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1
SCIENTIFIC PAPER
THE EFFECTS OF PASSIVATION PARAMETERS ON PITTING POTENTIAL OF
BIOMEDICAL STAINLESS STEEL
Dušan Lj. Petković
*
, Miloš J. Madić, Goran M. Radenković
University of Niš, Faculty of Mechanical Engineering, A. Medvedeva 14, 18000 Niš, Serbia
Received 27.11.2015.
Revised 2.4.2016.
Accepted 6.4.2016.
*
Corresponding author. Email: dulep@masfak.ni.ac.rs
Adress: Faculty of Mechanical Engineering, A. Medvedeva 14, 18000 Niš, Serbia.
Tel: +381 18 500624, Fax: +381 18 588244.
2
Abstract: Passivation is a chemical process where electrochemical condition of passivity is
gained on the surface of metal alloys. Biomedical AISI 316LVM stainless steel (SS) can be passivized
by means of nitric acid immersion in order to improve a protective oxide layer on the surface and
consequently increase corrosion resistance of the SS in the physiological solutions. In this study,
multiple regression analysis and artificial neural network (ANN) were employed for mathematical
modeling of the AISI 316LVM SS passivation process after immersion in the nitric acid solution.
Pitting potential, which represents the measure of pitting corrosion resistance, was chosen as the
response while passivation parameters were nitric acid concentration, temperature and passivation
time. The comparison between experimental results and models predictions showed that only the ANN
model provided statistically accurate predictions with a high coefficient of determination and a low
mean relative error. Finally, based on the derived ANN equation, the effects of the passivation
parameters on pitting potential were examined.
Key words: Stainless steel, nitric acid, passivation, multiple regression analysis, artificial neural
networks
Highlights:
Corrosion resistance of 316LVM stainless steel was increased by passivation
Multiple regression analysis and artificial neural network (ANN) were employed
Only the ANN model provided statistically accurate mathematical model
Pitting potential is highly nonlinear depended on the passivation parameters
Nitric acid concentration has maximum influence on the pitting potential
3
INTRODUCTION
AISI 316LVM is a vacuum melted stainless steel (SS) widely used for biomedical applications.
It has high tensile strength and fatigue resistance, good deformability, and relatively low price.
Examples of its biomedical applications include bone plates and screws, hip and knee prosthesis, nails
and pins, dental prostheses as well as vascular and urological stents [1]. The main disadvantages of
this steel are local corrosion susceptibility during prolonged contact with human tissue, and release of
metal ions [2]. Additionally, nickel is known as a strong immunological reaction medium and may
cause various health problems [3]. Despite the above listed weaknesses, SS has the ability to
spontaneously form a stable selfprotecting oxide layer (passive film) on its surface in the reaction
with air or most aqueous environments. This film consists mostly of chromiumoxide (Cr
2
O
3
) and
typically shows thicknesses of few nanometers [4]. The presence of nonmetallic inclusions on the
material′s surface, such as sulfide inclusions, represents a discontinuity of the passive film and
therefore a potential place of pitting corrosion initiation [5].
Localized corrosion may cause an accidental deterioration of the whole system with disastrous
consequences, while the total mass loss is insignificant [6]. Corrosion of SS implants have two effects
[7]: first, the implant may become weak and the premature failure of the implant may happen; and
second, the release of corrosion products from the implant can cause the tissue reaction.
Corrosion pits commonly start because of chemical or physical heterogeneities at the surface,
which include dislocations, mechanical damage, inclusions, or second phase particles [8]. The
resistance of SS to a pitting attack depends largely on the type of SS used, and on the subsequent
physicochemical properties of the protective passive oxide layer formed on its surface [9]. There has
been a constant attempt by engineers and scientists to improve the surfacerelated properties of
biomedical materials to reduce the failure of implants and leaching of ions due to wear and corrosion.
A number of research groups have done extensive research on the improvement of both general and
pitting corrosion resistance of SS by developing techniques for the modification of the material′s
surface and passive film. Further, pitting attack resistance directly depends on the physicochemical
properties of the protective passive oxide layer formed on the surface [10].
A beneficial effect of nitric acid solution on chromium enrichment in the modified passive layer
of SS was reported in the literature [1114]. Immersion in nitric acid solutions is particularly effective
in improving the pitting resistance of austenitic SS [15]. Also, immersion in nitric acid removes
sulphide inclusions, eliminating the preferential sites for attack [16].
Mathematical modeling of the passivation process based on the scientific principles allows one
to study and better understand this complex process. Multiple regression analysis (MRA) and ANNs
are two important competitive data mining techniques widely used for the development of predictive
mathematical models [17]. MRA is a conceptually simple method for development of the functional
relationships between several independent (input) variables and one dependent (output). ANNs are a
4
computational tool, based on the properties of biological neural systems, which have been used
successfully where conventional computer systems have traditionally been slow and inefficient. Both
methodologies can be successfully applied for different process modeling. However, when compared
to one another, different conclusions can be drawn in certain cases [18].
In the literature there are few studies which are aimed at modeling the passivation process of
biomedical material in nitric acid as well as in other fluids in general. Masmoudi et al. [19] studied the
passivation process of CP Ti (commercially pure titanium) and Ti6Al4V alloy by immersing in HNO
3
solution. Their main aim was to improve corrosion resistance of tested materials after acid treatment.
Mathematical models were obtained by employing MRA, while optimization was performed by
applying the least square method. JiménezCome et al. [20] presented an automatic model based on
artificial intelligence techniques to predict pitting potential values. Their model was aimed to compare
pitting corrosion resistance of AISI 316L austenitic SS in different environmental conditions without
requiring the use of electrochemical tests. They showed that the presented model provides an
automatic way to compare the pitting corrosion resistance of austenitic stainless steel in different
environmental conditions. Petković et al. [13] analyzed the possibilities for enhancing corrosion
resistance of biomedical AISI 316LVM SS by immersing in nitric acid solutions under different
passivation conditions. Namely, it was researched the effect of nitric acid solution concentration,
temperature and passivation time on the pitting potential, which was selected as a parameter for
corrosion resistance assessment. Totally 27 experimental trials were carried out according to 3
3
full
experimental design. Mathematical model was determined by using MRA, while optimal values for
passivation parameters were found by means of genetic algorithm.
Authors of this study decided to broaden the previous research in order to obtain the more
precise and accurate experimental results by repeating the experiment twice more and by applying the
ANNs for the purpose of mathematical modeling. Thus, in this paper the pitting potential value as
response, was calculated as a mean of the three pitting potential values measured for all 27 experiment
trials (test). Moreover, three additional measurements were carried out in order to determine the pitting
potential for non passivized sample (control). Hence there were a total of 84 experiment trials.
Compared to our previous study the application of the experiment designs with replications increases
its reliability significantly.
The aim of this study was to develop mathematical model relating passivation parameters with
pitting potential as the response. Striving to as better as possible mathematical model, a statistical
analysis of the results was performed. Based on the conducted statistical analysis one can argue that
MRA is not able, on a satisfactory level, to accurately model the underlying relationships between
passivation parameters and pitting potential. For this reason, a mathematical model of the passivation
process was developed by using ANN in combination with a 3
3
full factorial design with three
replications. Finally, the ANN model was compared with the MRA model to assess the adequate
methodology for further modeling of the similar processes.
5
EXPERIMENTAL
Biomedical SS
For this research, 81 test samples (3 per each of 27 experimental trials) and 3 control samples
were machined. The samples were cylindrical with the diameter of 6 mm and height of 20 mm made
of AISI 316LVM SS, containing Cr, Ni, Mo and Mn as main alloy elements. Chemical composition of
tested AISI 316LVM SS is in accordance to ISO 58321 [21].
Passivation process
In this study, three input variables (X
1
: HNO
3
concentration. X
2
: temperature of passivation
solution and X
3
: passivation time) were selected as passivation parameters. Also, the 3
3
full factorial
design with three replications was used. Real and coded values of the parameters and their levels used
in the experimentation are given in previous published paper [13].
Prior to each test, the exposed surface of the samples was wet ground with silicon carbide paper
up to 1200 grit and polished by using diamond paste with grain size of up to 0.25 µm. Then, the
samples were rinsed with distilled water and washed with ethanol in an ultrasonic cleaner. The
passivation treatment was performed by immersing samples in nitric acid solutions. Lastly, the
samples were rinsed in double distilled water and alcohol, respectively.
Electrochemical measurements
Electrochemical tests for each sample were performed using a threecompartment cylindrical
glass cell equipped with a saturated calomel electrode (SCE) as the reference electrode and a platinum
foil as the counter electrode. The average of pitting potentials for three samples with the same
treatment was chosen as a measure of corrosion resistance. The specimens were immersed 15 seconds
before the start of the potential rise and this time was set by the program. Starting potential was of 
400 mV with a scan rate of 0.25 mV/s to anodic potential direction. The tests were finished when the
current density reached about 0.2 mA/cm
2
. The pitting potential (Ep) was chosen as a measure of
corrosion resistance and represented a level of potential when the passive film broke down [22].
The electrochemical tests were conducted in the Hank’s solution, which is a simulated body
fluid and most frequently used for in vitro tests. During the experiments, the temperature was
maintained at 37±1°C (typical body temperature). The composition and instruction for preparation of
the Hank’s solution are described elsewhere [23].
6
Mathematical Models
MRA model
In this study, a second order polynomial was selected for mathematical modeling of pitting
potential depending on the passivation parameters forms, as follows:
2
333
2
222
2
1113223311321123322110
. XbXbXbXXbXXbXXbXbXbXbbE
p
(1)
where:
p
E
is pitting potential (output),
j
X
is coded values of the parameters (input),
0
b
is the model
constant,
j
b
is the first degree coefficient,
jk
b
are the crossproducts coefficients and
jj
b
are the
quadratic coefficients.
The regression coefficients,
0
b
,
j
b
,
jk
b
and
jj
b
, were estimated by the least squares method.
Values of regression coefficients and their statistical significance were determined by using MINITAB
15 statistical software package.
ANN model
Three neurons in the input layer (for each of passivation parameters), one neuron at the output
layer for pitting potential and only one hidden layer were used to define the ANN architecture [18,
24]. The number of hidden neurons was selected by considering the following: (i) too few neurons in
the hidden layer can lead to underfitting i.e. inability to perform appropriate function approximation,
whereas too many neurons can contribute to overfitting [25] which results in a lack of generalization
capability of the developed model; (ii) the more hidden neurons, the more expressive power of the
ANN, however, with the increase of the number of hidden neurons, the number of unknown
parameters (weights and biases) to be estimated also increases; (iii) the upper limit of the number of
hidden neurons can be determined considering that the total number of unknown parameters does not
exceed the number of available data for training process. As noted by Sha and Edwards [26], although
in the case where the number of the connections to be fitted is larger than the number of available data
for training, ANN can still be trained, the case is mathematically undetermined. Therefore, relatively
small ANN architecture 351 was selected to model this passivation process.
Since it was assumed that there existed a nonlinear relationship between passivation parameters
and pitting potential, the hyperbolic tangent sigmoid transfer (activation) function was used in the
hidden layer, and linear transfer function was used in the output layer. According to the selected
transfer functions in the input and output layer, all experimental data were normalized in the [1, 1]
range. The goal of ANN training process is to determine (near) optimal values of weights and biases in
7
the hidden and output layer, previously initialized by the NguyenWidrow algorithm, in order to
minimize the mean squared error between ANN predictions and experimental data. The ANN was
trained with gradient descent with momentum by using 23 out of 27 sets of input/output experimental
data and the rest was used for testing the ANN’s generalization performance capability. Learning rate
(
) and momentum (µ) were kept at 0.1 and 0.9, respectively. The training process was finished after
7800 epochs, with the minimal achieved mean squared error of 0.00548.
Statistical evaluation of developed models
Coefficient of determination R
2
was used to evaluate the performance of the developed models,
and indicate how well mathematical models fitted experimental data [24]. In addition, for the
estimation of the prediction performance of the developed mathematical models, relative error, as one
of the most stringent criteria, was calculated by using the following equation:
100
al valueExperiment
uedicted valPre al value Experiment
or (%) lative errRe
(2)
Also, mean relative error (MRE) was calculated.
RESULTS AND DISCUSSION
The results of modeling the passivation process by using MRA and ANN are displayed and
compared in this section. In addition, the results are discussed and analyzed.
The second order MRA model (full quadratic regression model with interactions), relating
passivation parameters and the pitting potential, was obtained as:
2
2
2
1
3221321
130.0227.0
056.0077.00334.00014.0086.050.1
XX
XXXXXXXE
p
(3)
Based on the Table 1, it should be noted that insignificant model terms X
1
X
3
and X
3
2
were
eliminated since they were highly correlated with other variables.
Table 1. Regression coefficients of the MRA model
The R
2
value indicates that the passivation parameters explain 53.7 % of variance in
pitting corrosion potential. Apart from that, adjusted coefficient of determination and
predicted coefficient of determination (given in Table 1) are considerably smaller indicating
8
that the model is inadequate and overfitted. Consequently, the MRA model is not reliable
enough to describe the investigated relationship. Moreover, analysis of variance (ANOVA),
shown in Table 2, reveals that Fratio of 2.19 corresponds to confidence level of 92.2 %,
which is lower than usual ones (95 % or 99 %).
Table 2. ANOVA results for the MRA model
Based on the conducted statistical analysis one can argue that MRA model is not able, on a
satisfactory level, to accurately model the underlying relationships between passivation parameters
and pitting potential. For these reasons, modeling of the passivation process was attempted by means
of ANN.
By regarding the data normalization, transfer functions used in the hidden and output layer and
by using the weights and biases from Table 3 one can obtain a mathematical equation for pitting
potential calculation. After denormalization, the mathematical model for pitting potential in terms of
the passivation parameters can be expressed by the following equation:
77.011
1
2
36.0
22
2
11
BW
e
E
BWX
p
(4)
where: X is column vector which contains the normalized values of HNO
3
concentration, temperature
of passivation solution and passivation time. Coefficient of determination R
2
for this model reveals that
the passivation parameters explain 81 % of variance in pitting corrosion potential, suggesting that the
model has a good fit. Therefore, obtained ANN model is better and more reliable than MRA one.
Details related to the ANN model are given in Table 3.
Table 3. The weights and biases of the developed ANN model
Comparison of the models
In order to compare the models as well as effectiveness of the passivation process, measured
and predicted values of the pitting potential for all experimental trials are listed in Table 4. Apart from
the results, relative errors of the models were calculated as well as standard deviation for measured
data. Moreover, measured pitting potential for the control sample are shown in Table 4. Maximal
effect of passivation was measured for passivation condition in 12
th
experimental trial.
9
Table 4. Comparative review of the measured pitting potential and predicted values for the pitting
potential by means of MRA and ANN models
At first, positive effect of the passivation on the corrosion resistance is obvious according to
measured pitting potential values. Standard deviation of measured pitting potentials is about of 5%
indicating high reliability of the measured values. Then, taking into consideration the coefficient of
determination for both models one can notice significantly higher value for the ANN model.
Additionally, MRE shows better prediction performance of the ANN model since it produces two
times less MRE than the MRA model. In other words, ANN model is more suitable for the analysis
process with a large nonlinearity such as SS passivation. Therefore, the influence of the passivation
parameters on the corrosion resistance of the SS is considered by using the ANN model only.
Effects of passivation parameters on pitting potential
The first part of the analysis is concerned with the analysis of main effects of passivation
parameters on pitting potential. To this aim, Eq. 4 was plotted by changing one passivation parameter
at a time, while keeping the other two constant at the center level (Figure 1).
Figure 1 Main effects of passivation parameters on pitting potential
At first sight it can be noticed that the mathematical relationships, presented graphically in Fig.
1, are highly nonlinear. Quantitatively, based on the analysis of the main effects, concentration is the
most influential parameter, followed by temperature and passivation time as less influential,
respectively. While passivation temperature and time are on central level the highest corrosion
resistance is achieved when the concentration is about 20 %. For central levels of concentration and
passivation time the highest corrosion resistance is achieved when the temperature is slightly lower
than 30 ° C. Finally, when the concentration and temperature are set on the central level, the highest
corrosion resistance is achieved when the duration of the process is about 25 min.
In order to determine the interaction effects of the passivation parameters on the pitting
potential, 3D surface plots were generated considering two parameters at a time, while the third one
was kept constant at the center level (Figure 2).
Figure 2 Interaction effects of passivation parameters on pitting potential
From Figure 2 it can be observed that the pitting potential is highly sensitive to the selected
passivation parameters. It is also obvious that the effects of the parameter are variable depending on
their own level, since there are significant interaction effects of passivation parameters on the pitting
10
potential. Functional dependence between the pitting potential and the passivation parameters is
strongly nonlinear, wherefore the effect of a given parameter on the pitting potential must be
considered through the interaction with the other parameters.
For instance, if the passivation time is set on the central level (40 min), Fig. 2a, and temperature
on the low level, an increase in concentration of the solution leads firstly to the pitting potential
increase up to some extreme value which corresponds with the middle level of the concentration.
Further increase in concentration leads to the reduction of the pitting potential. In this case, the pitting
potential is very low when the concentration is on the high level, while the middle one provides a
pretty high pitting potential. When the temperature is set on the high level, with an increase in
concentration from the low level the pitting potential firstly decreases, then increases, and the nearby
high level starts to impair.
When the temperature is set on the middle level (Fig. 2b) and concentration is on the low level,
an increase in passivation time leads firstly to the pitting potential increase up to some extreme value
and then decrease. In this case, the pitting potential is very low when the passivation time is on the low
and high level, while the middle one provides pretty high pitting potential. When the concentration is
set on the high level, with increasing passivation time from the low level the pitting potential firstly
increases rashly, then slightly decreases up to about 30 minutes, and then starts to grow again up to the
high level.
Based on Fig. 2a and Fig. 2b it can be concluded that the highest pitting potentials correspond
with a combination of parameters concentrationtemperature and concentrationpassivation time
slightly below the middle levels. As it can be seen in Fig. 2c (where concentration is on the middle
level) the lowest pitting potential predicted for temperature of 17 °C and passivation time 20 minutes;
the highest pitting potentials is predicted for the temperature and passivation time slightly below the
middle level.
CONCLUSION
Passivation by immersing in nitric acid solution is an effective method to improve corrosion
resistance of biomedical SS. In biomedical SS passivation process, MRA and ANN were introduced to
model functional relationship between pitting potential and passivation parameters such as nitric acid
concentration, temperature and passivation time. It was determined a nonlinear functional dependence
between the passivation parameters and the pitting potential. Hence ANN model has proven to be
more suitable for modeling the processes such as chemical passivation of SS. Nitric acid concentration
has maximum influence on the pitting potential followed by the temperature and passivation time. The
best experimental result was achieved by a combination of parameters: HNO
3
concentration  30 vol.
%; temperature 17 ° C; passivation time  60 min.
11
ACKNOWLEDGEMENT
This paper is a result of the projects ON174004 and TR35034 supported by the Ministry of
Science and Technological Development of the Republic of Serbia.
12
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13
LIST OF TABLES
Table 1. Regression coefficients of the MRA model
Таble 2. ANOVA results for the MRA model
Table 3. The weights and biases of the developed ANN model
Table 4. Comparative review of the measured pitting potential and predicted values for the pitting
potential by means of MRA and ANN models
14
Table 1. Regression coefficients of the MRA model
Coefficient
Calculated
coefficient
value
SE
Coefficient
T
Probability
density P
b
0
1.5003
0.9300
16.13
0.000
b
1
0.0856
0.0412
2.08
0.053
b
2
0.0014
0.0414
0.03
0.973
b
3
0.0334
0.0414
0.81
0.431
b
12
0.0769
0.0498
1.54
0.141
b
13
0.0297
0.0498
0.60
0.559
b
23
0.0558
0.0505
1.11
0.284
b
11
0.2269
0.0781
2.91
0.010
b
22
0.1300
0.0714
1.82
0.086
b
33
0.0517
0.0714
0.72
0.479
S= 0.174801; R
2
= 53.7%; R
2
(adj.) = 29,2%; R
2
(pred.) = 0,0%
15
Таble 2. ANOVA results for the MRA model
Source
DF
SS
MS
F
P
Regression
9
0.60322
0.06702
2,19
0,078
Residual Error
17
0.51944
0.03056
Total
26
1.12267
DF  degree of freedom; SS  sum of squares; MS  mean square; F  value of Fisher’s distribution; P 
Probability density
.
16
Table 3. The weights and biases of the developed ANN model
W
1
W
2
B
1
B
2
0.26021
2.5744
0.78867
0.36462
2.1845
1.2035
1.2355
2.2487
1.317
1.1196
1.3122
1.4764
1.5512
0.95885
1.1753
0.27368
1.9939
0.97443
0.30408
1.0401
2.539
1
1.6398
1.4029
1.0435
2.4896
W
1
: weights between input and hidden layer; W
2
: weights between hidden and output layer;
B
1
: biases of the hidden neurons; B
2
: bias of the output neuron
17
Table 4. Comparative review of the measured pitting potential and predicted values for the pitting
potential by means of MRA and ANN models
Exp. Trial
Passivation parameters
Experimental
MRA Model
ANN Model
HNO
3
concentration
(vol. %)
Temperature
(°C)
Passivation time
(min)
E
p
(V)
Standard deviation
(%)
E
p
(V)
Relative error
(%)
E
p
(V)
Relative error
(%)
Control



0.68
4.04




1
10
17
20
0.85
4.51
1.08
26.89
0.86
1.15
2
10
17
40
1.16
5.13
1.13
2.21
1.13
2.49
3
10
17
60
1.19
6.11
1.19
0.01
1.47
23.85
4
10
40
20
1.12
4.16
1.19
6.03
1.14
1.37
5
10
40
40
1.44
5.51
1.19
17.53
1.35
6.14
6
10
40
60
1.18
4.58
1.19
0.64
1.22
3.38
7
10
60
20
1.08
3.06
1.04
4.03
1.05
2.49
8
10
60
40
0.77
2.52
0.98
27.35
0.87
12.79
9
10
60
60
0.81
5.20
0.92
14.17
0.78
3.48
10
30
17
20
1.0
4.93
1.29
29.49
1.03
3.00
11
30
17
40
1.39
4.04
1.35
2.83
1.46
5.08
12
30
17
60
1.49
5.03
1.41
5.60
1.47
1.32
13
30
40
20
1.41
3.21
1.46
3.53
1.46
3.27
14
30
40
40
1.47
5.14
1.46
0.70
1.33
9.56
15
30
40
60
1.39
3.04
1.46
5.02
1.30
6.16
16
30
60
20
1.16
5.77
1.36
17.63
1.20
3.37
17
30
60
40
1.41
2.52
1.31
7.18
1.30
7.79
18
30
60
60
1.33
4.62
1.25
5.79
1.26
5.02
19
65
17
20
1.28
4.20
1.10
14.37
1.32
3.35
20
65
17
40
1.29
5.00
1.15
10.71
1.31
1.26
21
65
17
60
0.94
3.55
1.21
28.47
1.04
10.44
22
65
40
20
1.13
2.89
1.36
20.24
1.11
1.94
23
65
40
40
1.14
5.77
1.36
19.18
1.19
4.20
24
65
40
60
1.43
4.93
1.36
4.99
1.48
3.64
25
65
60
20
1.42
3.79
1.36
4.13
1.34
5.40
26
65
60
40
1.17
3.21
1.31
11.59
1.34
14.89
27
65
60
60
1.34
4.15
1.25
6.73
1.31
2.38
Mean Relative Error (MRE)
11.00
5.53
Important remark: Shaded rows  testing data for ANN model performance
18
FIGURE CAPTIONS
Figure 1 Main effects of passivation parameters on pitting potential
Figure 2 Interaction effects of passivation parameters on pitting potential
19
LIST OF FIGURES
Figure 1 Main effects of passivation parameters on pitting potential
20
Figure 2 Interaction effects of passivation parameters on pitting potential