh temperaturah na zarezno `ilavost
pri sobni temperaturi in pri 290 °C
a measure of the effect of the plastic strain on the defor-
mation resistance. It is deduced from equation14:



= k(0 + )
n (2)
where k is a constant, 0 is the initial strain,  is the
strain increase, and n is the strain-hardening exponent.
For tensile tests k is a constant, and 0 = 0 if the strain
hardening is started at the end of elastic deformation. In
our case equation (2) can be written in the form 
 = k n,
which also describes the dependences in Figures 8 and
9. Since the value of the strain-hardening exponent was
established from tests in equivalent conditions it can be
used as a comparative value.
3 DISCUSSION
In Tables 1 and 2 the numerical data established
from the stress-strain curves and the ferrite hardness are
given. The ratio of the proportion to the maximum stress
is, at room temperature, independent on the increase of
ferrite hardness, while it increases slowly with this hard-
ness at 290 °C. The plastic extension, a measure of the
plastic strain before the start of the reduction of area,
decreases very slowly with the increasing hardness of
ferrite at both testing temperatures. In contrast, the
approximate exponent of the deformation hardening is,
for the ferrite hardness up to approximately HV 537
units, significantly lower at room temperature than at
290 °C. Above this hardness level it increases up to a
value similar to that for testing at 290 °C. No similarity
was found between the effect of the increase of the
ferrite hardness on the coefficient of strain hardening and
the notch toughness, as the toughness is greatly dimi-
nished by an unchanged strain-hardening coefficient. On
the other hand, the coefficient of strain hardening is
higher with a higher notch toughness at 290 °C than at
room temperature. The notch toughness for ductile
fracturing also depends strongly on the extent of the
deformation before the crack is started at the notch tip15.
All the tensile properties are higher at room temperature
R. CELIN ET AL.: EFFECT OF AGEING A TWO-PHASE Fe-NiCrMo ALLOY ...
254 Materiali in tehnologije / Materials and technology 43 (2009) 5, 251–255
Figure 9: True-strain, true-stress dependence for the strain-hardening
part of the curves in Figure 7
Figure 7: Strain-stress curves at 290 °C for specimens aged for
different times at 350 °C
Slika 7: Odvisnost napetost – deformacija pri 290 °C za preizku{ance,
ki so bili starani razli~no dolgo pri 350 °C
Figure 8: True-strain, true-stress dependence for the strain-hardening
part of the curves in Figure 6
Slika 8: Odvisnost prave napetosti od prave deformacije za del krivulj
na sliki 6 z deformacijsko utrditvijo v logaritemskih koordinatah
Figure 6: Strain-stress curves at room temperature for specimens aged
for different times at 350 °C
Slika 6: Odvisnost napetost – deformacija pri sobni temperaturi za
preizku{ance, ki so bili starani razli~no dolgo pri 350 °C
than at 290 °C and, as only the exponent of strain
hardening is higher at 290 °C, the assumption is
confirmed that the higher notch toughness is related to
the share of energy consumed before the crack initiation
at the notch tip,11 which is greater at 290 °C than at room
temperature. The difference reflects the effect the
difference in the shape of the notch test specimen and the
loading geometry, the asymmetrical flexion for the notch
toughness test and the axial-symmetry for the tensile
test.
4 CONCLUSIONS
With the analysis of the stress-strain curves for
specimens with a duplex austenite-ferrite microstructure
and different ferrite hardnesses obtained with tests at
room temperature and 290 °C it was established that
with a higher temperature the strain hardening of the
austenite matrix is greater than at room temperature.
This finding is in agreement with the explanation that the
greater share of energy consumed before the crack is
opened at the notch tip is the cause of the higher notch
toughness at 290 °C, although the tensile properties are
higher at room temperature.
The authors are grateful to the Slovenian Research
Agency and to Nuclear Power Plant Kr{ko for their
support of this investigation. The assistance of Ms B.
Breskvar and D. Kmeti~ in the preparation of the alloy
and the heat treatment of specimens is acknowledged.
5 REFERENCES
1 F. Vodopivec, M. Pristavec, J. @vokelj, D. Gnidovec, F. Gre{ovnik:
Zaitschrift für Metallkunde, 79 (1988), 648–653
2 F. Vodopivec, D. Gnidovec, B. Arzen{ek, M. Torkar, B. Breskvar:
@elezarski Zbornik, 23 (1989), 73–78
3 F. Tehovnik, submitted for printing in Materiali in Tehnologije &
Materials and Technology
4 G. Slama, P. Petrequin, T. Mager: Assuring structural integrity of steel
reactor pressure boundary components: SMIRT post-conference
seminar, 1983, Monterey, USA, 211
5 C. Jannson: Degradation of cast stainless steel elbows after 15 years
of service: Fontenraud III-International Symposium, Royal Abbey of
Fontenraud-Franc, September, 1990, 1/8–8/8
6 H. M. Chung, T. R. Leax: Mater. Sci. Techn., 6 (1990), 249
7 O.K. Chopra: Estimation pof mechanical properties of cast stainless
steels during thermal ageing in LWR; Trans. 13th Intern. Conf. On
structural mechanics and reactor technology, Porto Allegre, Brazil,
August 1995
8 S. Jayet-Gendrot, P. Ould, T. Meylogan: Nucl. Eng. Des., 184
(1998), 3–11
9 J. Kwom, S.Woo, Y. Lee, J-C Park, Y-W Park: Nucl. Eng. Des., 206
(2001), 35–44
10 J. Vojvodi~-Tuma, B. [u{tar{i~, F. Vodopivec: Nucl. Eng. Des., 238
(2008), 1511–1517
11 J. Vojvodi~-Tuma, B. [u{tar{i~, R. Celin, F Vodopivec: Materiali in
Tehnologije & Materias and Technology (in print)
12 F. Vodopivec, B. Arzen{ek, J. Vojvodi~-Tuma, R. Celin: Metalur-
gija, 47 (2008), 173–179
13 D. Mc Lean: Trans. Metall. Soc. AIME 242 (1968), 1193–1203
14 G. E. Dieter: Mechanical metallurgy, McGraw-Hill, Boston, USA,
1986, 287
15 F. Vodopivec, B Arzen{ek, J. Vojvodi~-Tuma, R. Celin: Metalurgija,
47 (2008), 173–179
Materiali in tehnologije / Materials and technology 43 (2009) 5, 251–255 255
R. CELIN ET AL.: EFFECT OF AGEING A TWO-PHASE Fe-NiCrMo ALLOY ...
Table 1: Characteristic parameters of the stress-strain curves in Figures 6 and 8. Testing at room temperature, ageing temperature 350 °C
Tabela 1: Karakteristi~ni parametri iz odvisnosti napetost deformacija na slikah 6 in 8. Preizkus pri sobni temperaturi, temperatura staranja 350 °C
Ageing t/h Epr/MPa Em/MPa Epr/Em Plastic extension n Ferrite hardnessHV
0 341 708 0.48 0.27 0.20 295
24 362 703 0.51 0.25 0.21 350
168 356 720 0.49 0.24 0.21 419
720 352 729 0.49 0.25 0.21 465
4320 371 790 0.47 0.24 0.19 537
17520 376 832 0.47 0.19 0.40 648
Table 2: Characteristic parameters of the stress-strain curves in Figures 7 and 9. Testing at room temperature, ageing temperature 350 °C
Tabela 2: Karakteristi~ni parametri iz odvisnosti napetost deformacija na slikah 6 in 7. Preizkus pri sobni temperaturi, temperatuira staranja 350 °C
Ageing t/h Epr/MPa Em/MPa Epr/Em Plastic extension n Ferrite hardnessHV
0 268 567 0.47 0.24 0.37 295
24 268 572 0.47 0.24 0.35 350
168 278 583 0.48 0.23 0.33 419
720 299 573 0.52 0.22 0.36 465
4320 317 646 0.49 0.22 0.36 537
8760 327 656 0.50 0.23 0.35 589
17520 350 675 0.52 0.19 0.36 648
Epr is the stress at the end of proportionality  – E
Em is the maximum stress before the start of the reduction of area
Plastic extension is the extension between the points Epr and Em
n is the approximate exponent of strain hardening

R. ZEM^ÍK ET AL.: IDENTIFICATION OF MATERIAL PROPERTIES OF QUASI-UNIDIRECTIONAL ...
IDENTIFICATION OF MATERIAL PROPERTIES OF
QUASI-UNIDIRECTIONAL CARBON-EPOXY
COMPOSITE USING MODAL ANALYSIS
IDENTIFIKACIJA MATERIALNIH LASTNOSTI ZA
KVAZIENOSMERNI KOMPOZIT OGLJIK-EPOKSI Z MODALNO
ANALIZO
Robert Zem~ík, Radek Kottner, Vladislav La{, Tomá{ Plundrich
Faculty of Applied Sciences, Department of Mechanics, University of West Bohemia
Univerzitní 8, 306 14 Plze
, Czech Republic
zemcikkme.zcu.cz
Prejem rokopisa – received: 2008-10-13; sprejem za objavo – accepted for publication: 2009-04-30
This work focuses on the identification of material parameters of carbon-epoxy composite with continuous ultrahigh modulus
fibers. The tested structure is a cantilever beam with a rectangular cross-section manufactured with forming several fiber
bundles together, each wrapped with transverse layer of fibers. The wrapping fibers provide additional strength in transverse
loading. The eigen-frequencies of the beam are experimentally assessed using piezoelectric transducers and laser sensor.
Corresponding modal analysis is performed using finite element method and the axial Young’s modulus is deduced with the
mathematical optimization by minimizing the difference between measured and calculated eigen-frequencies. The model is then
verified with transient analysis when the piezoelectric patches are excited by harmonic signals covering the first two
eigen-frequencies.
Keywords: piezoelectric, composite, identification, finite element
Te`i{~e dela je na identifikaciji materialnih parametrov za kompozit ogljik-epoksi iz neprekinjenih vlaken z ultravelikim
modulom. Preizku{ena struktura je konzolni nosilec s pravokotnim prerezom, izdelan s povezavo snopov vlaken ovitih s
pre~nimi plastmi vlaken, ki zagotavljajo dodatno trdnost pri pre~ni obremenitvi. Lastne frekvence nosilca smo eksperimentalno
dolo~ili z uporabo piezoelektri~nih transduktorjev in laserskih senzorjev. Modalno analizo smo izvr{ili z uporabo kon~nih
elementov, osni Youngov modul pa je bil dolo~en z matemati~no optimizacijo z minimaliziranjem razlike med izmerjenimi in
izra~unanimi lastnimi frekvencami. Model je bil nato preverjen s tranzientno analizo, pri kateri so bili piezoelektri~ni merilniki
vzbujeni s harmonskim signalom, ki je obsegal dve prvi lastni frekvenci.
Klju~ne besede: piezoelektrik, kompozit, identifikacija, kon~ni elementi
1 INTRODUCTION
Light-weight structures are nowadays necessary
components in modern state-of-the-art products in all
sorts of industries. These structures usually utilize the
composite matererials in various form, such as shell-like
laminates made from unidirectional layers or fabrics,
wound or pultruded tubes and other profiles, or thick-
walled components made by sandwiching composite
skins and foam cores 1,2,3,4.
The increasing requirements on structural performan-
ce call for the use of embedded sensors and actuators and
the construction of the so-called adaptive, smart or even
intelligent structures that can respond to loading con-
ditions in real time 10. This enables, for instance, to
monitor the condition of the structure 5, suppress vibra-
tions or to adapt the desired shape 1,8, provided that
proper electronic control circuits are applied.
Commonly used types of sensors and actuators are
based on piezoelectric materials. The finite element
modeling of the piezoelectric materials began with the
first implementation in 1970 2. Many models have then
been developed to simulate the piezoelectric effect,
ranging from the simples using the similarity to the
theory of thermo-elasticity to models 3, multi-purpose
elements programmed for commercial software 11,12, up
to complex models with full piezoelectric coupling
incorporating layerwise approach for electric potential
across layers 7 or quadratic variation of electric potential
across the layer thickness 6.
The purpose of this work is to set up numerical
model of composite beam with novel material structure
and to use the piezoelectric actuators to identify the
structural properties using experiment and the correspon-
ding numerical simulation. This should be further
extended for the application of monitoring the structural
health in the future.
2 ANALOGY BETWEEN PIEZOELECTRICITY
AND THERMAL EXPANSION
Let us consider the theory of piezoelectricity which
assumes a symmetrical hexagonal piezoelectric structure
and only the laminar piezoelectric effect (also called d31
effect, both direct and converse), i.e., the material is
Materiali in tehnologije / Materials and technology 43 (2009) 5, 257–260 257
UDK 669.018.95:519.68 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 43(5)257(2009)
polarized in the thickness direction and the electric
potential varies linearly across the thickness 9.
The classical stress-strain law (Hooke’s law)
s e= C (1)
s being the stress vector, C stress-strain matrix and e
the strain vector, is extended in this case by the
piezoelectric coupling, hence
s e
e
=
+ ∈
C eE
D = e E
−
T
(2)
where e is the piezoelectric coupling matrix, E is the
electric field vector, D is the vector of electric flux
density (electric displacement), and  is the dielectric
permittivity matrix.
In many applications, the electric potential can be
considered as known (the piezoelectric material is in the
actuator mode) and, therefore, the second equation in (2)
does not need to be solved for the electro-mechanical
behavior. This allows to model the problem of piezo-
electricity using the analogy with thermal expansion 3.
This can prove very helpful if the used software does not
contain piezoelectric features.
The stress-strain law with thermal expansion for
one-dimensional problem can be written as
σ ε α∆= −E T( ) (3)
where E is the Young’s modulus, 
 the coefficient of
thermal expansion and T the change in temperature.
The corresponding piezoelectric equation is
σ ε= −E e U
d
(4)
with U being the voltage across electrodes and d the
distance between the electrodes. The analogy is obvious
and it is possible to write directly the resemblance
between
α ≈ e
E
and ∆T
U
d
≈ (5)
3 EXPERIMENT
Experimental investigation of oscillations caused by
harmonic excitations of quasi-unidirectional composite
beam was carried out. The beam consists of unidirec-
tional (0 degree) PITCH carbon fiber (K63712) sections
each wrapped by 90 degree fibers and then stacked
altogether. The matrix is composed of epoxy anhydride
resin. The dimensions of the cross-section (see Figure 1)
were (30  20) mm and the density was assessed to be 
= 1838 kg/m3. The beam was made by CompoTech
company.
Two collocated piezoelectric patches DuraAct
P876.A12 (see Figure 2) were glued with HBM Z70
glue to the beam upper and lower surfaces. The dimen-
sions of the patch are (61 × 35 × 0.5) mm while, the size
of the active piezoelectric material (E = 61.8 GPa, e =
5.6 C/m2,  = 7760 kg/m3), which is enclosed in a
protective foil (E = 8.2 GPa,  = 1528 kg/m3), was of
only (50  30  0.2) mm.
The beam of the free length of 1312 mm was
clamped at one end so that the gap between the fixture
and the active piezoelectric area was 10 mm. The
piezoelectric patches were loaded by a sine signal from
the generator (± 2V) connected to voltage multiplier (50
times) with final amplitude of 100 V. The connection of
patches resulted in bending of the beam. Laser sensor
OptoNCDT was used to measure the deflections of the
free end. The scheme of the experimental setup is shown
in Figure 3.
The two lowest bending eigen-frequencies of the
structure were found by sweeping the generator fre-
R. ZEM^ÍK ET AL.: IDENTIFICATION OF MATERIAL PROPERTIES OF QUASI-UNIDIRECTIONAL ...
258 Materiali in tehnologije / Materials and technology 43 (2009) 5, 257–260
Figure 2: Top and bottom view of the DuraAct P876.A12 piezo-
electric transducers (patches)
Slika 2: Pogled od zgoraj in od spodaj piezoelektri~nega transduktorja
DuraAct P876. A12
Figure 1: The cross-section of the composite beam showing the
wrapped unidirectional sections
Slika 1: Pre~ni prerez kompozitnega nosilca, ki prikazuje ovite osne
dele
Figure 3: Scheme of experimental setup
Slika 3: Shema eksperimentalne postavitve
quency and searching for the largest steady oscillations.
The values are f1 = 21 Hz and f2 = 134 Hz. The latter
analysis investigated the response to frequencies around
the two eigen-frequencies, namely the intervals 15,
25	 Hz and 125, 140	 Hz. The amplitudes of the steady
oscillations A were measured for each frequency using
the laser sensor.
Numerical analysis
Finite element model of the investigated structure
was designed in MSC.Marc/Mentat software utilizing
the analogy between piezoelectricity and thermal expan-
sion as introduced in (5). The beam consisted of eight-
node solid elements (with assumed strain option) as
shown in Figure 4. The prescribed boundary conditions
for the simulation of the clamped part are shown in
Figure 4, also. The detail of how the materials were
modeled within the structure is obvious from the
cross-section displayed in Figure 5.
The elasticity properties of the new material structure
were unknown. Since only the bending behavior was of
interest, it was possible to assume the composite and
piezoelectric materials to be homogeneous and isotropic
(the elasticity constants correspond to axial components,
Poisson’s ratios  = 0.3). The goal in this work was
therefore to identify at least the Young’s modulus from
the comparison of experiment and numerical model.
Simple optimization loop with interval partitioning was
used to minimize the error
( ){ }∆ = −
=
∑ f fi i
i
EXP FEA 2
1
2
(6)
where fiEXP and fiFEA are the measured and calculated
eigen-frequencies, respectively. The optimal value of
Young’s modulus was found to be 245 GPa whereas the
corresponding frequencies differed by less than 1 %.
The following investigation focused on the compa-
rison of the measured frequency characteristics of the
composite beam with the results of the numerical model.
The piezoelectric material was excited by harmonic
signals covering similar spectra as the experimental. The
calculated and measured amplitudes of steady oscilla-
tions A are shown in Figure 6. The decrease in eigen-
frequencies (given by the peaks in the graphs) from
those obtained by modal analysis (approx. by 3 %) and
in the maximum amplitudes can be explained using of
the single-step Houbolt time integration scheme in
MSC.Marc. The time step was set to 1/50 of the
corresponding signal period.
4 CONCLUSIONS
The experimental analysis of frequency characte-
ristics of hybrid composite cantilever beam was carried
out. The beam consists of carbon-fibers and epoxy
anhydride resin. Two collocated piezoelectric patches
glued to its surface were applied to induce bending.
R. ZEM^ÍK ET AL.: IDENTIFICATION OF MATERIAL PROPERTIES OF QUASI-UNIDIRECTIONAL ...
Materiali in tehnologije / Materials and technology 43 (2009) 5, 257–260 259
Figure 6: Amplitude characteristics around first two eigen-frequen-
cies
Slika 6: Zna~ilnosti amplitud okoli prvih dveh lastnih frekvenc
Figure 5: Detail of beam and patch cross-section
Slika 5: Detajl pre~nega prereza nosilca in merilnika
Figure 4: Finite element model of beam with attached piezoelectric
patch and applied boundary conditions
Slika 4: Kon~noelementni model nosilca s pritrjenimi piezoelek-
tri~nimi merilniki in uporabljene mejne vrednosti
Corresponding finite element model was designed in
MSC.Marc/Mentat software using the analogy between
piezoelectricity and thermal expansion. The axial modu-
lus of the quasi-unidirectional material was identified by
modal analysis using simple optimization loop with
interval partitioning. Moreover, the comparison of the
calculated and measured frequency characteristics when
the piezoelectric actuators were excited with harmonic
signals around the first two eigen-frequencies was per-
formed.
Acknowledgements
The work has been supported by the research project
MSM 4977751303 and by project GA CR 101/08/0299.
5 REFERENCES
1 Advancements and Challenges for Implementation: Structural Health
Monitoring 2005. Edited by Fu-Kuo Chang, DEStech Publications
Inc., 2005
2 Allik H., Hughes T. J. R., Finite element method for piezoelectric
vibration. International Journal for Numerical Methods in Engineer-
ing, 2 (1970), 151–157
3 Benjeddou A., Advances in piezoelectric finite element modeling of
adaptive structural elements: a survey. Computers and Structures, 76
(2000), 347–363
4 Berthelot J.-M., Composite materials, Mechanical behavior and
structural analysis. Springer, Berlin, 1998
5 Damage Prognosis: For Aerospace, Civil and Mechanical Systems.
Edited by D. J. Inman, C. R. Farrar, V. Lopes Jr., V. Steffen Jr., John
Wiley & Sons, 2005
6 Kögl M., Bucalem M. L., Analysis of smart laminates using piezo-
electric MITC plate and shell elements. Computers and Structures,
83 (2005), 1153–1163
7 Mitchell J. A., Reddy J. N., A refined hybrid plate theory for
composite laminates with piezoelectric laminae. Int. J. Solids
Structures, 32 (1995) 16, 2345–2367
8 Proceedings of the Third European Workshop: Structural Health
Monitoring 2006. Edited by Alfredo Guemes, DEStech Publications
Inc., 2006
9 Tzou H. S., Piezoelectric shells. Distributed sensing and control of
continua. Kluwer Academic Publishers, 1993
10 Varadan V., Vinoy K. J., Gopalakrishnan S., Smart Material Systems
and MEMS: Design and Development Methodologies. John Wiley &
Sons, 2006
11 Zem~ík R., Rolfes R., Rose M., Tessmer J., High-performance
4-node shell element with piezoelectric coupling. Mechanics of Ad-
vanced Materials and Structures, Special Issue: Smart Composites,
Edited by J. N. Reddy and A. Benjeddou, 13 (2006) 5, 393–401
12 Zem~ík R., Rolfes R., Rose M., Tessmer J., High-performance
four-node shell element with piezoelectric coupling for the analysis
of smart laminated structures. Int. J. Numer. Meth. Engng., 70
(2007), 934–961
R. ZEM^ÍK ET AL.: IDENTIFICATION OF MATERIAL PROPERTIES OF QUASI-UNIDIRECTIONAL ...
260 Materiali in tehnologije / Materials and technology 43 (2009) 5, 257–260
K. STRANSKY ET AL.: RE-OXIDATION PHENOMENA DURING ...
RE-OXIDATION PHENOMENA DURING THE
FILTRATION OF STEEL BY MEANS OF CERAMIC
FILTERS
REOKSIDACIJSKI PROCESI MED FILTRIRANJEM JEKLA S
KERAMI^NIMI FILTRI
1Karel Stránský, 2Jií Ba`an, 2Jana Dobrovská, 3Antonín Rek, 2Dana Horáková
1VUT Brno, FSI, Technická 2, 616 69 Brno, Czech Republic
2V[B-Technical University of Ostrava, Czech Republic
3ÚPT Academy of Science, Brno, Czech Republic
stranskyfme.vutbr.cz
Prejem rokopisa – received: 2008-10-13; sprejem za objavo – accepted for publication: 2009-03-27
This paper presents the results of experiments on the filtering of the melt of carbon steel with the use of five types of ceramic
filters with direct holes, which differed in terms of their basic ceramic nature. The objective of the experiments was to
determine the influence of filter ceramics on the re-oxidation reactions and the reactions between the filter ceramics and molten
steel flowing through the filter capillaries. The metallurgical and metallographic cleanliness of the steel filtered through
individual types of filters was also assessed.
Key-words: filtration of steel, ceramic filters, capillary tube re-oxidation, micro-cleanliness of steel
V ~lanku so prikazani rezultati preizkusov filtriranja ogljikovega jekla s filtri iz keramike razli~ne sestave in z neposrednimi
kapilarami. Cilj preizkusov je bil ugotoviti vpliv filtrne keramike na reakcije reoksidacije in naravo reakcij med to keramiko in
jeklom, ki te~e skozi kapilare. Metalur{ka in metalografska ~istota jekla sta bili tudi ocenjeni.
Klju~ne besede: filtriranje jekla, kerami~ni filtri, reoksidacija v filtrnih kapilarah, mikro~istost jekla
1 INTRODUCTION
Re-oxidation processes accompany the de-oxidised
steel from the furnace or from the ladle till its final
solidification in the mould or in the ingot-mould. The
main products of re-oxidation processes are usually
non-metallic oxide inclusions formed first from the
elements with a higher affinity for oxygen, and
progressively with the re-oxidation of elements with
decreasing and finally with a very low affinity for
oxygen. Among the elements present in the molten steel,
iron and manganese, silicon, and chromium, etc. 1–4 are
re-oxidised.
The paper presents the results of experiments of the
filtration of molten carbon steel using five types of
ceramic filters with direct holes, which differed in terms
of their primary ceramic basis. The experiments and
analyses of the chemical composition were aimed at
determining the influence of filter ceramics on the course
of re-oxidation processes and at assessing the reactions
between the filter ceramics and the molten steel flowing
through the filter capillaries. The aim of the experiments
was also to evaluate the metallurgical and metallo-
graphic cleanliness of the steel filtered with use of
individual types of filters.
2 CHANGES OF THE CHEMICAL
COMPOSITION OF THE CAPILLARIES’
CERAMIC SURFACE DURING FILTRATION
The five types of ceramic filters used for the
verification of re-oxidation processes consisted of
combinations of the following types of oxides: A – TiO2 ·
Materiali in tehnologije / Materials and technology 43 (2009) 5, 261–265 261
Figure 1: Design and placement of the ceramic filter
Slika 1: Shema in postavitev filtra
UDK 669.18:669.14.018:669.041 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 43(5)261(2009)
ZrO2; B – Al2O3 · TiO2; C – MgO · Al2O3; D – Al2O3 ·
ZrO2; E – Al2O3 · SiO2. The specimens of ceramic filters
were prepared in the company KERAMTECH, spol. s. r.
o., @aclé, Czech Republic. The sequence of the prepa-
ration of the experimental steel samples was melting of
the steel, stabilisation at a temperature of 1650 °C,
addition of pure aluminium and silicon-calcium for
de-oxidation of the molten steel prior to filtration and at
the same time the addition of a determined quantity of
iron sulphide (FeS) into the molten steel intended to
determine the reduction of sulphur content during the
flow of the molten steels through the filter. Then the
specimens for the determination of the initial chemical
composition and filtration of the steel through individual
types of filters were cast. During filtration the steel
flowed through the filter and (solidified) above the filter,
in the filter itself and in the filtered casting (sample).
Figure 1 shows the filtering scheme.
The chemical composition was determined with
energy-dispersive X-ray spectral micro-analysis using
the analytical systems JEOL JXA-8600/ KEVEX and
JEOL JSMU 840/LINK. The results of the chemical
analysis at the surface layer of the capillaries of the
ceramic filters during the filtration of the initial chemical
composition of the filter ceramics, which had no contact
with the filtered melt, are summarised in Table 1. The
working identification "coating" was used for the
different chemical compositions of the surface of the
ceramics after filtration. In Table 1 the differences in the
chemical composition of the ceramics-coating, (i.e., the
difference between the original chemical composition of
the ceramics and the chemical composition of the
coating), in which the symbol (–) means decrement, and
the symbol (+) means increment of an oxidic component
of ceramics on the surface of the coating in mass frac-
tions (%), are shown. The chemical composition of the
used ceramics is marked in Table 1 in bold characters.
The chemical composition of basic oxidic components of
the filter ceramics and the chemical composition of the
oxidic components of the coating were determined as an
arithmetic mean of two measurements.
It follows from the analyses of the chemical
composition in Table 1 that in the whole series of five
ceramic filters, which have a different oxidic base, the
processes of adsorption of the flowing molten steel
occur, which are related to the formation of the coating
on the surface of the filter capillaries. Physical-chemical
reactions occur between the flowing molten steel and the
ceramic of the filter capillaries, and the initial ceramic
composition is changed and a coating is formed on the
surface of the capillaries. In this coating the chemical
composition of the primary thermodynamically stable
oxides is reduced and particularly the share of the oxides
MnO and Fe2O3 is increased. The sum of the contents of
both types of oxides in the capillaries’ coating, i.e., MnO
+ Fe2O3, has a positive value for the whole series of
filters A to E (see the Table 1). Both types of oxides are
formed as a result of re-oxidation processes.
The ratios given in Table 1 are also given in a
graphical representation. The changes of the chemical
composition of the coating on the surface of filter
capillaries were compared as a ratio of the sums of the
concentrations of the decrements of the basic ceramic
components for the investigated series of five filters A to
E to the increments of the sums of the oxide MnO and
Fe2O3 contents formed in the coating as a result of
re-oxidation. This comparison is shown in bar form in
Figure 2. It can be concluded from Figure 2 that the
sum of the changes in the composition of basic oxidic
components in the filter ceramics on the coating of the
capillaries (which – according to the analyses in Table 1
– always has a negative value) is in all the investigated
K. STRANSKY ET AL.: RE-OXIDATION PHENOMENA DURING ...
262 Materiali in tehnologije / Materials and technology 43 (2009) 5, 261–265
Table 1: Changes in the chemical composition of the ceramics on the surface of the walls during the coating of the filter capillaries. The symbol
(–) means decrement, the symbol (+) means increment of an oxide component of ceramics on the surface of the coating (w/%)
Tabela 1: Sprememba sestave keramike na povr{ini kapilar. Simbol (–) pomeni zmanj{anje, simbol (*) pa pove~anje neke oksidne komponente
keramike na povr{ini kapilare.
Filter MgO Al2O3 SiO2 TiO2 S K2O CaO ZrO2 MnO Fe2O3
A
ceramics 2.09 7.55 13.04 41.60 0.00 0.62 0.16 33.42 0.07 1.96
coating 0.82 3.16 4.08 35.94 0.00 0.14 0.09 45.14 0.73 9.92
difference −1.27 −4.39 −8.96 −5.66 0.00 −0.48 −0.07 +11.72 +0.66 +7.96
B
ceramics 0.23 48.48 11.62 37.17 0.15 0.50 0.07 0.00 0.08 1.12
coating 0.51 48.99 12.34 30.55 0.12 0.20 0.47 0.00 4.55 1.67
difference +0.28 +0.51 +0.72 −6.62 −0.03 −0.30 +0.40 0.00 +4.47 +0.55
C
ceramics 21.52 49.50 22.97 0.75 0.22 0.67 0.41 0.00 0.11 3.29
coating 20.06 48.80 23.88 0.69 0.11 0.64 0.53 0.00 1.95 2.92
difference -1.46 -0.70 +0.91 −0.06 −0.11 −0.03 +0.12 0.00 +1.84 −0.37
D
ceramics 3.58 54.63 11.52 0.30 0.00 0.30 0.12 27.41 0.15 2.51
coating 1.95 27.68 22.80 0.18 0.00 0.40 0.35 13.15 13.51 20.01
difference −1.63 -26.9 +11.30 −0.12 0.00 +0.10 +0.23 –14.26 +13.36 +17.50
E
ceramics 3.78 31.62 57.17 1.01 0.10 0.93 0.32 0.00 0.09 4.45
coating 2.73 34.00 53.47 1.13 0.11 1.56 0.62 0.00 0.27 5.24
difference −1.05 +2.38 -3.70 +0.12 +0.01 +1.24 +0.30 0.00 +0.18 +0.79
types of filter compensated by an increment of the sum
of the less-stable manganese and iron oxides, formed
with the re-oxidation of the filtered molten steel.
The relationship between the sum of the decrements
and increments in the coating can also be expressed
analytically with the diagram in Figure 3, which
corresponds to the straight-line equation
(Increment of MnO + Fe2O3) = 3.97 + 0.606*(sum of
the decrements in the composition of the oxides of the
basis of filter ceramics), (1)
with a correlation coefficient of r = 0.9069, while the
critical value of the same quantity for 
 = 5 – 2 = 3
degrees of freedom has the confidence level  = 0.05
and rkrit = 0.8783.
The obtained results of the analyses show that the
decrement of the sum of the oxides of the basic ceramics
is replaced by the increment (in fact with the sum) of the
oxide MnO and the iron oxides (Fe2O3) in the coating of
the capillaries of individual filters. This observation is
related to the physical-chemical reactions of re-oxidation
processes during the filtration that should be considered
during the steel filtration.
3 METALLURGICAL CLEANLINESS OF THE
FILTERED STEEL
The results of the assessment of the metallurgical
cleanliness of the molten steel filtered with the checked
filters A to E are summarised in Table 2. The chemical
composition of the non-filtered steel was determined
from a sample taken above the filter, while the chemical
composition of the filtered steel was determined from a
sample taken from the casting below the filter.
The table also gives an efficiency of the filtration of
the individual filters. It is obvious from the data that the
filtration efficiency is different for elements that form
oxides – i.e., calcium, aluminium and oxygen – and for
elements that form nitrides and sulphides – i.e., nitrogen
and sulphur – as shown in Figure 4. The filtration
efficiency for elements forming oxides in steel is, on
average, i.e., without consideration of the type of
ceramic filter (for all types of filter), approximately four
times higher than for elements forming in steel nitride or
sulphide inclusions.
The symbols in Figure 4 mean the following:
 (Ca
),  (Al
),  (O
) – average efficiencies of the
whole series of five filters for the elements forming
oxides, and  (N
) and  (S) – average efficiencies of the
K. STRANSKY ET AL.: RE-OXIDATION PHENOMENA DURING ...
Materiali in tehnologije / Materials and technology 43 (2009) 5, 261–265 263
Figure 3: Relation between the decrements and increments of the
oxides in the coating of the filter capillaries
Slika 3: Razmerje med zmanj{anjem vsebnosti enih in pove~anjem
vsebnosti drugih oksidov v oblogi v kapilarah filtrov
Figure 2: Decrements and increments of oxides in the coating of the
filter capillaries
Slika 2: Zmanj{anje in pove~anje vsebnosti oksidov v oblogi v
kapilarah
Figure 4: Filtration efficiency for the elements Ca, Al, O, N, S
Slika 4: Povpre~na u~inkovitost za elemente Ca, Al, O, N in S. Sim-
boli  (Caz)  (Alz ), η (Oz) – povpre~je u~inkovitosti vseh filtrov za
elemente, ki tvorijo okside;  (Nz) in  (S) – povpre~je vseh filtrov za
elemente, ki tvorijo sulfide in nitride.
whole series of five filters for the elements forming
nitrides and sulphides.
Notes: filtration efficiency
η =
−−
−
w(x w x
w(x
non filtered filtered
non filtered
) ( )
)
symbol Xc means total content of the element in steel; x
is the arithmetic mean; and sx is the standard deviation.
The average filtration efficiency also depends on the
type of ceramic filter (see Table 1) and it is different for
each filter. The difference between the highest filtration
efficiency of the filter C – MgO·Al2O3 and lowest
filtration efficiency of the filter A – TiO2·ZrO2, is more
than double. The relation between the filtration effi-
ciency of individual types of ceramic filters is shown in
Figure 5. It is apparent from this figure that the filtration
efficiency of the individual types of filters decreases in
the given series of filters in the order C, B, E, D, A.
4 METALLOGRAPHIC CLEANLINESS OF THE
FILTERED STEEL
The assessment of the metallographic cleanliness of
the filtered steel in terms of the quantity of the oxide and
sulphide inclusions was performed in accordance with
the standard DIN 50 602 and according to the K0
methodology, for the filtered and non-filtered steels.
A graphical representation of the metallographic
cleanliness for the individual types of filters is shown in
Figure 6 and the filtration efficiency in % for the filters
as an evaluation of the micro-cleanliness according to
the DIN 50 602, scale K0 I, is shown in Figure 7.
The assessment of the metallographic micro-clean-
liness of the steel according to DIN 50602, scale K0,
indicates that the micro-cleanliness of the filtered steel
decreases in the order C, E, D, A, B for the filters
(Figure 6). Also, the filter efficiency – in terms of
K. STRANSKY ET AL.: RE-OXIDATION PHENOMENA DURING ...
264 Materiali in tehnologije / Materials and technology 43 (2009) 5, 261–265
Table 2: Metallurgical cleanliness of steel – chemical composition of steel prior to filtration and after filtration with the checked five filters w/%
and the filtration efficiency /%
Tabela 2: Metalur{ka ~istost jekla; kemi~na sestava jekla pred filtriranjem in po njem za vse preizku{ane filtre w/% in u~inkovitost filtriranja
/%
Element Non-filtered
After filtration of molten steel by the given type of filter
A B C D E
S 0.045 0.042 0.044 0.040 0.043 0.044
Al
 0.189 0.163 0.128 0.164 0.134 0.159
O
 0.0278 0.0256 0.0240 0.0122 0.0257 0.0250
N
 0.0189 0.0184 0.0181 0.0168 0.0181 0.0180
Ca
 0.0028 0.0023 0.0021 0.0023 0.0023 0.0018
Efficiency  A B C D E
 (S) – 6.7 2.2 11.1 4.4 2.2
 (Al
) – 13.8 32.3 13.2 29.1 15.9
 (O
) – 7.9 9.1 56.1 7.6 10.1
 (N
) – 2.6 4.2 11.1 4.2 4.8
 (Ca
), – 17.9 25.0 17.9 17.9 35.7
 () : x – 9.8 14.6 21.9 12.6 13.7
sx – 6.1 13.4 19.3 10.8 13.4
Figure 6: Micro-cleanliness of filtered steel according to DIN 50 602
Slika 6: Mikro~istota filtriranega jekla po DIN 50 602
Figure 5: Filtration efficiency by type of filter
Slika 5: U~inkovitost za vsak prezku{en filter
ensuring the minimum number of sulphide and oxide
inclusions – decreases in the same order. Thus, the best
micro-cleanliness is therefore ensured with filtration
with the ceramic filter C –MgO · Al2O3, and the lowest
are the filter A - TiO2 · ZrO2 and, particularly, the filter B
– Al2O3 · TiO2, with an efficiency of almost zero.
5 CONCLUSION
The paper presents results from the filtering of
molten carbon steel with five types of ceramic filters
with direct holes of different primary ceramic bases. The
objective of the experiments was to determine the
influence of filter ceramics on the re-oxidation reactions
and to evaluate the reactions between the filter ceramics
and the molten steel flowing through the filter
capillaries. The metallurgical and metallographic clean-
liness of the steel filtered by individual types of filters
was also assessed.
It was established that during the filtration of the
molten steel with ceramic filters of different oxide bases
of the used ceramics, the molten steel flowing through
the filter reacted with the surface of the filter capillaries.
The physical-chemical reactions between the molten
steel and the filter ceramic form a coating on the surface
of the capillaries in the coating. The chemical
composition of the used ceramics is changed and it is
enriched in the oxides of manganese and iron, which are
formed as a result of re-oxidation processes during the
filtration. The extent of the changes of the chemical
composition is a function of the thermodynamic stability
of the oxides forming the initial composition of the
ceramic filters. The metallurgical and metallographic
cleanliness of the same steel filtered through the
different ceramic filters is very different.
This work was realised within the frame of the grant
project reg. no. 106/06/0393 under the financial support
of the Czech Grant Agency.
6 REFERENCES
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ISSN: 1580–2949
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L. Application of the theory of physical similarity for the filtration of
metallic melts. Materi. Tehnol. / Materials and technology, 42,
(2008) 4, 175–178. ISSN 1580–2949
3 Stránský, K., Ba`an J., B`ek, Z., Rek, A., Belko, J. On the Fil-
tration of Steel by means of Different Types of Ceramics Filters. In
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4 Stránský, K., Ba`an, Z., B`ek, Z., Belko, J., Lev, P. Píspvek k
ú~innosti filtrace ocelí rznými typy keramických filtr Contri-
bution to efficiency of steel filtration by various types of ceramic
filters
. In Hutní keramika. TANGER, spol. s r.o. and V[B-TU
Ostrava, FMMI, Ro`nov pod Radho{tm 2001, pp. 123–130. ISBN
80-85988-64-X
K. STRANSKY ET AL.: RE-OXIDATION PHENOMENA DURING ...
Materiali in tehnologije / Materials and technology 43 (2009) 5, 261–265 265
Figure 7: Filtration efficiency as micro-cleanliness according to DIN
50 602
Slika 7: U~inkovitost filtriranja po DIN 50 602

F. KAHRAMAN: THE USE OF RESPONSE SURFACE METHODOLOGY FOR PREDICTION ...
THE USE OF RESPONSE SURFACE METHODOLOGY
FOR PREDICTION AND ANALYSIS OF SURFACE
ROUGHNESS OF AISI 4140 STEEL
UPORABA METODOLOGIJE ODGOVORA POVR[INE ZA
NAPOVED IN ANALIZO HRAPAVOSTI PRI JEKLU AISI 4140
Funda Kahraman
Mersin University, Tarsus Technical Education Faculty, Department of Mechanical Education, 33400 Tarsus-Mersin, Turkey
Prejem rokopisa – received: 2009-03-23; sprejem za objavo – accepted for publication: 2009-06-08
This paper utilizes regression modeling in turning process of AISI 4140 steel using Response Surface Methodology (RSM) with
rotatable Central Composite Design (CCD). A quadratic model was developed for the prediction and analysis of the relationship
between the cutting conditions and surface roughness. In the development of predictive models, cutting parameters of cutting
speed, feed rate and depth of cut were considered as model variables, surface roughness were considered as a response variable.
The statistical analysis showed that, cutting speed and feed rate have the most significant effect on surface roughness. The
predicted values was found similar to the actual values. The alternative solutions of the optimization approach using desirability
functions were used to determine the optimum processing conditions.
Keywords: turning, surface roughness, optimization, RSM (CCD)
V tem delu uporabljamo regresijsko modeliranje stru`enja jekla AISI 4140 po metologiji odgovora povr{ine (RSM) z vrtljivim
sredi{~nim kompositnim na~rtom (CCD). Kvadrati~en model je bil razvit za napovedovanje in analizo odvisnosti med pogoji
stru`enja in hrapavostjo povr{ine. Pri razvoju napovedovalnih modelov so bili parametri stru`enja hitrost, podajanje in globina
upo{tevani kot spremenljivke modela, hrapavost povr{ine pa kot spremenljivka odgovora. Statisti~na analiza je pokazala, da
imata hitrost stru`enja in globina podajanja najve~ji vpliv na hrapavost povr{ine. Napovedane vrednosti so bile podobne
izmerjenim. Za optimizacijo pogojev procesa so bile uporabljene alternativne `elelne funkcije.
Klju~ne besede: stru`enje, hrapavost povr{ine, optimizacija, RSM (CCD)
1 INTRODUCTION
The surface quality is an important parameter to
evaluate the productivity of machine tools as well as
machined components. Hence, achieving the desired
surface quality is of great importance for the functional
behaviour of the mechanical parts. Surface quality is
generally associated with surface roughness. The surface
roughness of machined parts is known to have
considerable effect on some properties such as wear
resistance and fatigue strength 1-3.
Several researchers have developed mathematical
models to predict the surface roughness in terms of
various process parameters during turning of different
materials. Sahin and Motorcu 1 machined the hardened
AISI 1040 steel with triangular and square tools in
different machining conditions and modeled the surface
roughness by using RSM. Sahin and Motorcu 2
developed the surface roughness model in terms of main
cutting parameters such as cutting speed, feed rate and
depth of cut using RSM. Kopac and Bahor 3 examined
the changes in surface roughness of AISI 1060 and AISI
4140 steels and analyzed the effect of cutting parameters
by using RSM. Noordin et al. 4 developed the empirical
models such as linear and quadratic functions by using
RSM to predict surface roughness and tangential force
when turning AISI 1045 steel. Mansour et al.5 studied a
surface roughness model that utilizing RSM for milling
steel in dry condition. Arbizu and Perez 6 presented a
surface roughness prediction model using RSM to deter-
mine surface quality in turning processes. Choudhury
and El-Baradie 7 developed surface roughness prediction
model in turning of high strength steel by factorial
design of experiments. Erzurumlu and Oktem 8 discussed
the effect of cutting parameters on surface roughness.
They developed RSM and an artificial neural network
(ANN) model to predict surface roughness values error
on mold surfaces. Ozel and Karpat 9 used regression and
ANN for predictive modeling of surface roughness and
tool wear in hard turning. Nalbant et al. 10 examined
Taguchi method in the optimization of cutting para-
meters for surface roughness in turning. Davim 11 studied
the influence of cutting conditions on the surface finish
obtained by turning, based on the techniques of Taguchi.
In this study, The Design-Expert software package
was used to develop RSM model and to apply the desira-
bility approach. RSM with CCD was adopted to obtain
an emprical model of surface roughness (response) as a
function of cutting speed feed rate and depth of cut
(input factors). The optimum process conditions were
determined by using desirability functions. Desirability
function is an attractive method for industry for
optimization of quality characteristic problems.
Materiali in tehnologije / Materials and technology 43 (2009) 5, 267–270 267
UDK 669.14.018:620.179.11:519.68 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 43(5)267(2009)
2 EXPERIMENTAL DETAILS
The cutting experiments were carried out a Goodway
GS-280 industrial type of CNC lathe. HSS tool ( = 8°, 
= 14°, r = 0.4 mm) was used for the machining of AISI
4140 steel bars with cutting fluid. The mean surface
hardness of samples was measured as 195 HB after
normalizing at 870 °C The chemical compositions of
AISI 4140 steel is given in Table 1.
Table 1: Chemical composition of AISI 4140 steel in mass fractions,
w/%
Tabela 1: Kemi~na sestava jekla AISI 4140
C Mn P S Si Cr Mo
0.38−
0.43
0.75−
1.00
0.035
max
0.040
max
0.15−
0.30
0.80−
1.10
0.15−
0.25
These bars of 30 mm diameter and 200 mm in length
were prepared. Test samples were trued, centered and
cleaned by removing a 1 mm depth of cut (ap) from the
outside surface, prior to actual machining tests. Three
replications of each cutting conditions were conducted
resulting in a total of 60 tests. A Mahr Perthometer-M1
type of portable surface roughness tester was used for
measuring surface roughness. Input parameters of the
models are cutting speed (vc), feed rate (f) and depth of
cut (ap). Output parameter of the models is the
corresponding surface roughness (Ra). Factors and levels
for CCD) are given in Table 2. The relationship between
the coded factors and the actual factors are shown in
Equations 1-3.
x
speed speed speed
speed speed
low high
high low
1
2
=
− +
−
( ) /
( ) / 2
(1)
x
feed feed feed
feed feed
low high
high low
2
2
2
=
− +
−
( ) /
( ) /
(2)
x
doc doc doc
doc doc
low high
high low
3
2
2
=
− +
−
( ) /
( ) /
(3)
where x1 is the coded factor that represent the cutting
speed, x2 is the coded variable that represent the feed
rate, x3 is the coded variable that represent the depth of
cut (doc).
Table 2: Factors and levels for CCD
Tabela 2: Faktorji in nivoji za CCD
Factors/Levels −1.68 −1 0 +1 +1.68
Cutting speed (vc) 16 47 92 137 167
Feed rate (f) 0.032 0.1 0.2 0.3 0.368
Depth of cut (ap) 0.160 0.5 1 1.5 1.840
3 DATA ANALYSIS AND DISCUSSION OF
RESULTS
The arrangement and the results of the 20 experi-
ments carried out. Experimental and predicted surface
roughness values for CCD are shown in Table 3. The
results of the model is given in Table 4. Significance
level () was selected as 0.05. The valu of p for the term
of model is less than 0.05 indicates that the obtained
model is considered to be statistically significant. This
value (p < 0.0001) showed that, the quadratic model fits
well to the experimental results.
Table 3: Experimental and predicted surface roughness (Ra) values
for CCD
Tabela 3: Eksperimentalne in napovedane vrednosti za CCD
Run
Cutting
speed vc
/(m/min)
Feed rate
f /(mm/r)
Depth of
cut
ap/mm
Actual
Ra/µm
Predicted
Ra/µm
1 47 0.1 0.5 1.60 1.64
2 137 0.1 0.5 2.20 2.24
3 47 0.3 0.5 2.47 2.66
4 137 0.3 0.5 2,14 2.14
5 47 0.1 1.5 1.91 2.00
6 137 0.1 1.5 1.77 1.68
7 47 0.3 1.5 2.84 2.90
8 137 0.3 1.5 1.40 1.46
9 16 0.2 1 2.62 2.44
10 167 0.2 1 1.70 1.74
11 92 0.032 1 1.67 1.67
12 92 0.368 1 2.48 2.34
13 92 0.2 0.160 2.51 2.40
14 92 0.2 1.840 2.17 2.14
15 92 0.2 1 2.72 2.68
16 92 0.2 1 2.74 2.68
17 92 0.2 1 2.64 2.68
18 92 0.2 1 2.70 2.68
19 92 0.2 1 2.51 2.68
20 92 0.2 1 2.74 2.68
Table 4: The results of the model
Tabela 4: Rezultati modela
Source Sum ofSquares df
Mean
Square F-value p-value
Linear 1.23 3 0.41 2.44 0.102
Quadratic 1.47 3 0.35 2.81 <0.0001suggested
Cubic 0.078 4 0.49 29.65 0.35
Quadratic regression equation was developed for
predicting surface roughness (Ra) within selected expe-
rimental conditions using RSM. Regression equation can
be expressed as follows.
R X X X X
X
a = − + − − −
− −
268 0 21 0 20 0 078 0 21
0 24 01
1 2 3 1
2
2
2
. . . . .
. . 4 0 28 0 233
2
1 2 1 3X X X X X− −. .
(4)
where x1 is cutting speed (vc), x2 is feed rate (f), x3 is
depth of cut (ap).
It is observed that cutting speed (vc) and depth of cut
(ap) have negative influence, feed rate (f) has positive
influence on the surface roughness (Ra). The surface
roughness (Ra) of AISI 4140 steel decreased with
increasing cutting speed (vc) and depth of cut (ap)
whereas increased with increasing feed rate (f). The
F. KAHRAMAN: THE USE OF RESPONSE SURFACE METHODOLOGY FOR PREDICTION ...
268 Materiali in tehnologije / Materials and technology 43 (2009) 5, 267–270
relationship between cutting speed (vc) and feed rate (f)
is shown in Figure 1a, the relationship between cutting
speed (vc) and depth of (ap) is shown in Figure 1b.
It can be realized that the combination between high
cutting speed and high feed rate (f) results in a conside-
rable reduction in surface roughness (Ra) and also
between high cutting speed (vc) and high depth of cut
results in a considerable reduction in surface roughness
(Ra). The response surface plot (Figure 1a) indicates that
the minimum surface roughness is at about 137 m/min
and 0.3 mm/r. The response surface plot (Figure 1b)
indicates that the minimum surface roughness is at about
137 m/min, and 1.5 mm.
An ANOVA table is commonly used to summarize
the tests performed. It was statistically studied the
relative effect of each cutting parameters on the surface
roughness (Ra) by using ANOVA. The ANOVA table for
response surface quadratic model for the surface
roughness (Ra) is given in Table 5.
The value of p is less than 0.05 indicates that the
obtained model is considered to be statistically
significant. Higher F value indicates that the variation of
the process parameter makes a big changes on the
surface roughness (Ra). As seen in Table 5 cutting speed
(vc) and feed rate (f) is the most significant parameters,
depth of cut (ap) is the least significant parameter. All the
F. KAHRAMAN: THE USE OF RESPONSE SURFACE METHODOLOGY FOR PREDICTION ...
Materiali in tehnologije / Materials and technology 43 (2009) 5, 267–270 269
Figure 1: 3D response surface graphs for surface roughness (Ra)
Slika 1: 3D-graf odgovora za hrapavost povr{ine (Ra)
Table 5: The ANOVA table for the quadratic model
Tabela 5: Anova tabela za kvadrati~en model
Source SS DF MS F-value p-value
Model 3.75 9 0.42 25.29 < 0.0001
x1 0.60 1 0.60 36.29 < 0.0001
x2 0.55 1 0.55 33.19 < 0.0002
x3 0.0.83 1 0.083 5.01 0.0491
x1
2 0.62 1 0.62 37.72 0.0001
x2
2 0.81 1 0.81 49.43 < 0.0001
x3
2 0.30 1 0.30 18.14 0.0017
x1x2 0.62 1 0.62 37.74 0.0001
x1x3 0.43 1 0.43 25.97 0.0005
x2x3 0.007813 1 0.007813 0.47 0.5067
Figure 3: The standardized residual versus observation order plot
Slika 3: Standardni reziduali v odvisnosti od napovedanih vrednosti
Figure 2: The normal probability plot of the residuals
Slika 2: Normalna verjetnost za reziduale
squared terms and among interaction term cutting speed
(vc) – feed rate (f) and cutting speed (vc) – depth of cut
(ap) appears to be highly significant.
We consider a measure of the model’s overall per-
formance referred to as the coefficient of determination
and denoted by R2. In the model, R2 is obtained equal to
95 %. The R2 value indicates that the cutting parameters
explain 95 % of variance in surface roughness (Ra). The
normal probability plot of the residuals is shown in
Figure 2.
The predicted values were found to be statistically
similar to the actual measured values, based on the
plotted probability plot. Figure 2 shows that the
residuals generally fall on a straight line implying that
the errors are distributed normally. The standardized
residual versus observation order plot, as shown in
Figure 3. It shows that the model proposed is adequate.
After building the regression model, a numerical
optimization technique using desirability functions can
be used to optimize the response. The objective of
optimization is to find the best settings that minimize a
particular response 12. Table 6 shows five alternative
solutions of the optimization approach used to determine
the optimum processing conditions. A desirability value,
where 0  d  1. The value of d increases as the "desi-
rability" of the corresponding response increases. The
factor settings with maximum desirability are considered
to be the optimal parameter conditions.
Table 6: Alternative solutions of optimum conditions
Tabela 6: Alternativne re{itve za optimalne pogoje
Solutions
Cutting
speed vc
/(m/min)
Feed rate
f / (mm/r)
Depth of
cut ap
/mm
Ra/µm Desira-bility (d)
1 137 0.3 1.5 1.46 0.957
2 47 0.1 0.5 1.63 0.835
3 137 0.26 1.5 1.64 0.830
4 47 0.1 1.5 2.00 0.580
5 137 0.3 0.67 2.10 0.509
Table 6 revealed that highest desirability could be
obtained at high level of cutting speed, feed rate and
depth of cut. Five different desirable ranges of input
parameters and response which gives high value of
desirability are shown in the table. These are the optimal
conditions to obtain high value of desirability. The
achieved maximum desirability of 0.957 means that it is
possible to meet surface roughness (Ra) target. The
lowest value of surface roughness (Ra) obtained is Ra =
1.46µm at a cutting speed of vc = 137 m/min, a feed rate
of f = 0.3 mm/r and a depth of cut of ap =1.5 mm.
4 CONCLUSION
In this study, a quadratic model was developed for
the prediction and analysis of the relationship between
the cutting parameters and surface roughness (Ra) in
turning process of AISI 4140 steel. It was observed that
significance of the main variables is cutting speed (vc)
and feed rate (f). The comparisons of experimental
results with the RSM predictions have been depicted in
terms of percentage absolute error. In the prediction of
surface roughness (Ra) values the average absolute errors
for RSM is found to be as 3.18 %. This value is
sufficiently low to confirm the high predictive power of
model. Experimental results show that, it can be inferred
that prediction models can be applied to determine the
appropriate cutting conditions, in order to achieve
specific surface roughness (Ra).
5 REFERENCES
1 Sahin Y, Motorcu AR. Surface roughness model for machining mild
steel with coated carbide tool, Materials&Design, 26 (2005),
321–326
2 Sahin Y, Motorcu AR. Surface roughness model in machining
hardened steel with cubic boron nitride cutting tool, Int. Journal of
Refractory Metals&Hard Materials, 26 (2008), 84–90
3 Kopac J, Bahor M. Interaction of the technological history of a
workpiece material and machining parametres on the desired quality
of the surface roughness of a product, Journal of Materials
Processing Technology, 92–93 (1999), 381–387
4 Noordin MY, Venkatesh VC, Sharif S, Elting S, Abdullah A.
Application of response surface methodology in describingthe
performance of coated carbide tools when turning AISI 1045 steel,
J.of Materials Processing Technology, 145 (2004), 46–58
5 Mansour A, Abdalla H, Meche F. Surface roughness model for end
milling: a semi free cutting carbon casehardening steel (EN 32) in
dry condition, Journal of Materials Processing Technology, 124
(2002), 183–191
6 Arbizu I.P, Perez CJL. Surface roughness prediction by factorial
design of experiments in turning processes, Journal of Materials
Processing Technology, 143–144 (2003), 390–397
7 Choudhury IA, El-Baradie MA. Surface roughness prediction in the
turning of high strength steel by factorial design of experiments in
turning processes, Journal of Materials Processing Technology, 67
(1997), 55–61
8 Erzurumlu T, Oktem H. Comparasion of response surface model
with neural network in determining the surface quality of moulded
parts, Materials & Design, 28 (2007), 459–465
9 Ozel T, Karpat Y. Predictive modeling of surface roughness and tool
wear in hard turning using regression and neural networks,
International Journal of Machine Tools & Manufacture, 45 (2005),
467–479
10 Nalbant M, Gokkaya H, Sur G. Application of Taguchi method in
the optimization of cutting parameters for surface roughness in
turning, Materials&Design (in press)
11 Davim J.P. A note on the determination of optimal cutting conditions
for surface finish obtained in turning using design of experiments,
Journal of Materials Processing Technology, 116 (2001), 305–308
12 Myers RH, Montgomery DC. Response surface methodology:
process and product optimization using designed experiments NY:
John Wiley & Sons Inc., 2002
F. KAHRAMAN: THE USE OF RESPONSE SURFACE METHODOLOGY FOR PREDICTION ...
270 Materiali in tehnologije / Materials and technology 43 (2009) 5, 267–270
A. SAGBAS, F. KAHRAMAN: DETERMINATION OF OPTIMAL BALL BURNISHING PARAMETERS ...
DETERMINATION OF OPTIMAL BALL BURNISHING
PARAMETERS FOR SURFACE HARDNESS
DOLO^ITEV OPTIMALNIH PARAMETROV KROGLI^NEGA
GLAJENJA ZA POVE^ANJE TRDOTE POVR[INE
Aysun Sagbas, Funda Kahraman
Mersin University, Tarsus Technical Education Faculty, Department of Mechanical Education, 33400, Tarsus-Mersin, Turkey
asagbashotmail.com
Prejem rokopisa – received: 2009-04-13; sprejem za objavo – accepted for publication: 2009-06-08
The objective of this study is to improve surface hardness of 7178 aluminum alloy using the ball burnishing process. The effect
of the main burnishing parameters on the objective function was examined using full factorial design and analysis of variance
(ANOVA). The main parameters were found as burnishing force, feed rate and number of passes among four controllable
factors that influence the surface hardness in ball burnishing process. Optimal ball burnishing parameters were determined after
the experiments of the Taguchi’s L9 orthogonal array. As result, the optimal burnishing parameters for surface hardness were
the combination of the burnishing force at 200 N, number of passes at 4, feed rate at 0.25 mm/r.
Key words: Ball burnishing, surface hardness, Taguchi technique, factorial design, ANOVA
Cilj tega dela je bil pove~ati trdoto aluminijeve zalitine 7178 s krogli~nim glajenjem. Vpliv glavnih parametrov glajenja na
trdoto je bil opredeljen z uporabo polnega faktorialnega na~rtovanja in analizo variance (ANOVA). [tirje glavni parametri
glajenja, ki vplivajo na trdoto povr{ine, so sila glajenja, hitrost podajanja in {tevilo prehodov. Optimalne parametre glajenja smo
dolo~ili z ortogonalno razporeditvijo Taguchi L9. Kon~ni rezultat so naslednji optimalni parametri: sila glajenja 200 N, {tevilo
prehodov 4 in podajanje 0,25 mm/r.
Klju~ne besede: krogli~no glajenje, trdota povr{ine, Taguchijeva metoda, faktorialno na~rtovanje, ANOVA
1 INTRODUCTION
The burnishing of metals is a cold-working process
that leads to an accurate change on the surface profile of
the workpiece by a minor amount of plastic deformation.
In burnishing process, surface irregularities is
redistributed without material loss 1–2. The burnishing
process gives many advantages in comparison with
chip-removal processes. Burnishing increases the surface
hardness of the workpiece, which in turn improves wear
resistance, increases corrosion resistance, improves
tensile strength, maintains dimensional stability and
improves the fatigue strength by inducing residual
compressive stresses in the surface of the workpiece 3–6.
A survey of references shows that work on bur-
nishing has been conducted by many researchers. Esme
et al. 7 developed an artificial neural network model for
the prediction surface roughness of AA 7075 aluminum
alloy in ball burnishing process. Yan et al 8 investigated
the feasibility and optimization of a rotary electrical
discharge machining with ball burnishing for inspecting
the machinability of Al2O3/6061 Al composite using
Taguchi method. Shiou and Chen 9 examined ball
burnishing surface finish of a freeform surface plastic
injection mold on a machining centre by using Taguchi
techniques. Seemikery et al. 10 focused on the surface
roughness, micro-hardness, surface integrity and fatique
life aspects of AISI 1045 work material using full facto-
rial design of experiments. Hassan et al. 11 investigated
the effect of the burnishing force and number of passes
on the surface roughness using Response Surface
Methodology (RSM). El-Axir et al. 12 studied the surface
finishing of 2014 aluminum alloy by using RSM with
central composite design in ball burnishing process.
El-Axir 13 determined the optimum combination of
burnishing parameters to improve surface integrity for
6061 aluminum alloy applying a vertical milling
machine using RSM with central composite design.
In this study, a factorial design and ANOVA were
used to find out the effect of the main ball burnishing
parameters. Taguchi’s orthogonal array method was
applied to determine the optimum levels of burnishing
process parameters.
2 EXPERIMENTAL WORK
For experimental work, 7178 aluminum alloy was
used as workpiece materials. Experiments were con-
ducted on the different burnishing parameters and no
coolant was used. The burnishing tool was mounted on
tool holder of the CNC lathe. The workpiece was
clamped by the three jaw chuck and tailstock centre of
the machine. Three replications of each factor level
combinations were conducted. Hardness measurements
were made by using Zwick hardness tester.
The effect of several parameters can be determined
efficiently with matrix experiments using factorial
design and the analysis of variances was employed to
Materiali in tehnologije / Materials and technology 43 (2009) 5, 271–274 271
UDK 669.715:620.178 ISSN 1580-2949
Professional article/Strokovni ~lanek MTAEC9, 43(5)271(2009)
find the significance of the factor effects. Taguchi’s
design method was applied to determine the optimal
levels of burnishing process. A flowchart of proposed
methods is shown in Figure 1.
The level of the factorial design is shown in Table 1.
Two levels of control factors are referred to as low and
high. Twenty experiments constitute the 24 factorial
design with an added centre point repeated four times.
Surface hardness was taken as output variable and
burnishing force, burnishing speed, feed rate and number
of passes were taken as input parameters for maximizing
the surface hardness of the 7178 aluminum alloy.
Table 1: Levels of the factors for factorial design
Tabela 1: Nivoji faktorjev za faktorialno na~rtovanje
Factors/Levels Low (-1) Centre (0) High (+1)
Burnishing force/N 100 150 200
Speed/mm/min 33 52 71
Number of passes 2 3 4
Feed rate/mm/r 0,25 0,35 0,45
The Taguchi design concept a L9 mixed orthogonal
arrays table was selected to conduct the matrix experi-
ments for four level factors of ball burnishing process
and designated in Table 2.
Table 2: Factors and levels for Taguchi design
Tabela 2: Faktorji in nivoji za Taguchijevo na~rtovanje
Factors/Levels 1 2 3
Burnishing force/N 100 150 200
Number of passes 2 3 4
Feed rate/ mm/r 0.25 0.35 0.45
The optimization of the engineering design problems
can be divided into the smaller-the better type, the
nominal-the best type, the larger-the better type. The
signal-to-noise (S/N) ratio is used as objective function
for optimizing the product or process design 14. The S/N
ratio was chosen according to the criterion the-larger-
the-better, in order to maximize the response. Based on
the Taguchi method, S/N ratio is defined by the Equation
1.
η j
ii
n
n y
= −
=
∑10 1 12
1
lg (1)
where: n is the number of experiment, yi is the observa-
tions of the quality characteristic, nj is the S/N ratio.
The optimization strategy of the larger the better
problem is to maximize  defined with Equation 1. The
levels that maximize  will be selected for the factors
that have a significant effect on  and the optimal
conditions for ball burnishing can then be determined.
The predicted opt under optimal conditions could be
calculated by using Equation 2
ηopt = + −∑m m mi( ) (2)
where: opt is the S/N ratio under the optimum condi-
tions, m is the overall mean value of  for the experi-
mental region, mi is the  under optimal condition.
3 RESULTS AND DISCUSSION
The effect of selected process parameters on the
surface hardness of aluminum alloy have been deter-
mined by using 24 full factorial design. ANOVA was
employed to find the significance of the factor effects
based on a 95 % confidence level. The ANOVA results
are shown in Table 3.
The ANOVA table shows that, the most significant
factors are the burnishing force and the number of
passes, respectively, while feed rate is the less significant
parameter of the ball burnishing process.
The optimum burnishing parameter combination was
obtained by using Taguchi design and analysis of S/N
ratio. Table 4 shows experimental measurements made
using the L9 orthogonal array based on the Taguchi
method. Also, the S/N ratios were considered to evaluate
the effect of burnishing parameters. The mean S/N ratio
for each level of burnishing parameters is summarized in
Table 5 and it is shown graphically in Figure 2.
A. SAGBAS, F. KAHRAMAN: DETERMINATION OF OPTIMAL BALL BURNISHING PARAMETERS ...
272 Materiali in tehnologije / Materials and technology 43 (2009) 5, 271–274
Figure 1: A flowchart of proposed methods
Slika 1: Potek uporabljenih metod
Table 3: The ANOVA results
Tabela 3: Rezultati ANOVA
Factor SS df MS F P
Model 2740. 10 274.0 5.9 0.020
A 1242 1 1242. 26. 0.002
B 663.0 1 663.0 14. 0.009
C 333.0 1 333.0 7.1 0.036
D 52.56 1 52.56 1.1 0.328
AB 27.56 1 27.56 0.5 0.470
AC 45.56 1 45.56 0.9 0.359
AD 68.06 1 68.06 1.4 0.271
BC 33.06 1 33.06 0.7 0.430
BD 264.0 1 264.0 5.6 0.054
CD 10.56 1 10.56 0.2 0.650
Residual 278.3 6 46.39
Pure error 4.50 1 4.50
Cor total 3477 17
A: Force, B: Speed, C: Number of passes, D: Feed rate
SS: Sum of square, df: Degrees of freedom, MS: Mean square
Table 4: Experimental results for surface hardness
Tabela 4: Rezultati preizkusov za trdoto povr{ine
Experiment
No
Burnishing
Force/N
Number of
passes
Feed rate/
mm/r
Surface
hardness
HV
1 100 2 0.25 167
2 100 3 0.35 170
3 100 4 0.45 179
4 150 2 0.45 175
5 150 3 0.25 179
6 150 4 0.35 181
7 200 2 0.35 178
8 200 3 0.45 192
9 200 4 0.25 202
Table 5: Mean S/N ratios for surface hardness
Tabela 5: Povpre~na razmerja za trdoto povr{ine
Factors/Levels 1 2 3
Burnishing Force 44.43 45.00 45.56
Number of passes 44.73 45.13 45.37
Feed rate 45.19 44.88 45.17
The confirmation experiment was conducted at the
optimum setting of the process parameters. The results
of the confirmation experiment for surface hardness is
given in Table 6.
Tabela 6: Rezultati potrditvenega preizkusa
Table 6: Results of the confirmation experiment
Initial setup
Optimal condition
Prediction Experiment
Level A2B2C2 A3B3C1 A3B3C1
Hardness 175 HV 202 HV
S/N ratio 44.89 dB 45.79 dB 46.00 dB
The estimated S/N ratio using the optimal burnishing
parameters for surface hardness was calculated using
Equation 2. The predicted S/N ratio (45.79) is very close
to the experimental S/N ratio (46.00) under optimal
burnishing conditions. Based on the result of the
confirmation test, the surface hardness is increased for
1.15 times.
4 CONCLUSIONS
In this experimental study, the effect "of the ball
burnishing" parameters on surface hardness was
examined and optimal settings of the ball burnishing
parameters were obtained. The effect of several
parameters can be determined efficiently with matrix
experiments using factorial design. The main parameters
were found as burnishing force, feed rate and number of
passes among four controllable factors that affect the
surface hardness in ball burnishing process. The
burnishing force is the dominant factor, while, the
number of passes is a major factor. The optimal
burnishing parameters were determined with the
Taguchi’s L9 matrix experiments. The optimal para-
meter combination for the maximum surface hardness
was obtained by using the analysis of S/N ratio. The
optimal combination of experimental parameters for
each factor is A3B3C1. As result, the optimal parameters
for surface hardness were as follows: burnishing force at
200 N, number of passes at 4, feed rate at 0.25 mm/r.
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