Y. KÜÇÜK et al.: EVALUATION OF THE WEAR BEHAVIOR OF NITRIDE-BASED PVD COATINGS USING DIFFERENT ...
307–316
EVALUATION OF THE WEAR BEHAVIOR OF NITRIDE-BASED
PVD COATINGS USING DIFFERENT MULTI-CRITERIA
DECISION-MAKING METHODS
OCENA OBRABE NITRIDNEGA PVD NANOSA Z UPORABO
RAZLI^NIH METOD VE^KRITERIJSKIH POSTOPKOV
ODLO^ANJA
Yýlmaz Küçük1, Ahmet Öztel2, Mehmet Yavuz Balalý3, Mecit Öge1,
Mustafa Sabri Gök1
1Bartin University, Faculty of Engineering, Department of Mechanical Engineering, 74100 Bartin, Turkey
2Bartýn University, Faculty of Economics and Administrative Sciences, Department of Management, 74100 Bartýn, Turkey
3Turkish Military Academy, 06654 Ankara,Turkey
mecitoge@bartin.edu.tr, mecitoge@yahoo.com
Prejem rokopisa – received: 2016-03-02; sprejem za objavo – accepted for publication: 2016-05-05
doi:10.17222/mit.2016.041
In this study, AISI 7131 (16MnCr5) case-hardened steel specimens were prepared in two groups, carbonitrided and without heat
treatment, and the specimen surfaces were coated with three different coating materials (CrN, TiAlN and TiN) as a single layer
using the physical vapor deposition (PVD) cathodic arc method. The wear behaviors of the coated specimens were tested with
the micro-abrasion method. The test results of the micro-abrasion wear tests were analyzed with Multi-Criteria Decision Making
(MCDM) techniques to determine the combination of coating and heat treatment that yields the lowest wear rate. According to
the analyses conducted with the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), Multiple Attribute
Utility Theory (MAUT) and Compromise Programming (CP) MDCM techniques, the TiAlN coating exhibited the best wear
performance. The MAUT and CP methods produced an identical ranking of the alternatives, whereas a slight deviation was
found in the ranking with the TOPSIS method. Uncoated and CrN-coated specimens exhibited the worst wear performance of
all the MCDM methods.
Keywords: wear, micro-abrasion, multi-criteria decision making, PVD coating
V {tudiji sta bili pripravljeni dve skupini jekla za cementacijo AISI 7131 (16MnCr5), karbonitrirana jekla in jekla brez toplotne
obdelave, katerih povr{ina vzorcev je bila prekrita s tremi razli~nimi nanosi (CrN, TiAlN in TiN) v enem sloju, s pomo~jo
fizikalne depozicije preko plinske faze (angl. PVD) z metodo obloka. Obna{anje vzorcev z nanosom pri obrabi je bilo
preizku{eno z mikroabrazijsko metodo. Rezultati preizkusov mikroabrazijske obrabe so bili analizirani z uporabo ve~kriterijske
tehnike odlo~anja (angl. MCDM), za dolo~itev kombinacije nanos – toplotna obdelava, ki ka`e najmanj{o hitrost obrabe. Glede
na analize, ki so bile izvedene s pomo~jo tehnike, ki je najbli`ja idealni re{itvi (angl. TOPSIS), s teorijo ve~kratne prednosti
(angl. MAUT) in s programsko tehniko (angl. CP) MDCM-kompromisov, je najbolj{o odpornost na obrabo pokazal TiAlN.
MAUT- in CP-metodi dajeta enakovredne alternative, medtem ko je bilo manj{e odstopanje ugotovljeno pri TOPSIS-metodi.
Vzorci brez nanosa in s CrN nanosom so pokazali najslab{o odpornost na obrabo od vseh MCDM-metod.
Klju~ne besede: obraba, mikroabrazija, ve~kriterijsko odlo~anje, PVD-nanos
1 INTRODUCTION
Many of the machine parts used in automotive, air-
craft and machine tools are exposed to mechanical loads
under certain conditions in which they are in contact
with their counterparts. Hence, many researches are con-
ducted to understand the tribological properties of such
parts to improve their service life and reduce the main-
tenance costs. One of the methods used to solve this
problem is the thin-film coating application. In the thin-
film coating process, the adhesive characteristics and
hardness of the coatings are improved through optimi-
zation of the coating parameters using various deposition
techniques.
In this work, the coatings (TiN, CrN and TiAlN)
widely employed in actual industrial applications were
selected and deposited by the cathodic arc-evaporation
PVD technique in order to make a comparative analysis
of their tribological performances. In general, TiN and
CrN coatings are known to be the most commonly
employed thin hard coatings,1,2 whereas TiAlN is gener-
ally used for the coating of cutting tools in special ma-
chining operations.3
TiN, CrN and TiAlN thin hard coatings exhibit diffe-
rent wear behaviors due to their differing characteristic
properties, such as friction coefficient, hardness, abrasive
wear and corrosion resistance under various service con-
ditions.3,4 Abrasive wear is one of the most commonly
known wear mechanisms and it is of great importance in
terms of the evaluation of the wear performance of
coatings and the selection of abrasive wear-resistant
coatings suitable for specific applications.5
The micro-abrasion wear-testing method is widely
used to determine the abrasive wear resistance of thin
Materiali in tehnologije / Materials and technology 51 (2017) 2, 307–316 307
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
UDK 620.193.95:621.793.8:669.058 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 51(2)307(2017)
hard coatings.6–11 In the micro-abrasion wear test, the
most effective test parameters that affect the test results
can be classified as the rotational speed of the ball,12,13
the normal load,12 the ball sliding distance,13–14 the ball
surface condition15, the size6,16–19 and the type of abrasive
particle in the slurry.20
The coating materials may exhibit different wear per-
formances depending on various test conditions. There-
fore, it is necessary to determine the optimum test para-
meters that simulate the best service conditions. To select
the most suitable material for a specific application, the
criteria affecting the material selection should be
properly identified.21,22 The selection of suitable thin hard
coatings having the best wear performance among seve-
ral choices for a specific application can be considered as
a MCDM problem.23–24 The selection of the best method
for a given problem is yet another important issue with
no definite answer.25 A. Abrishamchi et al.26 state that the
selection of an appropriate MCDM from a long list of
available MCDM methods is a multi-criteria problem
itself. There is no single MCDM technique that can be
deemed superior for all decision-making problems.27
TOPSIS, EXPROM2 (Preference Ranking Organization
Method for Enrichment Evaluation), VIKOR (Vi{ekri-
terijumsko Kompromisno Rangiranje – Multicriteria
Optimization and Compromise Solution), ELECTRE
(Elimination and Choice Expressing the Reality), Linear
Assignment Method, and COPRAS (Complex Propor-
tional Assessment)24 are among the MCDM methods
used by researchers for optimum selection among a
variety of options in industrial problems.
A determination of the effects of the coating material
and the nitriding processes on the wear behaviour of
coating is a complex, multi-factorial problem and a
limited number of studies are available in the literature
on the use of MCDM techniques in the selection of
coating materials. The TOPSIS method was used by A.
Chauhan and R. Vaish27 for the selection of the best
alternative among hard coatings based on their hardness,
Young’s modulus, thermal expansion coefficient, H/E
and H3/E2 ratios. H. Çalýþkan et al.24 used EXPROM2,
TOPSIS and VIKOR methods to select the best coating
material among a variety of multicomponent nano-
structured boron-based hard coatings deposited using
magnetron-sputtering and ion-implementation-assisted
magnetron-sputtering methods in consideration of their
hardness, Young’s modulus, elastic recovery, friction
coefficient, and critical load. Again, the EXPROM II,
TOPSIS and VIKOR methods were used by H. Çalýþkan
et al.24 to determine the best selection among a variety of
materials for tool holders used in hard milling.
TOPSIS was developed by Hwang and Yoon (1981)28
as a value-based compensatory method in conception
and application,29 which attempts to choose alternatives
that are both closest to the positive-ideal solution and
farthest from the negative-ideal solution.30 The benefit
criteria are maximized and the cost criteria are mini-
mized by a positive-ideal solution, and the opposite
applies for the negative-ideal solution.31 TOPSIS pro-
vides a cardinal ranking of alternatives through the full
use of the attribute information without a requirement for
independent attribute preferences.32,33 The main strengths
of the TOPSIS method can be listed as its understandable
principle and easy implementation, its applicability,
which requires a collection of precise and overall infor-
mation,34 a consideration of both positive and negative
ideal solutions, the provision of a well-structured ana-
lytical framework for ranking of alternatives, and the use
of fuzzy number to deal with alternatives.35 The require-
ment of vector normalization for multidimensional
problems can be regarded as a weakness of the method.
MAUT is a systematic method for the analysis and
identification of multiple variables for obtaining a
decision on a common basis.36 In this method, a
multi-attribute utility function is derived, which requires
single utility functions and related weighting factors.37,38
For an evaluation of the performance criteria individually
in the same units, single utility functions are used as a
means to render their aggregation possible in the multi-
attribute utility function. In this procedure an objective is
set and attributes are established for the goal; a range of
attributes are set; single utility functions are derived for
each attribute; weighting factors are estimated for each
attribute; and a multi-attribute utility function is de-
rived.39
The MAUT strategy allows the decision maker to
make more objective decisions based on their experience
and the result of the analysis.
The CP method was first developed by M. Zeleny40
and later extended by A. Bárdossy, I. Bogárdi, L. Duck-
stein41 as composite programming for dealing with
problems of a hierarchical nature. CP is within the class
of distance-based, multi-criteria analytical methods,
designed to identify non-dominated solutions, closest to
an ideal solution by some distance measure.42 Its simple
structure is one of the main advantages of this method.
This is a simple and easily understandable method that
provides good performance when compared with
complicated and time-consuming methods.43
In this study the micro-abrasion wear behaviour of
single-layer CrN, TiN and TiAlN coatings was inves-
tigated using the fixed-ball micro-scale abrasion test.
Afterwards, some of MCDM techniques such as
TOPSIS, MAUT and CP, were implemented to compare
their outputs as a means to determine the thin hard
coating having the highest wear resistance. As indicated,
there are studies23–24,28 available in the literature on the
use of the TOPSIS method for the selection of the best
alternative among a variety of coating applications. In
this study the MAUT and CP methods are used to make a
comparative analysis between TOPSIS and these me-
thods. Also, among the other MCDM methods, the
TOPSIS, MAUT and CP methods were chosen for their
widespread usage,44 easy computation and for being
Y. KÜÇÜK et al.: EVALUATION OF THE WEAR BEHAVIOR OF NITRIDE-BASED PVD COATINGS USING DIFFERENT ...
308 Materiali in tehnologije / Materials and technology 51 (2017) 2, 307–316
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
within the same class of unique synthesis criterion
approaches in which different points of view are merged
into a unique functional structure for further optimiza-
tion, which in turn facilitates the solution of material
selection problems.45
2 MATERIALS AND METHODS
2.1 Substrate and coating
Test samples made of AISI 7131 (16MnCr5) steel
with a diameter of 40 mm and a thickness of 10 mm
were used as a substrate for the deposition of TiN, TiAlN
and CrN thin hard coatings. After the sample polishing
process, all the test samples were subjected to a car-
burizing process performed in accordance with the heat
treatment procedure given in Figure 1.
The substrate surface is hardened through a duplex
surface treatment, a combination of nitriding and carbu-
rizing, since most of the applied forces must be
supported by the substrate due to the thin structure of the
PVD coatings.46–48 The nitriding process can provide a
significantly high wear and adhesion resistance for
TiAlN coatings.49
Therefore, in this study, in addition to carburizing, a
nitriding process was also applied to some samples to
determine its synergistic effect on the abrasive wear
behaviour of thin hard coatings. The nitriding process
parameters are given in Table 1. The list of prepared
samples is given in Table 2. After the carburizing and/or
nitriding surface-hardening processes, polishing was
performed as the last operation before the deposition
process to remove the white layer (oxide or nitride layer)
emerging during the heat treatment and having an
adverse effect on the coating’s adhesion.50 The average
surface roughness of the polished samples was measured
as Ra = 0.02 μm after measurements conducted with a
Mitutoyo SJ 201 profilometer. Before the coating pro-
cess, the sample surfaces were washed 2 times with an
alkaline detergent using an ultrasonic washing device.
Then, the samples were washed 3 times with distilled
water, each time for a period of 30 s, and then dried with
hot air.
Table 1: Nitriding parameters
Tabela 1: Parametri nitriranja
Process type Plasma nitriding
Temperature 480 °C
Duration 10 h
Gas mixture/ratio Nitrogen-Hydrogen / 3:1
Pressure 2.5 mbar (in vacuum)
Table 2: Test sample classification
Tabela 2: Razvrstitev preizkusnih vzorcev
Coating
material Carburizing Nitriding Notation
CrN + - CrN
CrN + + CrN+N
TiN + - TiN
TiN + + TiN+N
TiAlN + - TiAlN
TiAlN + + TiAlN+N
Table 3: PVD deposition parameters
Tabela 3: Parametri PVD-depozicije
Parameter Coating material
TiN CrN TiAlN
Cathode current 70 A 70 A 60 A
Bias voltage (DC) 50–60 V 50–60 V 50–60 V
Number of cathode 6 6 8
Duration 1 h 1 h 30 min 1 h 10 min
Following the ion bombardment on the coated sample
surface, thin hard coatings were deposited on the sample
surfaces using the parameters given in Table 3 by the
cathodic arc PVD technique.
2.2 Micro-abrasion test
The micro-abrasion wear test is a widely used
method in the determination of the abrasive wear perfor-
mance of thin hard coatings. In this study, micro-abra-
sion wear tests were carried out using a fixed-ball-crater-
ing device shown in Figure 2. In micro-abrasion tests, an
Y. KÜÇÜK et al.: EVALUATION OF THE WEAR BEHAVIOR OF NITRIDE-BASED PVD COATINGS USING DIFFERENT ...
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MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 1: Process diagram of carburizing
Slika 1: Diagram poteka naoglji~enja
Figure 2: Scheme of the fixed-ball micro-abrasion test set up
Slika 2: Shema postavitve mikro-abrazijskega preizkusa s fiksno
kroglo
abrasive slurry composed of 25 g of SiC in 75 mL
distilled water for each abrasive mesh size (800, 1000
and 1200) mesh, was applied as 3 drops per minute, onto
an AISI 52100 steel polished ball with a diameter of 25.4
mm.
2.3 Multi-criteria decision making method
2.3.1 Definition of the problem and setting up
Coating materials may yield differing wear results
under different test conditions. In such situations a
determination of the best choice for a coating material
may be addressed as a multi-criteria decision making
(MCDM) problem.23,24 In this study, implementation of
MCDM methods is based on the assumption that each
wear value obtained under different conditions is a
criterion. The alternatives for the coating material are
shown in Table 4.
Table 4: Alternatives for coating material
Tabela 4: Izbire materiala za nana{anje
Alternative Material
A1 CrN
A2 N+CrN
A3 N+TiAlN
A4 N+TiN
A5 TiAlN
A6 TiN
A7 Uncoated
Table 5: Wear test factors
Tabela 5: Faktorji preizkusa obrabe
Abrasive (mesh) Load (N) Speed (r/min)
800 0,5 45
1000 1 90
1200 1,5 140
The factors for the wear test and their levels are
shown in Table 5. 27 tests were conducted with these
coating materials for three different factors. On the
assumption that the wear rate found in each test is a
criterion for a decision, our criteria can be organized as
C(Abrasive, Load, Speed). Our criteria and the test
parameters are shown in Table 6.
2.3.2 Entropy method for criteria weighting
In MCDM problems, the significance level of each
criteria cannot be the same. A weighting value must be
specified for each criterion to evaluate this significance
level. Several objective weighting methods are proposed
by researchers. One of the most prominent of them is the
entropy method. This method is based on the concept of
Entropy, which is defined as a measure of uncertainty by
Shannon.51 In the information theory, entropy is a
criterion for the level of uncertainty given by discrete
probability distribution, such that, the ones with signifi-
cantly high values exhibit higher levels of uncertainty.52
If the decision matrix with sufficient information for the
alternatives is available, then the entropy method can be
used as a tool to determine the significance rankings, i.e.,
the weighting values of the criteria.28,53–55 The method
can be summarized as follows:56–57
Let the decision matrix for a multi-criteria decision
making problem with m alternatives and n criteria be
Equation (1):
X X X Xj n1 2  
D
A
A
A
A
x x x x
x x x x
x x
i
m
j n
j n
i
=
1
2
11 12 1 1
21 21 2 2
1


 
 
     
i ij in
m m mj mn
x x
x x x x
2
1 2
 
     
 
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
(1)
Here, xij: is the success value of i-th alternative
according to j-th criterion. i = 1,2,...,m and j = 1,2,...,n.
Here, A and X stand for the alternative and the
criterion, respectively.
Step 1:
With the following Equation (2):
r
x
x
ij
ij
pj
p
m=
=
∑
1
i = 1,2,...,m and j = 1,2,...,n (2)
[ ]R rij m n= × normalized decision matrix is obtained.
Y. KÜÇÜK et al.: EVALUATION OF THE WEAR BEHAVIOR OF NITRIDE-BASED PVD COATINGS USING DIFFERENT ...
310 Materiali in tehnologije / Materials and technology 51 (2017) 2, 307–316
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Table 6: Criteria parameters
Tabela 6: Merila parametrov
Criterion Abrasive(mesh)
Load
(N)
Speed
(r/min) Criterion
Abrasive
(mesh)
Load
(N)
Speed
(r/min) Criterion
Abrasive
(mesh)
Load
(N)
Speed
(r/min)
C1 800 0.5 45 C10 1000 0.5 45 C19 1200 0.5 45
C2 800 0.5 90 C11 1000 0.5 90 C20 1200 0.5 90
C3 800 0.5 140 C12 1000 0.5 140 C21 1200 0.5 140
C4 800 1 45 C13 1000 1 45 C22 1200 1 45
C5 800 1 90 C14 1000 1 90 C23 1200 1 90
C6 800 1 140 C15 1000 1 140 C24 1200 1 140
C7 800 1.5 45 C16 1000 1.5 45 C25 1200 1.5 45
C8 800 1.5 90 C17 1000 1.5 90 C26 1200 1.5 90
C9 800 1.5 140 C18 1000 1.5 140 C27 1200 1.5 140
Step 2:
With the following Equation (3):
e
m
r rj ij
i
m
ij= −
=
∑1
1ln
ln j = 1,2,...,n (3)
entropy value of each criterion is found. Here, ej is
the entropy value of the j the criterion.
Step 3:
The weighting values of the criteria are assigned with
Equation (4):
W
e
e
j
j
p
p
n=
−
−
=
∑
1
1
1
( )
j = 1,2,...,n (4)
It is apparent that Wj
j
n
=
∑ =
1
1
3 RESULTS AND DISCUSSION
In this study, TOPSIS, MAUT and CP methods
among the MDCM methods are used with the wear
results obtained from the conducted micro-abrasion tests
for the selection of the most suitable coating material,
and afterwards the solutions proposed by each method
are compared.
First, the criteria were weighted through the imple-
mentation of the Entropy method on the decision matrix
(Table 7) consisting of the test results obtained from the
micro-abrasion tests conducted in accordance with the
test parameters given in Table 3, and then the analyses
were carried out for each of the TOPSIS, MAUT and CP
methods, as a means for the selection of the most
suitable coating material. The resulting solutions were
listed in descending order (from the most to the least
suitable) by a comparative evaluation.
The criterion weights obtained with the Entropy
method are given in Table 8.
The criteria weights were objectively determined
with the Entropy method. The criteria weights calculated
using the Entropy method are given in Table 8.
According to these results, the criterion weights of the
26th, 22nd, 25th and 19th criteria were found to be higher
than the other criteria. This arises from the fact that the
7th alternative Uncoated sample and 1st alternative CrN
coating result in relatively higher wear rates, whereas
N+CrN,TiAlN and TiN coatings result in lower wear
rates. Consequently, the coatings providing lower wear
rates under these criteria are favored over the other coat-
ings. Other criterion weights generally had approximate
values.
3.1 Analysis using TOPSIS method
The Technique for order preference by similarity to
ideal solution (TOPSIS) method developed by C. - L.
Hwang and K. Yoon28 is based on the basic concept of
Y. KÜÇÜK et al.: EVALUATION OF THE WEAR BEHAVIOR OF NITRIDE-BASED PVD COATINGS USING DIFFERENT ...
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MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Table 7: The decision matrix for coating-material selection
Tabela 7: Matrica odlo~itev pri izbiri materiala nanosa
Material C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13
CrN 0.0097 0.0134 0.0135 0.0149 0.0195 0.0221 0.0169 0.0226 0.0267 0.0071 0.0047 0.0044 0.0050
N+CrN 0.0047 0.0061 0.0066 0.0073 0.0099 0.0106 0.0104 0.0096 0.0094 0.0016 0.0013 0.0055 0.0078
N+TiAlN 0.0060 0.0071 0.0074 0.0055 0.0067 0.0077 0.0043 0.0067 0.0123 0.0031 0.0079 0.0020 0.0054
N+TiN 0.0042 0.0060 0.0093 0.0085 0.0129 0.0161 0.0088 0.0185 0.0189 0.0015 0.0037 0.0059 0.0026
TiAlN 0.0030 0.0050 0.0073 0.0059 0.0119 0.0111 0.0073 0.0130 0.0190 0.0013 0.0024 0.0075 0.0019
TiN 0.0041 0.0059 0.0083 0.0070 0.0093 0.0130 0.0074 0.0156 0.0108 0.0042 0.0061 0.0065 0.0039
Uncoated 0.0094 0.0147 0.0147 0.0220 0.0214 0.0228 0.0196 0.0220 0.0267 0.0081 0.0102 0.0122 0.0117
Material C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27
CrN 0.0055 0.0072 0.0100 0.0064 0.0118 0.0021 0.0024 0.0013 0.0020 0.0021 0.0022 0.0024 0.0021 0.0029
N+CrN 0.0058 0.0093 0.0051 0.0036 0.0094 0.0005 0.0006 0.0009 0.0008 0.0006 0.0006 0.0005 0.0003 0.0004
N+TiAlN 0.0092 0.0026 0.0054 0.0068 0.0050 0.0003 0.0008 0.0005 0.0004 0.0015 0.0007 0.0009 0.0010 0.0005
N+TiN 0.0018 0.0117 0.0065 0.0016 0.0064 0.0009 0.0011 0.0015 0.0011 0.0014 0.0009 0.0012 0.0017 0.0012
TiAlN 0.0056 0.0054 0.0012 0.0028 0.0034 0.0015 0.0006 0.0006 0.0004 0.0004 0.0007 0.0004 0.0004 0.0007
TiN 0.0045 0.0011 0.0072 0.0092 0.0090 0.0004 0.0009 0.0012 0.0005 0.0007 0.0006 0.0006 0.0007 0.0008
Uncoated 0.0139 0.0246 0.0164 0.0166 0.0255 0.0048 0.0049 0.0024 0.0053 0.0030 0.0040 0.0055 0.0067 0.0027
Table 8: The criterion weights obtained using the entropy method
Tabela 8: Kriterijske ute`i, dobljene z metodo entropije
Criterion C1 C2 C3 C4 C5 C6 C7 C8 C9
Weight 0.0158 0.0163 0.0082 0.0245 0.0131 0.0120 0.0203 0.0126 0.0131
Criterion C10 C11 C12 C13 C14 C15 C16 C17 C18
Weight 0.0403 0.0297 0.0196 0.0279 0.0259 0.0571 0.0321 0.0414 0.0357
Criterion C19 C20 C21 C22 C23 C24 C25 C26 C27
Weight 0.0758 0.0616 0.0219 0.0866 0.0353 0.0540 0.0790 0.0922 0.0482
the selection of the alternative closest to ideal solution
and the farthest to anti-ideal solution. The consecutive
stages of this method are as follows:28,56
Step 1: Constructing the normalized decision matrix:
with the following Equation (5):
r
x
x
ij
ij
pj
p
m
=
=
∑ ( )
1
2
i = 1,2,...,m and j = 1,2,...,n (5)
Normalized decision matrix [ ]R rij= is obtained.
Step 2: Constructing the weighted normalized deci-
sion matrix, with the following Equation (6):
v w rij j ij= i = 1,2,...,m and j = 1,2,...,n (6)
Normalized decision matrix [ ]V v ij m n= × is obtained.
Here, wj : j-th criterion’s weight value obtained with
the entropy method.
Step 3: Determination of ideal and negative-ideal
solutions:
If the two artificial solutions A* (ideal solution) and
A– (negative-ideal solution) are defined as follows:
{ }A v j J v j J i m
v v
i ij i ij
* (max ), (min ' ) , , ...,
, , .* *
= ∈ ∈ =
=
1 2
1 2{ }.., , ... ,* *v vj n
(7)
{ }A v j J v j J i m
v v
i ij i ij
–
– –
(min ), (max ' ) , , ...,
, , .
= ∈ ∈ =
=
1 2
1 2{ }.., , ... ,– –v vj n
(8)
here,
{ }J j n= =1 2, , ..., in case of benefit criterion
{ }J j n' , , ...,= =1 2 in case of cost criterion
Step 4: Calculation of the separation measure:
Each alternative’s measure of separation from the
ideal solution S
i*
and from the negative-ideal solution
S
i –
, is given as follows:
S v v i m
i ij j
j
n
* ( ) , , , ...,
*= − =
=
∑ 2
1
1 2 (9)
S v v i m
i ij j
j
n
– ( ) , , , ...,
–= − =
=
∑ 2
1
1 2 (10)
Step 5: Calculation of the relative proximity to the
ideal solution:
The relative proximity to the i-th alternative to the
ideal solution (A*) is defined as follows:
C S S S C i m
i i i i i* – * – *
( ), , , ...,= − < < =0 1 1 2, (11)
Step 6: Performing the decision ranking: The deci-
sion ranking of the alternatives is performed in accord-
ance with the descending order of C
i*
values.
The weighted and normalized decision matrix,
related to the analysis conducted in accordance with the
steps defined in the TOPSIS method, is given in Table 9.
Ideal and anti-ideal solutions obtained using Equations
(7) and (8), are given in Table 10. As indicated in the
table, the highest C
i*
valued alternative stands for the
best selection in the TOPSIS method.
Positive and negative separation measures given in
Table 11 and relative proximities to the ideal solution are
calculated respectively with Equations (9), (10) and (11).
Also, the ranking of the coating materials based on the
relative proximities to ideal solution are given in
Table 11. According to this ranking, TiAlN is qualified
as the best coating material owing to its excellent
performance, which is followed by N+CrN, TiN and
N+TiAlN with similar performance values. N+TiN and
CrN resulted in low performance values, whereas the
uncoated material resulted in the worst performance
value.
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312 Materiali in tehnologije / Materials and technology 51 (2017) 2, 307–316
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Table 9: Weighted normalized decision matrix
Tabela 9: Pretehtana normalizirana matrica odlo~itev
Material C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13
CrN 0.0091 0.0091 0.0042 0.0118 0.0069 0.0063 0.0109 0.0066 0.0070 0.0235 0.0089 0.0047 0.0083
N+CrN 0.0044 0.0041 0.0020 0.0058 0.0035 0.0030 0.0067 0.0028 0.0024 0.0053 0.0024 0.0059 0.0130
N+TiAlN 0.0056 0.0048 0.0023 0.0044 0.0024 0.0022 0.0028 0.0020 0.0032 0.0102 0.0150 0.0021 0.0091
N+TiN 0.0039 0.0041 0.0029 0.0068 0.0045 0.0046 0.0057 0.0054 0.0049 0.0048 0.0069 0.0063 0.0044
TiAlN 0.0028 0.0034 0.0023 0.0047 0.0042 0.0032 0.0047 0.0038 0.0050 0.0042 0.0045 0.0080 0.0032
TiN 0.0038 0.0040 0.0026 0.0056 0.0033 0.0037 0.0048 0.0045 0.0028 0.0137 0.0116 0.0070 0.0065
Uncoated 0.0088 0.0100 0.0046 0.0175 0.0075 0.0066 0.0127 0.0064 0.0070 0.0267 0.0192 0.0131 0.0196
Material C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27
CrN 0.0072 0.0135 0.0141 0.0121 0.0132 0.0289 0.0257 0.0080 0.0292 0.0171 0.0244 0.0304 0.0259 0.0325
N+CrN 0.0076 0.0175 0.0072 0.0069 0.0105 0.0065 0.0062 0.0053 0.0115 0.0046 0.0069 0.0058 0.0037 0.0044
N+TiAlN 0.0119 0.0048 0.0075 0.0130 0.0055 0.0038 0.0082 0.0032 0.0055 0.0127 0.0073 0.0111 0.0122 0.0051
N+TiN 0.0023 0.0220 0.0092 0.0030 0.0070 0.0128 0.0112 0.0093 0.0159 0.0114 0.0104 0.0155 0.0209 0.0133
TiAlN 0.0073 0.0101 0.0017 0.0053 0.0037 0.0206 0.0062 0.0036 0.0055 0.0030 0.0082 0.0051 0.0044 0.0073
TiN 0.0058 0.0020 0.0102 0.0176 0.0100 0.0048 0.0096 0.0073 0.0069 0.0059 0.0066 0.0070 0.0088 0.0089
Uncoated 0.0181 0.0464 0.0231 0.0316 0.0283 0.0651 0.0526 0.0149 0.0784 0.0243 0.0447 0.0696 0.0845 0.0302
Table 11: Positive and negative separation measures, relative proxi-
mities to the ideal solution and the ranking
Tabela 11: Pozitivni in negativni ukrepi lo~evanja, relativni pribli`ki
idealni re{itvi in razvrstitev
Material S+ S- C+ Sýra
CrN 0.0724 0.1104 0.6039 6
N+CrN 0.0234 0.1632 0.8747 2
N+TiAlN 0.0262 0.1610 0.8602 4
N+TiN 0.0371 0.1433 0.7946 5
TiAlN 0.0212 0.1648 0.8861 1
TiN 0.0255 0.1620 0.8640 3
Uncoated 0.1742 0.0023 0.0132 7
3.2 Analysis using MAUT method
According to the basic principle of MAUT (Multiple
Attribute Utility Theory) method, there is an U utility
function with a real value, defined over the set of suitable
alternatives, and the decision maker maximizes this.58
The procedure followed in the MAUT method is defined
in 4 steps:59–60
Step 1: Utility values are determined according to the
benefit criteria and the normalized values rij are calcu-
lated using these values:
r
x l
u lij
ij l
j l
=
−
−+
–
– , u xj i ij
+ = max , l xj i ij
– min= (12)
Similarly, the utility values are also determined based
on the cost criterion, and normalized values rij are calcu-
lated accordingly:
r
u x
u lij
l ij
j l
=
−
−
+
+ – , u xj i ij
+ = max , l xj i ij
– min= (13)
Step 2: Weighted sum of rij values gives the total uti-
lity value.
U w ri j
j
n
ij=
=
∑
1
(14)
Step 3: Decision ranking is performed. The alterna-
tive with the highest total utility value is deemed the best
alternative.
The single-attribute utility function values of the
alternatives calculated with MAUT method based on the
criteria, are given in Table 12.
MAUT multi-attribute utility function values and
their ranking are given in Table 13. As shown in Table
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Materiali in tehnologije / Materials and technology 51 (2017) 2, 307–316 313
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Table 10: Ideal and anti-ideal solutions
Tabela 10: Idealne in neidealne re{itve
Criterion C1 C2 C3 C4 C5 C6 C7 C8 C9
A* 0.0028 0.0034 0.0020 0.0044 0.0024 0.0022 0.0028 0.0020 0.0024
A– 0.0091 0.0100 0.0046 0.0175 0.0075 0.0066 0.0127 0.0066 0.0070
Criterion C10 C11 C12 C13 C14 C15 C16 C17 C18
A* 0.0042 0.0024 0.0021 0.0032 0.0023 0.0020 0.0017 0.0030 0.0037
A– 0.0267 0.0192 0.0131 0.0196 0.0181 0.0464 0.0231 0.0316 0.0283
Criterion C19 C20 C21 C22 C23 C24 C25 C26 C27
A* 0.0038 0.0062 0.0032 0.0055 0.0030 0.0066 0.0051 0.0037 0.0044
A– 0.0651 0.0526 0.0149 0.0784 0.0243 0.0447 0.0696 0.0845 0.0325
Table 12: MAUT single-attribute utility function values
Tabela 12: Posamezni MAUT-atributi vrednosti funkcije koristnosti
Material C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13
CrN 0.0000 0.1299 0.1556 0.4352 0.1283 0.0498 0.1777 0.0000 0.0000 0.1428 0.6139 0.7683 0.6856
N+CrN 0.7483 0.8835 1.0000 0.8920 0.7841 0.8094 0.6014 0.8183 1.0000 0.9493 1.0000 0.6587 0.3997
N+TiAlN 0.5519 0.7813 0.8990 1.0000 1.0000 1.0000 1.0000 1.0000 0.8310 0.7342 0.2495 1.0000 0.6384
N+TiN 0.8212 0.8924 0.6653 0.8215 0.5769 0.4445 0.7070 0.2588 0.4521 0.9742 0.7299 0.6205 0.9282
TiAlN 1.0000 1.0000 0.9083 0.9812 0.6450 0.7784 0.8047 0.6033 0.4462 1.0000 0.8771 0.4622 1.0000
TiN 0.8332 0.9034 0.7956 0.9099 0.8235 0.6514 0.7982 0.4395 0.9160 0.5800 0.4557 0.5562 0.7969
Uncoated 0.0450 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0399 0.0000 0.0000 0.0000 0.0000 0.0000
Material C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27
CrN 0.6906 0.7401 0.4203 0.6811 0.6160 0.5904 0.5791 0.5917 0.6755 0.3393 0.5349 0.6074 0.7250 0.0000
N+CrN 0.6669 0.6501 0.7451 0.8653 0.7248 0.9560 0.9991 0.8200 0.9174 0.9229 0.9944 0.9889 1.0000 1.0000
N+TiAlN 0.3921 0.9361 0.7284 0.6518 0.9275 1.0000 0.9580 1.0000 1.0000 0.5444 0.9827 0.9071 0.8948 0.9741
N+TiN 1.0000 0.5491 0.6526 1.0000 0.8645 0.8520 0.8925 0.4780 0.8575 0.6050 0.9001 0.8378 0.7873 0.6851
TiAlN 0.6856 0.8163 1.0000 0.9198 1.0000 0.7259 1.0000 0.9622 1.0000 1.0000 0.9589 1.0000 0.9915 0.8953
TiN 0.7755 1.0000 0.6055 0.4903 0.7436 0.9834 0.9266 0.6537 0.9804 0.8625 1.0000 0.9698 0.9372 0.8410
Uncoated 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0822
13, TiAlN takes the first place with its superior perfor-
mance, followed by N+CrN, N+TiAlN and TiN with
similar performance values. N+TiN, CrN and especially
uncoated material exhibited significantly low perfor-
mances, as the highest total utility valued alternative
stands for the best selection.
Table 13: MAUT Multi-utility function and the ranking
Tabela 13: MAUT Ve~vrednostna funkcija in razvrstitev
Material Multi utility values Ranking
CrN 0.509431 6
N+CrN 0.879946 2
N+TiAlN 0.860277 3
N+TiN 0.784909 5
TiAlN 0.909513 1
TiN 0.841247 4
Uncoated 0.005178 7
3.3. Analysis using CP method
CP (Compromise Programming) is a MCDM method
developed in the 1970s by M. Zelen61 and P. – L. Yu.62
This method is based on minimization of the distance to
the ideal point f*. The Lp metric is used for the calcul-
ation of distance. The method can be summarized as
follows:63–66
Step 1: Ideal point f* and anti-ideal point f* are estab-
lished.
f f f fn
* * * *, , ...,≡ 1 2 , f f f fn* * * *, , ...,≡ 1 2 (15)
here,
f
j
j
i m
i
* , ,... ,
,
max
min=
=
=
1 2
1 2
{x }ij . criterion utility
,... , m j{x }ij . criterion cost
⎧
⎨
⎩
(16)
f
j
j
i m
i
*
, ,... ,
,
min
max=
=
=
1 2
1 2
{x }ij . criterion utility
,... , m j{x }ij . criterion cost
⎧
⎨
⎩
(17)
here, xij: is the success value of the i-th alternative
according to the j-th criterion. i = 1,2,...,m, j = 1,2,...,n.
Step 2: The distance to the ideal point is minimized:
min
( )*
*
*
L W
f f x
f fp jj
n
j j i
j j
p /p
=
−
−
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
⎡
⎣
⎢
⎤
⎦
⎥
=
∑
1
1
, i = 1,2,...,m (18)
Step 3: The alternative giving the minimal value is
the best alternative.
L1, L2 and L are, respectively, named as the Man-
hattan, Euclidean and Tchebycheff metrics.
The optimal values obtained using the CP method
and the ranking are shown in Table 14. Given that in the
CP method the alternative giving the lowest optimal
value is the best alternative; TiAlN may be considered to
have shown the best performance by far, as the highest
total utility valued alternative stands for the best selec-
tion. N+CrN, N+TiAlN and TiN materials underper-
formed compared to the performance values of TiAlN.
The performance values of N+TiN, CrN and the un-
coated materials lined up at the bottom of the
performance list.
Table 14: CP optimal values and the ranking
Tabela 14: CP optimalne vrednosti in razvrstitev
Material Optimal value Rank
CrN 0.269379 6
N+CrN 0.070013 2
N+TiAlN 0.080999 3
N+TiN 0.120416 5
TiAlN 0.055632 1
TiN 0.089914 4
Uncoated 0.543521 7
The rankings obtained using the TOPSIS, MAUT and
CP methods are shown in Figure 3. As seen in the
figure, the MAUT and CP methods produced the
identical ranking of the alternatives, whereas there is a
slight deviation in the ranking obtained with the TOPSIS
method. However, all the methods indicate that TiAlN is
the best material, followed by N+CrN. CrN and the
uncoated materials displayed the best performances,
according to all the MCDM methods implemented in the
study.
4 CONCLUSIONS
In this study, abrasive wear tests were conducted
using the micro-abrasion wear technique on TiN, CrN
and AlTiN coatings, which were deposited on nitrided
and non-nitrided substrates with the PVD technique, then
the measured wear values were used so as to determine
the best coating selection through analyses with each of
the TOPSIS, MAUT and CP methods among the MCDM
techniques. The most suitable coating types, according to
each method, were determined and comparatively eva-
luated. The obtained results are summarized as follows:
• According to the TOPSIS method TiAlN was deter-
mined to be the coating with the best performance;
which was followed by N+CrN, TiN and N+TiAlN,
respectively. The N+TiN and CrN coatings under-
Y. KÜÇÜK et al.: EVALUATION OF THE WEAR BEHAVIOR OF NITRIDE-BASED PVD COATINGS USING DIFFERENT ...
314 Materiali in tehnologije / Materials and technology 51 (2017) 2, 307–316
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 3: Ranking of the alternatives obtained with MCDM methods
Slika 3: Razvrstitev alternativnih variant, dobljenih z MCDM meto-
dami
performed compared to other coatings; however, the
uncoated material displayed the worst performance,
with a dramatic decline compared to all the coated
materials.
• According to the MAUT method, TiAlN exhibited
the best performance. Other coatings were ranked as
N+CrN, N+TiAlN and TiN, respecively. N+TiN, CrN
and especially the uncoated material displayed re-
markable underperformances.
• The CP and MAUT methods produced the same
ranking of alternatives. In the TOPSIS method only
N+TiAlN and TiN shifted places in the ranking
differently from the CP and MAUT methods. How-
ever, all the methods indicate that TiAlN is the best
material, which is followed by N+CrN. Again, the
CrN and uncoated materials became the alternatives
with worse performances according to all the MCDM
methods.
• The highest Ci* valued alternative is deemed the best
selection in the TOPSIS method. While the highest
total utility valued alternative is the best selection for
MAUT, in the CP method the shortest distance is
favored.
• Increasing the number of MCDM methods could be
useful for a comparative analysis of the obtained
results in further studies.
Acknowledgements
The authors would like to acknowledgement the
funding support of the Scientific Research Project (BAP)
no 2013.1.85. provided by Bartin University Scientific
Research Projects Unit. All other support provided by
the Engineering Faculty of Bartin University and its staff
is also acknowledged.
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