artificial neural network modeling to evaluate and predict

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: [email protected]; [email protected]; [email protected]

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 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 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 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

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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 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.


tensile strength for training set.

Figure 7. Comparison between experimental and predicted yield

strength for training set.

Sådhanå (2021) 46:197 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


percent elongation for validation set.Figure 10. Comparison between experimental and predicted

yield strength for validation set.


tensile strength for validation set.

197 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 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 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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