artificial neural network modeling to evaluate and predict
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Artificial neural network modeling to evaluate and predictthe mechanical strength of duplex stainless steel during casting
TITUS THANKACHAN1,*, K SOORYA PRAKASH2 and SATHISKUMAR JOTHI3
1Karpagam College of Engineering, Coimbatore, Tamil Nadu 641 032, India2Anna University Regional Campus, Coimbatore, Tamil Nadu 641 046, India3College of Engineering, Swansea University, Bay Campus, Swansea SA1 8EN, UK
e-mail: titusmech007@gmail.com; k_soorya@yahoo.co.in; s.jothi@swansea.ac.uk
MS received 30 May 2018; revised 6 July 2021; accepted 13 September 2021
Abstract. This paper presents the modeling of tensile properties of cast duplex stainless steel using the
artificial neural network model, exclusively developed for this work. For this research, melts of varying chemical
composition were poured, heat treated and tested for the tensile properties. The artificial neural network model
was developed using the composition as input and tensile properties as the targets. The prediction performances
of the models were evaluated by the mean absolute error (MAE), and the model with less MAE was considered
for predicting the properties. Multilayer feed forward back propagation models with two hidden layers were
implemented to predict the tensile properties of cast duplex stainless steel. The ANN model developed and
validated shows a reliable correlation between chemical compositions and tensile properties.
Keywords. Artificial neural network (ANN); chemical composition; casting; duplex stainless steel; tensile
properties.
1. Introduction
Duplex stainless steel well known for its corrosion-resistant
nature was first studied by Bain and Griffith in the year
1927 [1]. This material with duplex microstructure consists
of ferrite and austenite structure, exhibits high yield
strength, ultimate tensile strength, fracture toughness and
elongation along with its ability to resist to chloride-in-
duced stress corrosion cracking, pitting corrosion and
localized form of corrosion attack. These properties of
duplex stainless steel motivated material engineers to use
this material in saline and chemical environments, as well
as for heat exchangers, water heaters, rotors, pulp and paper
production, structures such as bridges and roofs, etc., [2–4].
The duplex microstructure ferrite and austenite at more
or less equal proportions are obtained by the controlled
addition of austenite stabilizers (Nitrogen, Nickel) and
ferrite stabilizer (Chromium) [5]. The presence of ferrite in
duplex stainless steel contributes to its high strength and
corrosion resistance while the ductility, toughness and
uniform corrosion resistance are influenced by the austenite
content. Based on the application, the alloying element
content in the duplex stainless steel is changed leading the
development of different families of duplex stainless steel.
For achieving optimal properties, trial and error method
which is a tedious and expensive method of material design
has to be carried out forcing the researchers to go for other
statistical as well as interpolation techniques. However, the
accuracy of the result was far beyond the limit which was
solved to a great extent after the emergence of Artificial
Neural Network (ANN).
ANN changed the course of material design to a great
extent by predicting the properties based on available data.
It has evolved in such a way that for problems with com-
plex or no algorithmic solution; ANN can be efficiently
utilized [6]. Steel being considered as one of the essential
materials for the development of a country is undergoing its
development from one stage to another. ANN has also been
an effective part in designing the properties of steels
according to the requirement of the application. Research-
ers have developed models which predicted efficiently the
mechanical properties, corrosive properties, microstructure,
re-crystallization behavior, etc ., based upon the chemical
composition, temperature, microstructure and processing
conditions such as melting, heat treatment, welding, forg-
ing, bending, rolling, etc., [7–11].
Ali Nazari used a multilayer back propagation neural
network for predicting the Vickers microhardness of func-
tionally graded steel and thereby modeled the charpy
impact energy [12]. Carlos Garcia-Mateo et al constructedan artificial neural network model, for predicting the aust-
enizing temperature along with the bainitic and martensitic
start temperature of steels based on its chemical composi-
tion [13]. Tohid Azimzadegan proposed an artificial neural*For correspondence
Sådhanå (2021) 46:197 � Indian Academy of Sciences
https://doi.org/10.1007/s12046-021-01742-w Sadhana(0123456789().,-volV)FT3](0123456789().,-volV)
network model to investigate the impact properties of X70
pipelines, high grade HSLA steel based on its chemical
composition and tensile strength. A multilayer feed forward
network with topology 18-10-8-1 was developed for pre-
dicting the same [14]. Gholamreza Khalaj et al constructeda multilayer neural network with hidden layers 10 and 8
trained with back propagation algorithm for predicting the
transformation start temperature of a micro alloyed steel
based on the chemical composition, grain size and heat
treatment temperatures [15]. Gholamreza Khalaj et al uti-lized 19-10-8-1 topology feed forward back propagation
neural network model for predicting the Vickers hardness
of low carbon niobium micro alloyed steels [16].
Mohammad Javad Faizabadi et al developed an artificial
neural network model for predicting the impact toughness
and hardness of microalloyed steel line pipes, considering
the chemical composition and tensile properties of the
material [17]. Dehghani and Shafiei utilized a back propa-
gation neural network model to predict the bake harden-
ability of steels which mainly comprises bake hardening
values, yield strength and work hardening amount. In this
research, a model incorporating two hidden layers was
employed to predict based on the carbon content, initial
yield stress, baking temperature and prestrain value [18]. In
all the above researches a feed forward neural network with
two hidden layers was built to predict the mechanical
properties of steel under various processing.
Chemical composition has always been a significant
parameter in the casting quality and as of now thermal
analysis can be put forward as the method for identifying
the chemical composition of poured molten metal. How-
ever, correlation between the elemental composition and
the parameters attained from cooling curve can be put
forward as the foundation of thermal analysis. And these
correlations can be established through multivariate
regression methods which have been found to be having
minimal precision and adaptability. ANN can be proposed
enough to solve these problems [19]. It is evident from the
literature review that artificial neural network has been able
to predict the properties of the steel with better agreement
and at the same time proved more accurate than classical
and statistical models. Therefore, based on the above
studies ANN proves that it can be employed as an excellent
modeling tool in predicting the properties of steel and
thereby providing itself to be exploited in different terrain
of steel property modeling.
In this research, one of the main research gaps, that is use
of ANN for modeling of duplex stainless steel is attempted.
Even though ANN has been effectively used in the dual
phase steels, bainitic steels, austenitic stainless steels, etc.,
the use of this tool in modeling the duplex stainless steel
has been hardly ever reported. In this work, the mechanical
properties such as yield strength, ultimate tensile strength
and percent elongation of the duplex stainless steel have
been modeled based on the chemical compositions by the
effective use of artificial neural network.
2. Methodology
2.1 Materials and experimentation
For this research work, melts of duplex stainless steel of
grade 4A[J92205] per ASTM A890 for varying chemical
proportion was collected from different foundries in and
around Tamil Nadu, Inida. The duplex stainless steel was
prepared in a basic lined induction furnace, deoxidized with
0.1% Ca-Si, 0.1% Fe-Si-Zr, 0.1% Fe-Ti and 0.03% sele-
nium and poured at 1560�C into the Y block moulds made
of CO2 sand. The dimension of the Y block prepared
according to the ASTM 370 standard specification is shown
in figure 1.
The solidified test blocks were cut using arc cutting,
solution heat treated at 1130�C for two hours and charac-
terized for tensile properties [yield strength, tensile strength
and percent elongation]. The chemical compositions were
checked using an ARL 3460 vacuum spectrometer. Optical
microscopy images for the cast duplex stainless steels were
investigated so as to study the phase formation of the
considered stainless steel. So as to attain the results the
samples were polished employing varying grits of emery
sheets and velvet disc polisher as per metallographic stan-
dards and then etched using 10% Oxalic acid mixed with
distilled water. The attained images for randomly selected
three images are as shown in figure 2.
2.2 Artificial neural network modelling
Artificial Neural Network (ANN), inspired from the
working of biological nervous system was developed by
Mc Culloh and co-workers during the 1940s, as a model of
the human brain. ANN consists of nodes, similar to the
Figure 1. ASTM 370 standard test bar specification.
197 Page 2 of 12 Sådhanå (2021) 46:197
neurons in the nervous system, which accepts the inputs
through the input layer and transmits a processed data to the
output layer through a hidden layer in which the processing
is carried out. The nodes in the hidden layer will adjust the
weights according to the training examples during the
training process, and by linear mapping and summing
provides an output as a function of weights and bias
[20–22]. From its establishment as a strong modeling tool,
ANN is used for solving complex problems at this point of
time because of its ability to study from the sample
examples and provide the output employing the co-efficient
obtained from the sample example.
Multilayer perceptron based feed forward network is one
of the effective networks in ANN that has been effectively
utilized by researchers for solving complex problems
thereby prompting the researchers to use the same in the
material design. The above statements can be proved by
data from literature. In this research, feed forward network
is trained with a back propagation learning algorithm which
has been considered to be the best training method for
forecasting [23, 24]. The weights and bias in this research
are optimized employing Levenberg- Marquardt (trainlm)
training functions considering its reliability and processing
speed [25]. It has been proved by Hornik et al that multi-
layer perceptron with sigmoid transfer function provides
better outputs [26]. The ANN model developed in this
research yield sigmoid transfer function in the hidden layer
and purelin transfer function in the output layer.
The literature survey gives a clear-cut proof that the
complexity and accuracy of the neural network are evalu-
ated by the number of hidden layers [27]. Unavailability of
Figure 2. Schematic diagram of ANN model for the prediction
of mechanical properties.
Figure 3. Optical micrographs for randomly selected three specimens.
Sådhanå (2021) 46:197 Page 3 of 12 197
a specific method in selecting the number of hidden layer
forced us to opt for the trial-and-error method, which has
been widely used by many researchers. Based on literature
review two main methods have been considered throughout
this research work for selecting the number of hidden
nodes. This mainly included
i. N2 = (No of outputs ?1) or (No of outputs ?2) for the
model with fewer numbers of outputs were N1 has to be
Figure 4. Training set data with chemical composition and mechanical properties.
197 Page 4 of 12 Sådhanå (2021) 46:197
found out by trial-and-error method and N1 and N2
indicates the number of nodes in first and second hidden
layer respectively.
ii. Number of hidden nodes = [0.5(no of inputs ? no of
outputs) ? sqrt (No of training patterns)] which was put
forward by neuroshell.
The shape of a multi layer perceptron that has been
effectively used for this research is shown in figure 2.
In designing a steel alloy for specific application ANN is
playing a major role by predicting the properties required
based on its chemical composition and processing param-
eters. For modeling the properties of steel the following
steps have to be followed: i) determining the input and
output variables; composition of the alloy, processing
parameters such as temperature, cooling rate, etc. can be
considered as input while, tensile strength hardness,
toughness, microstructure, etc. can be considered as output,
ii) collection of sample data, iii) preprocessing of the data if
required, iv) neural network training with the target data, v)
validation of the trained network and vi) simulation and
prediction using the network.
Matlab R2013a was utilized in this study to train an
artificial neural network model with the provided inputs and
outputs. In this work, the mechanical properties such as
yield strength, ultimate tensile strength and elongation is
modeled based upon the chemical composition of the
duplex stainless steel. The chemical elements such as car-
bon (C), Silicon (Si), Manganese (Mn), Phosphorous (P),
Sulphur (S), Chromium (Cr), Molybdenum (Mo), Nick-
el(Ni), Copper (Cu) and Nitrogen(N) are considered to be
the governing inputs for the ANN model. Out of the 220
experimentally obtained samples, 75 percent of the total
readings were considered for training of the model, 20% for
the validation of the developed model and the rest five
percent for the testing of the model, respectively. The data
set should be reliable as it affects the performance of the
developing model. The statistical analysis of the data set
that has been used in this research work for the training of
the model and thereby modeling the mechanical strength of
cast duplex stainless steel is analysed through R program-
ming software and is as provided in figure 4. In order to
achieve equal importance for the process parameters while
training and to make the training an easy procedure, pre-
processing of the samples has to be carried out by nor-
malizing the values within the range of -1 to 1. In this
work, normalizing has been carried out based on the
equation (1):
Yn ¼ ðYi� Y minÞðY max�Y minÞ
� �ð1Þ
Where Yn is the normalized value Yi is the value to be
normalized, and Ymax and Ymin are the maximum and
minimum values within the array.
The model with different hidden layers and hidden nodes
with the same specification explained above was trained for
about 25000 iterations in order to achieve the best model
with low error. The mean square error (MSE) of the
experimental and the predicted data are efficiency for
finding out the efficiency of the model which is calculated
using equation (2).
MSE ¼ 1
m� n
Xmx¼0
Xny¼1
ty xð Þ � py xð Þh i2
ð2Þ
Where n is the number of samples, m is the number of
training parameter, t is the target output and p is the pre-
dicted output by the network.
3. Results and discussions
3.1 Microstructural characterization
Microstructural characterization of a developed material is
essential so as to confirm the identity of a material. It
explains a lot about the grain formation and thereby helps
in relating the mechanical properties of the developed
material based on the phase formation, grain morphology
and grain distribution [28–31]. From figure 3, theFigure 5. MAE for different hidden nodes and layers.
Table 1. The values of parameters used in artificial neural
network.
Parameters ANN
Number of input layer nodes 10
Number of hidden layer 2
Number of first hidden layer nodes 11
Number of second hidden layer nodes 5
Number of output layer nodes 3
Sådhanå (2021) 46:197 Page 5 of 12 197
distribution of ferritic and austenitic phases of the consid-
ered cast duplex stainless steel can be observed at equal
proportion concluding it to be cast duplex stainless steel.
3.2 ANN modeling
The results attained for the tensile tests in terms of tensile
strength (TS), yield strength (YS) and percent elongation
(El) were analyzed through R programming and the data
Figure 6. Validation data with chemical composition and predicted mechanical properties.
197 Page 6 of 12 Sådhanå (2021) 46:197
along with its chemical composition that has been used for
training procedure is represented in figure 4.
In this research, ANN model with single (input – hidden-
output) and two hidden layers (input- hidden1 - hidden2 -
output) was tried out. The chemical composition of (C, Si,
Mn, P, S, Cr, Mo, Ni, Cu, and N) the duplex stainless steel
was considered as the input and tensile strength, yield
strength and percent elongation as the output for the
training of a model. The weight values between the input,
hidden and output layers are adjusted for the available input
and target values during the training process by changing
the number of hidden nodes and layers. The training pro-
cedure was continued till a model was able to predict an
output which was more or less similar to the desired output.
The major step in modeling the properties of a material
based on artificial neural network is to validate the ability
of the model created by testing the same with an unknown
data that has not been utilized in the training procedure.
The twenty percent of the patterns employed for validating
the accuracy of the model were selected from the same
probabilistic distribution possessed by the training sets. In
this research the potential of the developed feed forward
back propagation artificial neural network models with
varying hidden nodes and layers was validated based on the
statistical data that is shown in figure 5. Mean Absolute
Error (MAE) is considered in this research to evaluate the
accuracy of the model and can be calculated by the equa-
tion (3) below:
MAE ¼X t� pj j
nð3Þ
Where p = P- P’; p is the predicted output and P’ is its
mean, t= T-T’; T is the target output and T’ is the mean of T
and n is the number of samples. The accurate predicted
values can be provided by a model which has the low MAE
values. The MAE value of the different models yielding
different number of hidden nodes and layers with less MAE
value out of the total developed models is shown in
figure 5.
Figure 9. Comparison between experimental and predicted
percent elongation for training set.
Figure 8. Comparison between experimental and predicted
tensile strength for training set.
Figure 7. Comparison between experimental and predicted yield
strength for training set.
Sådhanå (2021) 46:197 Page 7 of 12 197
From figure 5, the ANN model with two hidden layers
with hidden nodes N1 = 11 and N2 = 5 has the least MAE
of 3.9 and hence better accuracy. In this study, to predict
the mechanical strength of the as cast duplex stainless steel
based on the composition, a model with 10 nodes in input
layer, two hidden layers with nodes 11 and 5 along with 3
nodes in output layer is employed (10-11-5-3) network
topology model. The values of the parameters engaged in
this study are given in table 1.
When considering the modeling of the mechanical
strength of a cast duplex stainless steel based on the
experimental values, the researcher has to ensure that the
artificial neural network model has the capability to over-
come the relative errors caused due to casting and
mechanical testing. At the same time the model has to be
more accurate and precise than the mathematical modeling
incorporating each and every factor that has an influence on
the materials property. The characteristics of the artificial
neural network model in predicting the mechanical strength
of cast duplex stainless steel is feed forward 10-11-5-3
network topology model that requires a back propagation
algorithm. Eventhough the developed model was able to
correlate between the inputs and outputs of the training set
data; an appropriate validation of the developed model was
carried over with an input data of chemical composition
which was not used for training procedure. The validation
set of input data along with its predicted values are anal-
ysed and plotted through R programming and is presented
as figure 6. The trained model was then utilized to compare
the predicted and experimental values. The predicted out-
comes for the yield strength, tensile strength and percent
elongation for the training and validation samples is com-
pared with the experimental values and is revealed in fig-
ures 7–12, respectively.
From figures, it is demonstrated that the feed forward
back propagation artificial neural network model with
topology 10-11-5-3 was able to predict the data with better
accuracy. From figures 7 to 9, it can be understood that the
developed feed forward back propagation artificial neural
Figure 12. Comparison between experimental and predicted
percent elongation for validation set.Figure 10. Comparison between experimental and predicted
yield strength for validation set.
Figure 11. Comparison between experimental and predicted
tensile strength for validation set.
197 Page 8 of 12 Sådhanå (2021) 46:197
network model exhibits a better agreement with the pre-
dicted and experimental values. The trained data and the
predicted data exhibited a better correlation with an R value
of 0.98, 0.96 and 0.93 for the tensile strength, yield strength
and percent elongation respectively. The validation data
also exhibited a good correlation between the trained and
predicted value with an R value of 0.98, 0.94, 0.97 for yield
strength, tensile strength and percent elongation,
Figure 13. Testing data with chemical composition and predicted mechanical properties.
Sådhanå (2021) 46:197 Page 9 of 12 197
respectively. The developed ANN model with a network
topology of 10-11-5-3 was able to predict the mechanical
strength of the given validation values with slightest devi-
ation that is less than five percent which can be account-
able in any modeling system.
In terms of the results from figures 7 to 12, based on the
agreement of predicted and experimental values of the
strength and elongation it can be easily pointed out that the
ANN approach can be very handy in modeling the
mechanical properties of a duplex stainless steel before
being casting based on the chemical composition. When
considering the contribution of error which is inevitable in
any type approach, there are many casting related issues
that can affect the accuracy of the developed model for
predicting the values with better efficiency such as porosity,
non uniform microstructure, etc.
The model thus developed with the available data was
tested with a set of another data to study the behavior of the
model and the results showcased by the model were seen
magnificent. A set of ten data as shown in figure 13 was fed
into the artificial neural network model with a network
topology 10-11-5-3 with a feed forward back propagation
algorithm. The model predicted the mechanical strength
which included the yield, tensile strength and percent
elongation with a slight variation. The results for the test
samples are provided in figures 14 to 15.
From figures 14 and 15, it is clear that the ANN model
has been capable to predict the results with accuracy and at
the same time the model was been trained to achieve the
results with better predictability. But from figure 16, a clear
view of the ability of the model in predicting the percent
elongation can be studied. Even though the model was able
to predict the yield and tensile strength, it was not able to
create a better correlation in predicting the percent elon-
gation when comparing with the other two outputs. Even
though slight variation has been showcased in the percent
elongation of duplex stainless steel by the developed ANN
model based on its chemical compositions, it is clear that
the deviations is too small to be considered with a variation
of 5% which can be accepted in the modeling process. This
explains that the feed forward back propagation model with
a network topology 10-11-5-3 is proficient enough to pre-
dict the required outputs from the provided chemical
composition with minor errors. Based on the model created
the effect of each alloying element on the mechanical
strength can also be evaluated. The study can be done
Figure 14. Testing Procedure Outcome for yield strength.
Figure 15. Testing Procedure Outcome for predicted tensile
strength.
Figure 16. Testing Procedure Outcome for percent elongation.
197 Page 10 of 12 Sådhanå (2021) 46:197
through increasing the values of inputs and thereby ana-
lyzing the attained results.
4. Conclusions
Artificial neural network model with a feed forward back
propagation algorithm was used to predict the tensile
properties of a cast 4A grade duplex stainless steel. The
chemical composition of the same was chosen as the input
data to predict the yield strength, tensile strength and per-
cent elongation. The conclusions are given below.
I. The artificial neural network was able to predict the
yield strength, tensile strength and percent elongation
based on its composition.
II. ANN model with two hidden layers yielding hidden
nodes 11 and 05 gave the least mean absolute error of
3.9 and predicted the results with better confirmation.
III. The ANN model developed showcased a better
correlation between the predicted and experimentally
validated data showing the effectiveness of the
model.
IV. Verification of mechanical properties based on the
compositional limits given in ASTM A890 for
duplex stainless steels with the developed ANN
model meets the specification requirement.
V. The composition to be maintained in the melt can be
predicted based on the properties demanded using
this developed artificial neural network model based
on trial and error method.
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