The main research area of this article is the analysis and modelling of the physical and mechanical characteristics of epoxy composites. The value of internal stresses was investigated using artificial neural networks. The results of the modelling studies of these parameters obtained by the authors are in good agreement with the experimental data of other scientists. It was found that the correlation coefficient in the presented test sample is 0.98. For these features in the test samples, the prediction error when using artificial neural networks is 0.35% for aluminium oxide filler, 0.55% for chromium oxide, and 0.12% for carbon black. It is shown that neural networks are able to analyse data and use them for the next stage of research training. Therefore, modelling the properties of materials by neural networks provides an increase in the accuracy of experimental studies of the main physical and mechanical features of materials based on epoxy composites activated by electrospark water hammer containing dispersed fillers.
The current development of the global industry involves the widespread use of new
materials with predefined characteristics for various functional purposes. From both a scientific
and practical point of view, the use of composite materials, including coatings based on polymer
composites [
0000-0001-9067-5543 (P. Stukhliak); 0000-0001-6002-1477 (O. Totosko); 0000-0002-9414-2477 (O. Vynokurova); 0000-0002-9404-4359 (D. Stukhlyak); 0000-0001-7311-4103 (I. Lytvynenko).
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Composites based on cold-cured epoxy diane resins demonstrate high performance features.
[
Artificial neural networks are a promising tool for predicting processes with many variables and complex interactions of various factors [25,26]. Such networks are designed like the neural structures of the human brain, which processes information using a large number of neuronal connections. In the last few years, there has been a steady increase in the use of neural network modelling for analysis in various fields of science to predict the properties of an object both at the stage of its formation and at the next stage of processing the results of experimental studies [27-30]. In particular, the use of artificial neural networks is effective in the study of polymeric composite materials based on reactoplastics, where a number of factors should be taken into account both in their formation and in the study of properties. It is worth noting that the chosen parameters of neural networks affect the accuracy of the systems in research [31-33]. In general, the properties of polymer composites can be accurately modelled using machine learning algorithms. The advantage of this approach is the opportunity to obtain research results using the proposed non-destructive testing method. In this case, the effects on the structure change in the composite, which is crucial for the control of their features, are not only in the formulation of the composite, but also in the study of their properties. [25-27].
The main task of modern polymer composite materials technology is to ensure high
technological and operational properties.This is achieved by targeted control of the structure of
polymeric materials.This approach is based on the general theoretical understanding of the
structure formation processes and their impact on the properties of composites, and the analysis
of empirical data when studying the characteristics of the developed materials.A number of
complex requirements are imposed on composite materials (CM) with optimal performance
characteristics at the stage of their formation. This is primarily true for the polymer matrix as
the basis for the composite materials. It should have high physical, mechanical, adhesion and
thermal characteristics and sufficient technological properties. This is achieved by selecting the
ingredients of the polymer binder, modifiers, plasticisers, catalysts, fillers, etc. [
In particular, a necessary condition for obtaining composites with high technological and operational properties is to ensure a strong and long-term connection between the active centers on the filler surface and the binder macromolecules. The change in the value of internal stresses should be explained on the basis of the basic principles of physical and chemical surface effects, and in particular, the active influence of the surface of dispersed particles on the crosslinking processes of the matrix in the surface layers.
In view of the above, the use of artificial neural networks in the study of internal stresses, which is an important feature of the mechanical properties of epoxy composites, is an important problem of modern materials science. However, modern scientists have not yet paid enough attention to modelling the physical features, specifically the internal stresses of epoxy composite materials, with neural networks. It is important to study the internal stresses of materials at different stages of the formation of epoxy composites filled with aluminium oxide, chromium oxide and carbon black by neural networks based on a matrix activated by electric spark water hammer.
Artificial neural networks (ANNs) have emerged as a new branch of computing that can be used in a wide range of experimental studies. Many studies have been published on predicting the properties of composites [31,33-35]. ANNs are based on the neural structure of the human brain, which processes information between many neurons, and in the last few years there has been a steady increase in interest in neural network modelling in various fields of materials science [3638]. The basic unit in the ANN is a neuron. Neurons are connected to each other by a weighting factor that determines the existing and strength of interconnections and thus affects the performance of the next groups of neurons. ANNs can be trained to perform a function by adjusting the values of the weights between neurons either based on information from outside the network or by the neuron itself in reaction to input data. This is the key point of the ability of ANNs to learn and record research results. The multilayer neural network (MLP) is the most widely used in most experimental studies25-27. A backpropagation algorithm can be used to train these multilayer feedforward networks with a differential transfer function for approximation, pattern matching, and pattern classification. The term ‘backpropagation’ refers to the process by which the derived network errors in terms of network weights and biases can be calculated and taken into account in later stages of the experiments.
Fig. 1 shows a general view of an MLP network. As you can see from the figure, a multilayer perceptron (MLP) is a feed-forward artificial neural network model that maps a set of input data to a set of related output data. An MLP consists of multiple layers of units in an oriented field, with each layer fully connected to the next. Except for the input units, each unit is a neuron (or processing unit) with a nonlinear activation function. MLP uses a supervised learning technique called backpropagation to train the network. MLP is a modification of the standard linear perceptron and can distinguish between data that cannot be separated linearly 27-31.
In this research, a 2-9-1 MLP network was built for composites filled with aluminium oxide, chromium oxide and carbon black. The training algorithm was BFGS, the error function was SOS, the hidden layer activation functions were tangential for carbon black and chromium oxide, and exponential for aluminium oxide. The activation functions of the outer layer are identity for chromium oxide and carbon black filler, and tangential for aluminium oxide filler [29, 35,37,39]. It should be noted that the epoxy diane binder ED-20 pretreated with electric spark water hammer was used as a matrix. In this case, the activity of such a matrix increases when interacting with dispersed fillers of aluminium oxide, chromium oxide and carbon black, improving the degree of crosslinking of the composite as a whole.
The main task of the modern technology of manufacturing polymeric composite materials is to study the ways of directed control of the structure of polymeric materials. The targeted control of its parameters is used to ensure high technological and operational properties[4,40,41. This approach is based on the general theoretical understanding of structure formation processes and the analysis of the influence of the empirical data on the physical, mechanical and operational properties of the developed materials. Much attention has been paid to improving the polymer matrix to form materials with high physical, mechanical, adhesive, and thermal characteristics and sufficient rheological properties. Also, modification of compositions by external force fields is a promising direction for improving the properties of heterogeneous composites at the current stages of materials science development. The technology of activation of oligomeric compositions by magnetic, ultrasonic, ultraviolet, radiation fields and electrospark water hammer at the initial stages of material formation opens up fundamentally new possibilities for controlling the processes of interaction between components, which can be used to regulate the performance characteristics of the material [1,6,7.
Processing in external fields of both compositions as a whole and individual components
under selected modes allows creating new classes of materials with a given set of performance
properties. In this regard, interesting from a scientific and practical point of view, special
attention was paid to the use of electrospark water hammer to activate the binder by
electrospark water hammer. It is known that the treatment of oligomers by electric arc spark
discharge provides cracking of binder macromolecules. [
Changes in molecular and segmental mobility during crosslinking of oligomeric compositions due to the formation of new physical and chemical links, as well as increase in molecular weight to gelation, depend heavily on the rheological characteristics and concentration relations of the input components of the system. Therefore, in further studies, the effect of the plasticiser on the physical, mechanical, and thermal properties of the CM under optimised material forming regimes was investigated. It has been experimentally established that the introduction of aliphatic resin DEG-1 into an epoxy oligomer at a concentration of 10 wt% per 100 wt% of ED-20 provides an increase in heat resistance by 19...21%, a destructive bending stress by 63...65%, and a decrease in internal stresses by 45...52% relative to the original epoxy matrix.
The non-monotonic nature of the dependence of the physical and mechanical characteristics of CM on the concentration of the plasticiser was experimentally established. It has been found that the maximum values of the dependence of properties on the concentration of DEG-1 occur as a result of the introduction of an aliphatic resin in the amount of 10...20 wt% per 100 wt% of the modified epoxy oligomer. It should be noted that at these concentrations, the destructive stress, flexural modulus, and impact strength of the treated ED-20 resin with plasticiser increase by 1.5...1.8 times, and the internal stresses decrease by 2.1 times relative to the untreated plasticised matrix.
It is known that one of the ways to reduce internal stresses in CM is to regulate the relaxation
processes at the polymer-base, polymer-filler interface, due to the creation of a homogeneous
ordered structure in the coatings [
It is important to study the value of internal stresses in ESWH-modified composites at
different concentrations of fillers. The analysis of the research results shows that with an
increase in the concentration of fillers, the internal stresses in the CM increase. This is explained
by an increase in the degree of gelation and better physical crosslinking of the matrix in the
surface layers with an increase in the concentration of dispersed particles in the ESWH, which
allows creating a material with a more crosslinked structure. At the same time, the introduction
of carbon black particles as a filler ensures the formation of CMs with minimal internal stresses
compared to other composites under study. This is due to the active influence of the surface of
these particles on the physical and chemical processes of interfacial interaction of active centers
on the surface of the solid phase with free radicals formed during the ESWH of epoxy oligomer
[
In order to confirm the above-described mechanism of CM structure formation, it is
important to study the dynamics of internal stress growth at different stages (including
hightemperature) of the formation of epoxy composites containing selected fillers at different
concentrations. It has been experimentally established that an increase in internal stresses was
observed for all composite materials with increasing temperature. This is confirmed by the
analysis of the results of calculating internal stresses at different stages of sample
thermostatting. It should be noted that a general analysis of the kinetics of internal stress
growth in all samples, without exception, shows the highest gradient of internal stress growth at
the stages of CM crosslinking. The first stage is the period after heat treatment of the composites
at a temperature of T = 393 ± 2 K for τ= 2 ± 0.1 h. In our opinion, after heat treatment, the
processes of chemical crosslinking are completed in epoxy composites, and a material with a
thermodynamically balanced structure is formed. During cooling of the CM, as well as in the
future, processes occur that are accompanied by the formation of physical units both between
macromolecules or free radicals and the filler surface, and between the active radicals
themselves, in particular at temperatures below the glass transition temperature of the polymer
matrix. This, in turn, is followed by the formation of a thermodynamically unbalanced system
[
In addition, it should be noted that in all the studied samples, after the EIGU matrix treatment, an increase in internal stresses in the CM was observed compared to the original composites (at the same concentrations) at all stages of composite thermostatting. The obtained results confirm the above assumption about the formation of new physical nodes after ESWH of the matrix at the last stages of material crosslinking.
The value of internal stresses was modelled using the experimental data obtained in the work by neural networks [28,29,33,34]. In particular, a sample of 28341 elements for each epoxy polymer filled with carbon black, aluminium oxide and chromium oxide was used to train the neural networks. Of this data, 80% was randomly selected for the training set, and the remaining 20% was left to evaluate the quality of the forecast. Here, the output parameter was the value of internal stresses (sint, MPa). The filler concentration (wt% per 100 wt% of binder) and temperature were considered as input parameters.
The dependences of the experimental data of internal stresses on the predicted ones obtained by the neural network method are shown in Figs. 2-4. It is proved that the prediction results are in good agreement with the experimental data obtained by the authors [30,35]. The data obtained using neural networks coincide with the input data (research results). It was confirmed that the created models adequately match the research results. This allows us to assert that neural network models can be used to predict the parameters of polymers treated with electric spark water hammer. The dependences of the predicted value of internal stresses on the filler concentration in the composite and temperature are shown in Figs. 5-7. These figures make it possible to visually assess the dependence of internal stresses on temperature and filler concentration at certain points, which allows to reduce the time and material costs for further research [36-38]. The diagrams of residual values for composites filled with aluminium oxide, chromium oxide, and carbon black, respectively, are shown in Figs. 8-10. The histogram data of the residual values shows the frequency of each value interval compared to the residual values. In particular, the residuals show the difference between the experimental and predicted values. They are found to be concentrated around zero and have a normal distribution 29,34,36,39,42.
To analyse the data, a statistical graph in the form of residual value diagrams is often used. It was found that these characteristics have a dependence close to the normal distribution law, which allows the use of statistical mathematical methods for processing the results of the experiment.
Neural networks have modelled the changes in the internal stresses of epoxy polymers filled with aluminium oxide, chromium oxide and carbon black. The results obtained are in good agreement with experimental data. The prediction error of the neural networks is 0.35, 0.55, and 0.12 % in the test samples. The obtained results will allow to create conditions for targeted regulation of physical, mechanical and thermal characteristics by controlling the structural organisation in the material. Further research is planned to optimise the processes of developing epoxy composites for various functional purposes. [12] Markashova, L., Tyurin, Y., Berdnikova, O., Kolisnichenko, O., Polovetskyi, I., Titkov, Y. (2019). Effect of Nano-Structured Factors on the Properties of the Coatings Produced by Detonation Spraying Method. In: Pogrebnjak, A.D., Novosad, V. (eds) Advances in Thin Films, Nanostructured Materials, and Coatings. Lecture Notes in Mechanical Engineering.
Springer, Singapore. https://doi.org/10.1007/978-981-13-6133-3_11 [13] Berdnikova, O., Kushnarova, O.,Bernatskyi, A., T. Alekseienko, Polovetskyi, Y., Khokhlov, M. Structure Peculiarities of the Surface Layers of Structural Steel under Laser Alloying. Proceedings of the 2020 IEEE 10th International Conference on "Nanomaterials: Applications and Properties", NAP2020, 2020, 9309615 [14] Fialko, N., Dinzhos, R., Sherenkovskii, J., ...Lazarenko, M., Koseva, N. Establishing Patterns In The Effect Of Temperature Regime When Manufacturing Nanocomposites On Their Heat-Conducting Properties. Eastern-European Journal of Enterprise Technologies, 2021,4(5-112), рр.21-26 [15] G. M. Hryhorenko, L. I. Adeeva, A. Yu. Tunik, M. V. Karpets, V. N. Korzhyk, M. V.
Kindrachuk, and O. V. Tisov, Formation of Microstructure of Plasma-Arc Coatings Obtained Using Powder Wires with Steel Skin and B4 C+(Cr,Fe)7С3+Al Filler, Metallofiz.
Noveishie Tekhnol., 42, No. 9: 1265—1282 (2020) https://doi.org/10.15407/mfint.42.09.1265 [16] Berdnikova, O.M., Tyurin, Yu.M., Kolisnichenko, O.V., ...Titkov, E.P, Yerеmyеyevа, L.Т.
Nanoscale Structures of Detonation-Sprayed Metal–Ceramic Coatingsof the Ni–Cr–Fe–B– Si System. Nanosistemi, Nanomateriali, Nanotehnologii. 2022, 20(1), pp. 97–109 [17] Korzhyk, V., Khaskin, V., Grynyuk, A., Ganushchak, O., Peleshenko, S., Konoreva, O., Demianov, O., Shcheretskiy, V., & Fialko, Comparing features in metallurgical interaction when applying different techniques of arc and plasma surfacing of steel wire on titanium . Eastern-European Journal of Enterprise Technologies, 4(12-112), 6–17. https://doi.org/10.15587/1729-4061.2021.238634 [18] Grigorenko, G.M., Adeeva, L.I., Tunik, A.Y., Korzhik, V.N., Karpets, M.V., Plasma Arc Coatings Produced from Powder-Cored Wires with Steel Sheaths, Powder Metallurgy and Metal Ceramics, 2020, 59(5-6), pp 318–329 [19] Sydorets, V., Berdnikova, O., Polovetskyi, Ye., Titkov, Ye., & Bernatskyi, A. (2020). Modern Techniques for Automated Acquiring and Processing Data of Diffraction Electron Microscopy for Nano-Materials and Single-Crystals. In Materials Science Forum (Vol. 992, pp. 907–915). Trans Tech Publications, Ltd. https://doi.org/10.4028/www.scientific.net/msf.992.907 [20] Kvasnytskyi, V., Korzhyk, V., Kvasnytskyi, V., Mialnitsa, H., Dong, C., Pryadko, T., Matviienko, M., Buturlia, Y. Designing brazing filler metal for heat-resistant alloys based on NI3AL intermetallide, Eastern-European Journal of Enterprise Technologies, 2020, 6 (12), рр. 6-19: Materials Science. https://doi.org/10.15587/1729-4061.2020.217819 [21] L. I. Markashova & O. S. Kushnareva. Effect of Structure on the Mechanical Properties of the Metal of Welded Joints of Aluminum Alloys of the Al–Cu–Li System. Materials Science, 2014, V. 49, pр. 681–687. [22] Grigorenko, G.M., Adeeva, L.I., Tunik, A.Y., ...Titkov, Y.P., Chaika, A.A., Structurization of Coatings in the Plasma Arc Spraying Process Using B C + (Cr, Fe)7C3-Cored Wires., Powder Metallurgy and Metal Ceramics, 2019, 58(5-6), pp 312–322 [23] Fialko, N.M., Prokopov, V.G., Meranova, N.O., ...Korzhik, V.N., Sherenkovskaya, G.P. Fizika i Khimiya Obrabotki Materialov, Thermal physics of gasothermal coatings formation processes. State of investigations, 1993, (4), р.р. 83–93 [24] Borisov, Yu.S., Oliker, V.E., Astakhov, E.A., Korzhik, V.N., Kunitskii, Yu.A., Structure and properties of gas-thermal coatings of Fe-B-C and Fe-Ti B-C alloys, Soviet Powder Metallurgy and Metal Ceramics, 1987, 26(4), pp 313–318 [25] O. Khatib, S. Ren, J. Malof and W. Padilla, “Deep Learning the Electromagnetic Properties of Metamaterials—A Comprehensive Review,” Adv. Funct. Mater, vol. 31, no. 2101748, May. 2021. doi:10.1002/adfm.202101748. [26] R. Tan, N. Zhang and W. Ye, “A deep learning–based method for the design of microstructural materials,” Struct. Multidisc. Optim., vol. 61, pp. 1417–1438. Nov. 2019, doi:: 10.1007/s00158-019-02424-2. [27] Mazumder, Rahinul & Govindaraj, Premika & Mathews, Lalson & Salim, Nisa & Antiohos, Dennis & Hameed, Nishar. (2023). Modeling, Simulation, and Machine Learning in Thermally Conductive Epoxy Materials, Multifunctional Epoxy Resins, 295-326.
DOI:10.1007/978-981-19-6038-3_11. [28] Jiang, M. Chen and J. Fan, “Deep neural networks for the evaluation and design of photonic devices,” Nature Reviews Materials, vol. 6, pp. 679–700. Dec. 2021. doi:10.1038/s41578-02000260-1. [29] B. Cunha, C. Droz, A. Zine, S. Foulard and M. Ichchou, “A review of machine learning methods applied to structural dynamics and vibroacoustic,” Mechanical Systems and Signal Processing, vol. 200, pp. 110535, Jun. 2023, doi:10.1016/j.ymssp.2023.110535. [30] O. Khatib, S. Ren, J. Malof and W. Padilla, “Deep Learning the Electromagnetic Properties of Metamaterials—A Comprehensive Review,” Adv. Funct. Mater, vol. 31, no. 2101748, May. 2021. doi:10.1002/adfm.202101748. [31] Rajkovic V, Bozic D, Jovanovic MT. Characteristics of Cu–Al2O3 composites of various starting particle size obtained by high-energy milling. Journal of the Serbian Chemical Society 2009;74(5):595–605. [32] Mukhtar A, Zhang DL, Kong C, Munroe P. Variation in hardness of ultrafine grained Cu– Al2O3 composite hollow balls and granules produced by high energy mechanical milling.
Materials Forum 2008;32:105–9. [33] Wu. Lingling, L. Lei, W. Yong, Z. Zirui, Z. Houlong, K. Deepakshyam, W. Qianxuan and J.
Hanqing, “A machine learning-based method to design modular metamaterials,” Extreme Mechanics Letters, vol. 36, no. 100657, Apr. 2020. doi:10.1016/j.eml.2020.100657. [34] Ian Goodfellow, Yoshua Bengio, Aaron Courville: Deep Learning, The MIT Press, 2016 [35] M. Zozyuk, D. Koroliouk, P. Krysenko, A. Yurikov and Y. Yakymenko, Prediction of characteristics using a convolutional neural network based on experimental data on the structure and composition of metamaterials, Statistics, optimization and information computing, vol. 11, pp. 777–787, doi:10.19139/soic-2310-5070-1707. [36] Haykin S. Neural Networks - A Comprehensive Foundation - Simon Haykin. McMaster
University, Hamilton, Ontario, Canada, 2006. P. 823. [37] N. Richard: Applied regression analysis, third ed., John Wiley & Sons, New York, 1998 [38] Wan, X., Feng, W., Wang, Y., Wang, H., Zhang, X., Deng, C., et al.: Materials discovery and properties prediction in thermal transport via materials informatics: a mini review. Nano Lett. 19, 3387–3395 (2019). https://doi.org/10.1021/acs.nanolett.8b05196 [39] Wenzhu Zhang, Youwei Xu, Yu Shi, Guoxing Su, Yufen Gu, Korzhyk Volodymyr, Intergranular corrosion characteristics of high-efficiency wire laser additive manufactured Inconel 625 alloys, Corrosion Science, Volume 205, 2022, 110422, ISSN 0010-938X, https://doi.org/10.1016/j.corsci.2022.110422. [40] Stukhlyak, P.D., Moroz, K.M., Influence of porosity in the epoxy matrix-polyvinyl alcoholdisperse filler system on the impact toughness, Materials Science, 2011, 46(4), pp.455-463. [41] Stukhlyak, P.D., Antifriction and adhesive properties of coatings of thermosetting plastics modified with thermoplastic polymers., Soviet Journal of Friction and Wear (English translation of Trenie i Iznos), 1986, 7(1), рр..138-141. [42] Buketov, A., Maruschak, P., Sapronov, O., Zinchenko, D., Yatsyuk, V., Panin, S. Enhancing performance characteristics of equipment of sea and river transport by using epoxy composites. Transport, 2016, 31(3), pp. 333-342.