=Paper=
{{Paper
|id=Vol-3742/paper2
|storemode=property
|title=The use of neural networks for modeling the thermophysical characteristics of epoxy composites treated with electric spark water hammer
|pdfUrl=https://ceur-ws.org/Vol-3742/paper2.pdf
|volume=Vol-3742
|authors=Petro Stukhliak,Vasyl Martsenyuk,Oleg Totosko,Danulo Stukhlyak,Iryna Didych
|dblpUrl=https://dblp.org/rec/conf/citi2/StukhliakMTSD24
}}
==The use of neural networks for modeling the thermophysical characteristics of epoxy composites treated with electric spark water hammer==
https://ceur-ws.org/Vol-3742/paper2.pdf
The use of neural networks for modeling the
thermophysical characteristics of epoxy composites
treated with electric spark water hammer
Petpo Stukhliak1,†, Vasyl Martsenyuk2,†, Oleg Totosko1,∗,†, Danulo Stukhlyak1,† and
Iryna Didych1,†
1 Ternopil Ivan Puluj National Technical University, 56, Ruska str., Ternopil, 46001, Ukraine
2 University of Bielsko-Biala, Willowa St. 2, Bielsko-Biala, 43-300, Poland
Abstract
In this work, the properties of epoxy composites modified with an active plasticizer were
modeled. The material was treated with electrospark water hammer. The material was treated
with electric spark water hammer, which improves their physical and mechanical properties.
The main attention is paid to the study of the thermal coefficient of linear expansion, which is a
critical parameter for the use of composites in different temperature conditions. The results of
modeling the thermophysical characteristics showed a high correlation with the experimental
data, where the correlation coefficient in the test sample was 0.99%. The prediction error of
epoxy polymers filled with DEG-1, aluminum oxide, chromium oxide, and carbon black by
neural networks is 0.11, 0.17, 0.93, and 0.04% in test samples for different fillers. It has been
shown that neural networks are capable of analyzing data and learning from it. Therefore,
modeling the properties of materials by neural networks allows achieving high prediction
accuracy.
Keywords
Machine learning, neural networks, composite 1
1. Introduction
The development of modern industry raises the problem of using new materials with
predetermined characteristics. In this area of research, the use of automation systems for
research processes is promising when creating such materials. The use of automated
systems, namely, neural networks [1, 2], creates conditions for predicting and targeted
regulation of the performance characteristics of materials. Neural networks are used in
CITI’2024: 2nd International Workshop on Computer Information Technologies in Industry 4.0, June 12–14, 2024,
Ternopil, Ukraine
∗ Corresponding author.
† These authors contributed equally.
stukhlyakpetro@gmail.com (P. Stukhliak); vmartsenyuk@ath.bielsko.pl (V. Martsenyuk);
Totosko@gmail.com (O. Totosko); itaniumua@gmail.com (D. Stukhlyak); iryna.didych1101@gmail.com (I.
Didych)
0000-0001-9067-5543 (P. Stukhliak); 0000-0001-5622-1038 (V. Martsenyuk); 0000-0001-6002-1477 (O.
Totosko); 0000-0002-9404-4359 (D. Stukhlyak); 0000-0003-2846-6040 (I. Didych)
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
research to predict the properties and process the experimental results obtained for
polymer composites containing various additives [3, 4]. It is known [5, 6] that machine
learning uses intelligent data analysis with the ability to build a meaningful relationship
between the results of experiments in the system "material composition - properties". In
particular, this approach is effective in the study of polymeric composite materials based
on reactoplastics. An epoxy diane binder was used in the successful cutout. It should be
emphasized that the accuracy of the systems depends on the selected parameters of
neural networks [7]. In general, the properties of polymer composites are modeled with
great accuracy using machine learning algorithms, namely, neural networks. The
advantage of this approach is the possibility of obtaining research results by the proposed
method of non-destructive testing without its effect on changes in the structure of the
epoxy composite.
The modern technology of creating polymer composites, including epoxy composites, is
aimed at studying methods of controlled directed changes in the material structure
parameters. The latter, in most cases, determine the physical, mechanical, and operational
characteristics of epoxy composites [8-11]. This approach is based on theoretical concepts
of structure formation processes and analysis of empirical data on the performance
properties of the developed materials. To obtain composites with optimal characteristics,
a set of requirements for the polymer matrix is established, such as high physical,
mechanical, adhesive, and thermal characteristics, as well as the necessary rheological
properties. This is achieved through the selection of ingredients in the polymer binder,
such as modifiers, plasticizers, catalysts, and fillers [12-17]. In addition, one of the
promising areas for improving the properties of heterogeneous composite systems at the
present stage of development of materials science is the modification of compositions
using external force fields: electromagnetic, ultrasonic, ultraviolet, and electrospark water
hammer [18]. The technology of activation of oligomeric compositions by these fields at
the initial stages of material formation opens up new opportunities for scientifically
directed regulation of the processes of interaction between components. The possibility
of adjusting the structure parameters for the targeted creation of epoxy composite
materials with predetermined performance characteristics has been proven.
Polymer composite materials are used in various industries: mechanical engineering,
construction, automotive, and aviation. Composite materials are increasingly used in
critical elements of aircraft and automobiles. They are also used as protective coatings in
oil and pumping units due to their high physical, mechanical, thermal and corrosion
properties. However, to realize the potential properties of composite epoxy materials, it is
necessary to use fillers, plasticizers, and modify the epoxy matrix itself with force fields. In
particular, obtaining composites with high technological and operational characteristics is
based on ensuring a strong and stable bond between the active centers on the surface of
the filler and the macromolecules of the binder [8, 12]. It is known that the parameters of
the thermal coefficient of linear expansion (TCLE) of polymers in the region of their glass
transition temperature depend on the rate of temperature change.
In connection with the above, the use of neural networks in the study of TCLE, which is
an important property of the thermal characteristics of epoxy composites, is an urgent
problem of modern materials science.
The article [19] gives the results of the study of qualitative neural networks, including
discrete and distributed time delays. A method for calculating the exponential decay rate
for a neural network model based on differential equations with a discrete delay was
developed and applied [20, 21].
When studying the properties of thermomechanical characteristics of epoxy
composites, important characteristics of converters are taken into account [22, 23], the
main of which is stability [24, 25]. Scientific studies [26] and [27] give examples of sensor
response modelling. Numerical modelling in cyber-physical sensor systems [28, 29] is
important at the stage of their design.
However, insufficient attention has been paid to modeling the thermal and physical
characteristics of neural networks. It is important to study the materials at different
temperatures of plasticized epoxy composites filled with DEG-1, aluminum oxide,
chromium oxide, and carbon black using neural networks.
2. Method of research by neural networks
Neural networks are one of the most widespread machine learning methods. In
particular, the prerequisite for their emergence was the study of the human nervous
system. In general, a neural network is a system with a large number of neurons that can
approximate rather complex dependencies and find patterns between input and output
data [30]. It is known that each neuron communicates with the other through axons and
synapses to process the received data and perform appropriate actions. Therefore, to
simulate such a process, a perceptron is used, i.e., an artificial neuron that receives several
inputs and produces one output (Fig. 1).
Figure 1: Model of an artificial neuron [5].
To achieve the minimum error in a neural network, it is necessary to adjust the weights
between neurons [31]. That is, you need to find a set of parameters that most accurately
reflects the real data distribution.
The back-propagation method is a way to adjust the weights so that the neural network
produces a smaller error on training examples. Therefore, iteration after iteration, feeding
the neural network with example after example and adjusting the weights, it is necessary
to bring the connection vector closer to a state in which the data is obtained that meets
expectations.
In general, the main parameters affecting the training process are the step size,
methods of changing the step, and the method of initializing the initial values of the
weights in the network. In addition, when building neural networks, it is important to
choose the architecture, learning algorithm, error function, activation function of the
hidden and output layers [32, 33]. The neural network training stop parameter is 1000
epochs.
In particular, in this study, such networks were built as MLP 2-10-1, for composites
filled with DEG-1 and carbon black, respectively, MLP 2-8-1 for aluminum oxide and
chromium oxide. The learning algorithm was BFGS, the error function was SOS, and the
hidden layer activation functions were logarithmic for all fillers. Whereas the activation
function of the original layer was logarithmic, and for the filler with aluminum oxide -
tangential [34, 35].
3. Experimental approach
The introduction into the epoxy oligomer (ED-20), as a plasticizer, of the aliphatic resin
DEG-1, which is chemically inert to the binder, but participates in the structural
organization of the "sol in gel" matrix. In the process of crosslinking such a two-
component system, an increase in the molecular weight of the components and gelling is
accompanied by a change in the compatibility of the ingredients and, as a result, leads to
the separation of the system into phases. In this case, it was assumed that the
supramolecular structure of chains of aliphatic oligomer is formed in the mesh structure
of the crosslinked material. The existence of globular structures of the aliphatic resin DEG-
1 in the form of inclusions in the glassy epoxy mesh was established by electron
microscopy. At the same time, such inclusions can be in both glassy and viscous states
depending on the polymerization conditions.
It should be noted that the processes of phase separation in such two-component
systems are accompanied by a change in physical properties, in particular, volumetric
shrinkage, due to a decrease in the free volume in the epoxy composite material. At the
same time, the gelation viscosity of the compositions is significantly reduced due to a
decrease in the number of physical bonds between the macromolecules of the original
epoxy oligomer. However, during polymerization, filling the free volume of the system
with plasticizer molecules and, accordingly, independent crosslinking of the two-phase
system leads to an improvement in the cohesive characteristics of the composite material
(CM), which is confirmed by thermophysical and physicomechanical studies. The main
factor in improving these characteristics is, first of all, the compatibility of the matrix
components. If the considered mechanism is correct, then the improvement of the above
properties should also be expected as a result of modification of the matrix components by
electric spark water hammer (ESWH).
The first stage of the research was to study its effect on the physical, mechanical and
thermal properties of heterogeneous materials during arc discharge treatment of matrix
components. Experimentally, it was found that an excessive amount of plasticizer in the
matrix, i.e. sol fraction, which is in a viscous-fluid state, significantly reduces the degree of
crosslinking of the matrix. In addition, dilatometric studies have shown that the thermal
coefficient of linear expansion of TCLE composites at different temperature ranges varies
in the range of 293...433 K. TCLE was calculated from the curve of relative strain versus
temperature, approximating this dependence with an exponential function. It is shown
that the TCLE of composites with modified epoxy resin compared to a CM containing the
original ED-20 is an order of magnitude lower, regardless of the concentration of the
plasticizer.
It should be noted that in the temperature range of 293...383 K, a sharp decrease in the
TCLE value was observed compared to other temperature ranges after the water hammer
action. In this temperature range, a more significant contribution of crosslinking is
realized due to the appearance of physical nodes in the spatial grid of the binder. [35, 36].
This is explained by a decrease in the strain value when the material is heated during
temperature tests. We observed a decrease in the value of the thermal expansion
coefficient of the TCLE. It has been experimentally established that the degree of
crosslinking in the material increases [36-39]. This mechanism of TCLE reduction is
confirmed by the high value of the sol fraction in the system (92-94 %). It has been proven
that the yield strength of composites containing unmodified ED-20 resin in the glass
transition zone is significantly higher than that of plasticized composites with a modified
plasticizer. This indicates an increase in the degree of cross-linking of the matrix material
after treatment with an electrohydraulic arc discharge.
It should be noted that the activity of the radicals formed during electrospark water
hammering is determined by both the kinetic and thermodynamic parameters of the
system. From the thermodynamic point of view, free radicals in the form of segments
should be considered as active dipoles. The electric forces of both attraction and repulsion
determine the behavior of active radicals when crosslinking the system. As a result, a
double electric layer was observed in the system in some areas at the interface, which, in
turn, significantly increases the cohesive characteristics of the material at the epoxy resin-
plasticizer interface.
It was found that with an increase in temperature, the TCLE of all samples without
exception also increases. Therefore, the next stage of research to reduce the TCLE was the
filling of the plasticized binder with dispersed particles of aluminum oxide, chromium
oxide, and carbon black. It was found that with an increase in the content of dispersed
particles in the composite, the thermal coefficient of linear expansion decreases only up to
certain limits. Based on this, we have determined the critical concentrations of each of the
selected fillers. It has been experimentally proven that the introduction of dispersed
particles at optimal concentrations (aluminum oxide 100 wt%, chromium oxides (50
wt%), carbon black (40 wt%) per 100 wt% of epoxy oligomers (hereinafter, the
concentration of fillers is presented in wt. wt. % per 100 wt. % of the binder) with
simultaneous pretreatment of the epoxy composite by electric spark water hammer,
provides a 2.5...3.0-fold reduction in the TCLE of composites compared to the treated
matrix.
The thermal coefficient of linear expansion was modeled using the experimental data
obtained in [35] by neural networks. In particular, in the process of training neural
networks, the data were divided into two parts - training and test samples. That is, 18,000
elements for each epoxy polymer filled with DEG-1 and carbon black, and 31,000 elements
for the polymer filled with aluminum oxide and chromium oxide, respectively. Of this data,
80% was randomly selected for the training set, and the remaining 20% was left to
evaluate the quality of the prediction. Here, the output parameter was the thermal
coefficient of linear expansion 10-5, К-1. Filler concentration (wt%) of the plasticizer and
temperature were considered as input parameters.
The dependences of the experimental data of the thermal coefficient of linear
expansion on the predicted ones obtained by the neural network method are shown in
Figs. 2-5.
Figure 2: Predicted and experimental Figure 3: Predicted and experimental
dependences for the composite filled with dependences for an aluminum oxide-filled
plasticizer DEG-1 composite
Figure 4: Predicted and experimental Figure 5: Predicted and experimental
dependences for a chromium oxide-filled dependences for a composite filled with gas
composite soot
The dependences of the predicted thermal coefficient of linear expansion on the filler
concentration in the composite and temperature are shown in Figs. 6-9.
To analyze data, a statistical graph in the form of residuals diagrams is often used. It
was found that the residuals have a normal distribution.
Figure 6: Temperature dependence of the Figure 7: Temperature dependence of the
thermal coefficient of linear expansion filled thermal coefficient of linear expansion of
with DEG-1 aluminum oxide filled with aluminum oxide
Figure 8: Temperature dependence of the Figure 9: Temperature dependence of the
thermal coefficient of linear expansion of thermal coefficient of linear expansion
chromium oxide filled glass filled with carbon black
The diagrams of residual values for composites filled with DEG-1, aluminum oxide,
chromium oxide, and carbon black, respectively, are shown in Figs. 10(a, b, c, d).
a) b)
c) d)
Figure 10: Diagram of residual values for composites filled with : a) DEG-1; b) aluminum oxide;
c) chromium oxide; d)carbon black
4. Conclusion
The neural networks modeled the change in the thermal coefficient of linear expansion of
epoxy polymers filled with DEG-1, aluminum oxide, chromium oxide, and carbon black.
The results are in good agreement with the experimental data. The prediction error of the
neural networks is 0.11, 0.17, 0.93, and 0.04 % in the test samples in particular, the
prediction accuracy depends on such parameters as the architecture of the neural
network, the activation functions of the hidden and output layers, and the learning
hyperparameters. In general, optimization of each of them is critical to achieving high
results. The obtained results will allow to create conditions for targeted regulation of
physical and thermal characteristics by forming a structural organization in the material.
The practical value of the obtained results lies in the possibility of implementing the
neural network method in production processes to improve the characteristics of
composite materials in various industries. Thus, the results of the study will help to
increase the productivity and competitiveness of enterprises that use neural network
modeling of thermal and physical characteristics in their activities. Further research is
planned to optimize the processes of developing epoxy composites for various functional
purposes.
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