Issues $\rightarrow$ Volume 24, Issue 2 (2023)

Design of a Two-Layer Al–Al2O3 Coating with an Oxide Layer Formed by the Plasma Electrolytic Oxidation of Al for the Corrosion and Wear Protections of Steel

L. Ropyak$^1$, T. Shihab$^{1,2}$, A. Velychkovych$^1$, O. Dubei$^1$, T. Tutko$^1$, and V. Bilinskyi$^1$

$^1$Ivano-Frankivsk National Technical University of Oil and Gas, 15 Karpatska Str., UA-76019 Ivano-Frankivsk, Ukraine
 $^2$Technical College of Engineering, Al-Bayan University, International Airport Road, Near of Abbas Bin Firnas Sq., 10070 Baghdad/Jadriya, Iraq

Received 06.04.2023; final version — 06.06.2023 Download PDF logo PDF

Abstract
The article analyses technologies for the formation of coatings to protect machine and equipment parts from corrosion and wear in aggressive environments. The study considers plasma electrolytic oxidation (PEO) regimes of valve metal materials on the core, microstructure, and physical and mechanical properties of oxide coatings. To solve this problem, it is promising to develop a combined technology: application of a layer of aluminium on the surface of steel parts followed by its PEO. The purpose of this work is a theoretical study of the temperature distribution in a steel cylinder covered with a layer of aluminium during PEO to substantiate the thickness of the layers of the two-layer aluminium–aluminium oxide coating. An installation for PEO and a technological process of forming a two-layer Al–Al2O3 coating on long-dimensional parts are developed. A mathematical model is created for an infinite three-layer cylinder with an internal coaxial surface cylindrical source of heat that moves at a constant speed in the radial direction deep into the aluminium layer of the cylinder. It is based on solving the boundary value problem of thermal conductivity with the condition of ideal thermal contact between the layers. During PEO, a solid oxide layer is formed, but the thickness of the unoxidized aluminium layer decreases. The thermophysical characteristics of such a cylinder are functions of both the radial co-ordinate of the cylinder and the time. During the construction of a two-layer coating, it is advisable to use the results of thermal calculations to justify the thickness of the unoxidized aluminium layer adjacent to the surface of the steel under the condition of ensuring the flow of mutual diffusion processes at the interface between aluminium and steel to increase the adhesion strength of the coating to the base due to heating by instantaneous heat sources caused by the action of electric-spark discharges in the PEO process. The thickness of the outer solid layer of aluminium oxide is chosen based on the condition of ensuring the necessary service life of machine parts for wear with a certain reservation. The results of mechanical, tribological, and corrosive cracking tests for steel samples with the developed two-layer Al2O3 coating show its high operational properties.

Keywords: two-layer coating, aluminium, aluminium oxide, steel, mathematical model, temperature, diffusion.

DOI: https://doi.org/10.15407/ufm.24.02.319

Citation: L. Ropyak, T. Shihab, A. Velychkovych, O. Dubei, T. Tutko, and V. Bilinskyi, Design of a Two-Layer Al–Al2O3 Coating with an Oxide Layer Formed by the Plasma Electrolytic Oxidation of Al for the Corrosion and Wear Protections of Steel, Progress in Physics of Metals, 24, No. 2: 319–365 (2023)

References  
  1. P. Le Billon and B. Kristoffersen, Environment and Planning A: Economy and Space, 52, No. 6: 1072 (2020); https://doi.org/10.1177/0308518X18816702
  2. D. Mara, S. Nate, A. Stavytskyy, and G. Kharlamova, Energies, 15, No. 2: 658 (2022); https://doi.org/10.3390/en15020658
  3. International Energy Agency (IEA), World Energy Outlook. Flagship Report — 2021 (Paris, France: 2021); https://www.iea.org/reports/world-energy-outlook-2021
  4. J.-H. Kim and Y.-G. Lee, Sustainability, 12, No. 16: 6628 (2020); https://doi.org/10.3390/su12166628
  5. I.I. Chudyk, Ya.M. Femiak, M.I. Orynchak, A.K. Sudakov, and A.I. Riznychuk, Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu 2021, No. 4: 17 (2021); https://doi.org/10.33271/nvngu/2021-4/017
  6. O. Ovetska, S. Ovetskyi, and O. Vytiaz , E3S Web of Conferences, 230: 01021 (2021); https://doi.org/10.1051/e3sconf/202123001021
  7. V. Klymenko, S. Ovetskyi, O. Vytyaz, A. Uhrynovskyi, and V. Martynenko, Mining of Mineral Deposits, 16, No. 3: 11 (2022); https://doi.org/10.33271/mining16.03.011
  8. O. Bazaluk, A. Velychkovych, L. Ropyak, M. Pashechko, T. Pryhorovska, and V. Lozynskyi, Energies, 14, No. 14: 4198 (2021); https://doi.org/10.3390/en14144198
  9. T. Tutko, O. Dubei, L. Ropyak, and V. Vytvytskyi, Advances in Design, Simulation and Manufacturing IV. DSMIE 2021. Lecture Notes in Mechanical Engineering (Eds. V. Ivanov, J. Trojanowska, I. Pavlenko, J. Zajac, and D. Peraković) (Cham, Switzerland: Springer: 2021), p. 153; https://doi.org/10.1007/978-3-030-77719-7_16
  10. I. Shatskyi, I. Vytvytskyi, M. Seniushkovych, and A. Velychkovych, IOP Conf. Series: Materials Science and Engineering, 564, 012073 (2019); https://doi.org/10.1088/1757-899X/564/1/012073
  11. A. Velychkovych, Engineering Solid Mechanics, 2022, No.10: 287; https://doi.org/10.5267/j.esm.2022.3.002
  12. T. O. Pryhorovska, Machining Science and Technology, 21, No. 1: 37 (2017); https://doi.org/10.1080/10910344.2016.1260429
  13. O. Slabyi, East.-Eur. J. Enterp. Technol., 3, No. 7: 27 (2018); https://doi.org/10.15587/1729-4061.2018.132661
  14. O. Bazaluk, O. Slabyi, V. Vekeryk, A. Velychkovych, L. Ropyak, and V. Lozynskyi, Energies, 14, No. 12: 3514 (2021); https://doi.org/10.3390/en14123514
  15. O. Bazaluk, O. Dubei, L. Ropyak, M. Shovkoplias, T. Pryhorovska, and V. Lozynskyi, Energies, 15, No. 1: 83 (2022); https://doi.org/10.3390/en15010083
  16. O.V. Panevnyk and O.Ya. Dubei, Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, No. 4: 98 (2015).
  17. O. Mandryk, V. Artym, M. Shtohry, and V. Zaytsev, Management Systems in Production Engineering, 28, No. 3: 168 (2020); https://doi.org/10.2478/mspe-2020-0025
  18. S. Ilin, L. Adorska, V. Samusia, D. Kolosov, and I. Ilina, E3S Web of Conferences, 109: 00030 (2019); https://doi.org/10.1051/e3sconf/201910900030
  19. V. Lozynskyi, R. Dychkovskyi, P. Saik, and V. Falshtynskyi, Solid State Phenomena, 277: 66 (2018); https://doi.org/10.4028/www.scientific.net/SSP.277.66
  20. M. Petlovanyi, V. Lozynskyi, P. Saik, and K. Sai, E3S Web of Conferences, 123: 01019 (2019); https://doi.org/10.1051/e3sconf/201912301019
  21. M. Khoma, V. Vynar, M. Chuchman, and C. Vasyliv, Lecture Notes in Civil Engineering 102: 2311 (2021); https://doi.org/10.1007/978-3-030-58073-5_18
  22. H.M. Nykyforchyn, O.I. Zvirko, and O.T. Tsyrulnyk, Procedia Structural Integrity, 2: 501 (2016); https://doi.org/10.1016/j.prostr.2016.06.065
  23. M. Khoma, V. Vynar, C. Vasyliv, M. Chuchman, B. Datsko, V. Ivashkiv, and O. Dykha, Journal of Bio- and Tribo-Corrosion, 8: 53 (2022); https://doi.org/10.1007/s40735-022-00655-3
  24. O.Y. Andreikiv, I.Y. Dolins’ka, I.P. Shtoiko, O.K. Raiter, and Y.Y. Matviiv, Materials Science, 54: 638 (2019); https://doi.org/10.1007/s11003-019-00228-9
  25. М.М. Student, V.M. Dovhunyk, V.M. Posuvailo, I.V. Koval’chuk, and V.M. Hvozdets’kyi, Materials Science, 53: 359 (2017); https://doi.org/10.1007/s11003-017-0083-x
  26. V. Hutsaylyuk, M. Student, V. Dovhunyk, V. Posuvailo, O. Student, P. Maruschak, and I. Koval’chuck, Metals, 9, No. 3: 280 (2019); https://doi.org/10.3390/met9030280
  27. K.O. Cooke, Aluminium Alloys and Composites (Ed. K.O. Cooke) (London, United Kingdom: IntechOpen: 2020), р. 1; https://doi.org/10.5772/intechopen.90569
  28. V.I. Pokhmurskii, I.M. Zin, V.A. Vynar, O.P. Khlopyk, and L.M. Bily, Corrosion Engineering Science and Technology, 47, No. 3: 182 (2012); https://doi.org/10.1179/1743278211Y.0000000022
  29. K. Berladir, T. Hovorun, O. Gusak, Y. Reshetniak, and D. Khudaybergenov, Advances in Design, Simulation and Manufacturing III. DSMIE 2020. Lecture Notes in Mechanical Engineering (Eds. V. Ivanov, J. Trojanowska, I. Pavlenko, J. Zajac, and D. Peraković) (Cham, Switzerland: Springer: 2020) p. 473; https://doi.org/10.1007/978-3-030-50794-7_46
  30. C.-H. Hsu, Metals, 10, No. 5: 605 (2020); https://doi.org/10.3390/met10050605
  31. M.C. Santos, A.R. Machado, and W.F. Sales, Int. J. Adv. Manuf. Technol., 86: 3067 (2016); https://doi.org/10.1007/s00170-016-8431-9
  32. O. Vlasiy, V. Mazurenko, L. Ropyak, and O. Rogal, East.-Eur. J. Enterp. Technol., 1, No. 7 (85): 25 (2017) (in Ukrainian); https://doi.org/10.15587/1729-4061.2017.65718
  33. V.I. Pokhmurskii, I.M. Zin, V.A. Vynar, O.P. Khlopyk, and L.M. Bily, Corrosion Engineering Science and Technology 47, No. 3: 182; https://doi.org/10.1179/1743278211Y.0000000022
  34. M. Sathish, N. Radhika, and B. Saleh, Composites. Part B: Engineering, 225: 109278 (2021); https://doi.org/10.1016/j.compositesb.2021.109278
  35. J. Kusyj and A. Kuk, East.-Eur. J. Enterp. Technol., 1, No. 7: 41 (2015); https://doi.org/10.15587/1729-4061.2015.36336
  36. V.І. Kyryliv, V.І. Gurey, О.V. Maksymiv, І.V. Hurey, and Y.О. Kulyk, Materials Science, 57: 422 (2021); https://doi.org/10.1007/s11003-021-00556-9
  37. B.N. Mordyuk, V.V. Silberschmidt, G.I. Prokopenko, Y.V. Nesterenko, and M.O. Iefimov, Materials Characterization, 61, No. 11: 1126 (2010); https://doi.org/10.1016/j.matchar.2010.07.007
  38. H.V. Pokhmurs’ka, M.M. Student, N.R. Chervins’ka, Kh.R. Smetana, A. Wank, T. Hoenig, and H. Podlesak, Materials Science, 41: 316 (2005); https://doi.org/10.1007/s11003-005-0168-9
  39. M.M. Student, I.M. Pohrelyuk, V.M. Hvozdetskyi, H.H. Veselivska, K.R. Zadorozhna, R.S. Mardarevych, and Y.V. Dzioba, Materials Science, 57: 240 (2021); https://doi.org/10.1007/s11003-021-00538-x
  40. F. Peltier and D. Thierry, Coatings, 12: 518 (2022); https://doi.org/10.3390/coatings12040518
  41. O. Gaponova, C. Kundera, G. Kirik, and V. Tarelnyk, V. Martsynkovskyy, I. Konoplianchenko, M. Dovzhyk, A. Belous, and O. Vasilenko, Advances in Thin Films, Nanostructured Materials, and Coatings. Lecture Notes in Mechanical Engineering (Eds. A. Pogrebnjak and V. Novosad) (Singapore: Springer: 2019), p. 249; https://doi.org/10.1007/978-981-13-6133-3_25
  42. S.I. Kryshtopa, D.Yu. Petryna, I.M. Bogatchuk, I.B. Prun’ko, and V.M. Mel’nyk, Alloying Mater. Sci., 53, No. 3: 351 (2017); https://doi.org/10.1007/s11003-017-0082-y
  43. Z.A. Duryagina, S.A. Bespalov, V.Ya. Pidkova, and D.Yu. Polockyj, Metallofiz. Noveishie Tekhnol., 33, Spec. Iss.: 393 (2011).
  44. V. Hutsaylyuk, M. Student, K. Zadorozhna, O. Student, H. Veselivska, V. Gvosdetskii, P. Maruschak, and H. Pokhmurska, J. Mater. Res. Technol., 9, No. 6: 16367 (2020); https://doi.org/10.1016/j.jmrt.2020.11.102
  45. T. W. Clyne and S. C. Troughton, Int. Mater. Rev., 64, No. 3: 127 (2019); https://doi.org/10.1080/09506608.2018.1466492
  46. F. Simchen, M. Sieber, A. Kopp, and T. Lampke, Coatings, 10, No. 7: 628 (2020); https://doi.org/10.3390/coatings10070628
  47. S. Sikdar, P. V. Menezes, R. Maccione, T. Jacob, and P. L. Menezes, Nanomaterials 11, No. 6: 1375 (2021); https://doi.org/10.3390/nano11061375
  48. M. Kaseem and B. Dikici, Coatings, 11, No. 6: 374 (2021); https://doi.org/10.3390/coatings11040374
  49. L. Ropyak, T. Shihab, A. Velychkovych, V. Bilinskyi, V. Malinin, and M. Romaniv, Ceramics, 6, No. 1: 146 (2023); https://doi.org/10.3390/ceramics6010010
  50. M.M. Student and I.M. Pohrelyuk, Mater. Sci., 57: 377 (2021); https://doi.org/10.1007/s11003-021-00552-z
  51. Q. Tang, T. Qiu, P. Ni, D. Zhai, and J. Shen, Coatings, 12, No. 8: 1191 (2022); https://doi.org/10.3390/coatings12081191
  52. V.A. Andrei, C. Radulescu, V. Malinovschi, A. Marin, E. Coaca, M. Mihalache, C.N. Mihailescu, I.D. Dulama, S. Teodorescu, and I.A. Bucurica, Coatings, 10, No. 4: 318 (2020); https://doi.org/10.3390/coatings10040318
  53. N. Attarzadeh, M. Molaei, K. Babaei, and A. Fattah-Alhosseini, Surf. Interfaces, 23: 100997 (2021); https://doi.org/10.1016/j.surfin.2021.100997
  54. X. Nie, R. Cai, C. Zhao, J. Sun, J. Zhang, and D.T.A. Matthews, Surf. Coat. Technol., 442: 128403 (2022); https://doi.org/10.1016/j.surfcoat.2022.128403
  55. L. Ropyak and V. Ostapovych, East.-Eur. J. Enterp. Technol., 2, No. 5: 50 (2016); https://doi.org/10.15587/1729-4061.2016.65719
  56. V.S. Protsenko, L.S. Bobrova, A.S. Baskevich, S.A. Korniy, and F.I. Danilov, J. Chem. Technol. Metallurgy, 53: 906 (2018).
  57. V.S. Protsenko, L.S. Bobrova, D.E. Golubtsov, S.A. Korniy, and F.I. Danilov, Russ. J. Applied Chemistry 91: 1106 (2018); https://doi.org/10.1134/S1070427218070066
  58. O.Y. Dubei, T.F. Tutko, L.Y. Ropyak, and M.V. Shovkoplias, Metallofiz. Noveishie Tekhnologii, 44, No. 5: 251 (2022); https://doi.org/10.15407/mfint.44.02.0251
  59. M. Dutkiewicz, A. Velychkovych, I. Shatskyi, and V. Shopa, Materials, 15, No. 13: 4671 (2022); https://doi.org/10.3390/ma15134671
  60. K. Ye and Z. Li, Corrosion, 76, No. 10: 895 (2020); https://doi.org/10.5006/3560
  61. P. Hartjen, A. Hoffmann, A. Henningsen, M. Barbeck, A. Kopp, L. Kluwe, C. Precht, O. Quatela, R. Gaudin, M. Heiland, R.E. Friedrich, C. Knipfer, D. Grubeanu, R. Smeets, and O. Jung, In Vivo (Athens, Greece), 32, No. 2: 241 (2018). https://doi.org/10.21873/invivo.11230
  62. A. Chuzhak, V. Sulyma, L. Ropyak, A. Velychkovych, and V. Vytvytskyi, J. Healthc. Eng., 2021: 6607364 (2021); https://doi.org/10.1155/2021/6607364
  63. O. Bazaluk, A. Chuzhak, V. Sulyma, A. Velychkovych, L. Ropyak, V. Vytvytskyi, V. Mykhailiuk, and V. Lozynskyi, Appl. Sci., 12, No. 10: 4903 (2022); https://doi.org/10.3390/app12104903
  64. S. Dobrotvorskiy, M. Balog, Y. Basova, L. Dobrovolska, and A. Zinchenko, Advanced Manufacturing Processes. InterPartner 2019. Lecture Notes in Mechanical Engineering (Eds. V. Tonkonogyi, V. Ivanov, J. Trojanowska, G. Oborskyi, M. Edl, I. Kuric, I. Pavlenko, and P. Dasic) (Cham, Switzerland: Springer: 2020), p. 32; https://doi.org/10.1007/978-3-030-40724-7_4
  65. L.S. Saakiyan, A.P. Efremov, L.Ya. Ropyak, and A.V. Gorbatskii, Soviet Mater. Sci., 23, No. 3: 267 (1987); https://doi.org/10.1007/BF00720884
  66. L.S. Saakiyan, A.P. Efremov, and L. Ya. Ropyak, Protection of Metals, 25, No. 2: 185 (1989).
  67. V.А. Vynar, V.І. Pokhmurs’kyi, І.М. Zin’, K.B. Vasyliv, and О.P. Khlopyk, Mater. Sci., 53: 717 (2018); https://doi.org/10.1007/s11003-018-0128-9
  68. A. Gulyarenko and M. Bembenek, Agriculture (Switzerland), 12, No. 6: 841 (2022); https://doi.org/10.3390/agriculture12060841
  69. S.I. Kryshtopa, I.B. Prun’ko, B.V. Dolishnii, M.V. Panchuk, I.M. Bogatchuk, and V.M. Mel’nyk, Mater. Sci., 55: 187 (2019); https://doi.org/10.1007/s11003-019-00288-x
  70. J. Pawlik, A. Wróblewska-Pawlik, and M. Bembenek, Materials, 15, No. 16: 5783 (2022); https://doi.org/10.3390/ma15165783
  71. X. Qi, H. Shang, B. Ma, R. Zhang, L. Guo, and B. Su, Materials, 13, No. 4: 970 (2020); https://doi.org/10.3390/ma13040970
  72. J.M. Wheeler, J.A. Curran, and S. Shrestha, Surf. Coat. Technol. 207: 480 (2012); https://doi.org/10.1016/j.surfcoat.2012.07.056
  73. М.М. Student, V.V. Shmyrko, М.D. Klapkiv, І.M. Lyasota, and L.N. Dobrovol’ska, Mater. Sci., 50: 290 (2014); https://doi.org/10.1007/s11003-014-9720-9
  74. J. Dean, T. Gu, and T.W. Clyne, Surface and Coatings Technology, 269: 47 (2015); https://doi.org/10.1016/j.surfcoat.2014.11.006
  75. Z.-Q. Wu, Y. Xia, G. Li, and F.-T. Xu, Dalian Ligong Daxue Xuebao/Journal of Dalian University of Technology, 46: 60 (2006).
  76. B.A. Lyashenko, V.S. Veremchuk, N.A. Dolgov, and V.M. Ivanov, Strength of Materials, 28: 452 (1996); https://doi.org/10.1007/BF02209316
  77. L.Y. Ropyak, A.S. Velychkovych, V.S. Vytvytskyi, and M.V. Shovkoplias, J. Phys. Conf. Ser., 1741: 012039 (2021); https://doi.org/10.1088/1742-6596/1741/1/012039
  78. R. Tatsiy, M. Stasiuk, O. Pazen, and S. Vovk, Proceedings of the 2018 International Scientific-Practical Conference on Problems of Infocommunications Science and Technology (Kharkiv, Ukraine: 2018), p. 21; https://doi.org/10.1109/INFOCOMMST.2018.8632131
  79. M. Bembenek, A. Uhryński, Materials, 14, No. 7: 1770 (2021); https://doi.org/10.3390/ma14071770
  80. R.M. Tatsiy, O.Y. Pazen, S.Y. Vovk, and D.V. Kharyshyn, Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, 3: 27 (2020); https://doi.org/10.33271/nvngu/2020-3/027
  81. J. Pawlik, J. Cieślik, M. Bembenek, T. Góral, S. Kapayeva, and M. Kapkenova, Materials, 15, No. 17: 6019 (2022); https://doi.org/10.3390/ma15176019
  82. I. P. Shatskyi, L. Ya. Ropyak, and M. V. Makoviichuk, Strength of Materials, 48, No. 5: 726 (2016); https://doi.org/10.1007/s11223-016-9817-5
  83. L.Ya. Ropyak, I.P. Shatskyi, and M.V. Makoviichuk, Metallofiz. Noveishie Tekhnol., 39, No. 4: 517 (2017); https://doi.org/10.15407/mfint.39.04.0517
  84. L.Y. Ropyak, M.V. Makoviichuk, I.P. Shatskyi, I.M. Pritula, L.O. Gryn, and V.O. Belyakovskyi, Functional Mater., 27, No. 3: 638 (2020); https://doi.org/10.15407/fm27.03.638
  85. M. Bembenek, M. Makoviichuk, I. Shatskyi, L. Ropyak, I. Pritula, L. Gryn, and V. Belyakovskyi, Sensors, 22, No. 21: 8105 (2022); https://doi.org/10.3390/s22218105
  86. I.P. Shatskyi, M.V. Makoviichuk, and A.B. Shcherbii, Proc. 11th Int. Conf. Shell Structures: Theory and Applications (SSTA 2017), 4: 165 (2018); https://doi.org/10.1201/9781315166605-34
  87. І.P. Shats’kyi, М.V Makoviichuk, and А.B. Shcherbii, J. Math. Sci., 238, No. 2: 165 (2019); https://doi.org/10.1007/s10958-019-04226-9
  88. I.P. Shatskyi, M.V. Makoviichuk, and A.B. Shcherbii, Mater. Sci., 55: 484 (2020); https://doi.org/10.1007/s11003-020-00329-w
  89. A.A. Bedzir, I.P. Shatskii, and V.M. Shopa, Int. Appl. Mech., 31, No. 5: 351 (1995); https://doi.org/10.1007/BF00846842
  90. I.P. Shats’kyi, O.M. Lyskanych, and V.A. Kornuta, Strength Mater., 48, No. 3: 469 (2016); https://doi.org/10.1007/s11223-016-9786-8
  91. I.P. Shats’kyi, V.M. Shopa, and A.S. Velychkovych, Strength Mater., 53: 277 (2021); https://doi.org/10.1007/s11223-021-00286-y
  92. R.M. Tatsiy, O.Y. Pazen, S.Y. Vovk, L.Y. Ropyak, and T.O. Pryhorovska, J. Serb. Soc. Comput. Mech., 13, No. 2: 36 (2019); https://doi.org/10.24874/JSSCM.2019.13.02.04
  93. R.M. Tatsii, M.F. Stasyuk, and O.Y. Pazen, J. Eng. Phys. Thermophys., 94: 298 (2021); https://doi.org/10.1007/s10891-021-02302-z
  94. R.M. Tatsii, O.Yu. Pazen, and S.Ya. Vovk, Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, 2020, No. 1: 36 (2020); https://doi.org/10.33271/nvngu/2020-1/036
  95. V.S. Kolesov, N.V. Vlasov, L.O. Tisovskii, and I.P. Shatskii, Int. Appl. Mech., 28: 426 (1992); https://doi.org/10.1007/BF00847125
  96. N.I. Malanchuk, B.S. Slobodyan, and R.M. Martynyak, Materials Science, 52: 819 (2017); https://doi.org/10.1007/s11003-017-0026-6
  97. Y. Kusyi, O. Onysko, A. Kuk, B. Solohub, and V. Kopei, Lecture Notes in Networks and Systems, 472: 135 (2022); https://doi.org/10.1007/978-3-031-05230-9_16
  98. T. Pryhorovska and L. Ropyak, Proc. Int. Conf. on Advanced Optoelectronics and Lasers (CAOL) (Sozopol, Bulgaria, 2019), p. 493; https://doi.org/10.1109/CAOL46282.2019.9019544
  99. L. Ropyak, V. Vytvytskyi, A. Velychkovych, T. Pryhorovska, and M. Shovkoplias, IOP Conf. Ser.: Mater. Sci. Eng., 1018: 012014 (2021); http://doi.org/10.1088/1757-899X/1018/1/012014
  100. Y. Kusyi, V. Stupnytskyy, O. Onysko, E. Dragašius, S. Baskutis, and R. Chatys, Eksploatacja i Niezawodnosc, 24: 655 (2022); https://doi.org/10.17531/ein.2022.4.684
  101. Y.M. Kusyi and A.M. Kuk, J. Phys. Conf. Ser., 1426: 012034 (2020); https://doi.org/10.1088/1742-6596/1426/1/012034
  102. W. Dai, C. Li, D. He, D. Jia, Y. Zhang, and Z. Tan, Surf. Coat. Technol., 380: 125014 (2019); https://doi.org/10.1016/j.surfcoat.2019.125014
  103. F. Xi, Y. Huang, Y. Zhao, Y. Liu, W. Dai, and Y. Tian, Materials, 15, No. 12: 4256 (2022); https://doi.org/10.3390/ma15124256
  104. E. Matykina, R. Arrabal, A. Pardo, M. Mohedano, B. Mingo, I. Rodríguez, and J. González, Mater. Lett., 127: 13 (2014); https://doi.org/10.1016/j.matlet.2014.04.077
  105. M. Vakili-Azghandi, A. Fattah-Alhosseini, and M. K. Keshavarz, Measurement, 124: 252259 (2018); https://doi.org/10.1016/j.measurement.2018.04.038
  106. L. An, Y. Ma, X. Yan, S. Wang, and Z. Wang, Transactions of Nonferrous Metals Society of China, 30, No. 4: 883 (2020); https://doi.org/10.1016/S1003-6326(20)65262-1
  107. F. Songur, E. Arslan, and B. Dikici, Surf. Coat. Technol., 434: 128202 (2022); https://doi.org/10.1016/j.surfcoat.2022.128202
  108. M.M. Student, I.B. Ivasenko, V.M. Posuvailo, H.H. Veselivs’ka, A.Y. Pokhmurs’kyi, Y.Y. Sirak, and V.M. Yus’kiv, Mater. Sci., 54: 899 (2019); https://doi.org/10.1007/s11003-019-00278-z
  109. M. Bembenek, T. Mandziy, I. Ivasenko, O. Berehulyak, R. Vorobel, Z. Slobodyan, and L. Ropyak, Sensors, 22, No. 19: 7600 (2022); https://doi.org/10.3390/s22197600
  110. I. Ivasenko, V. Posuvailo, H. Veselivska, and V. Vynar, Int. Sci. Tech. Conf. Comp. Sci. Inform. Technol., 2, 9321900: 50 (2020); https://doi.org/10.1109/CSIT49958.2020.9321900
  111. V.B. Kopei, O.R. Onysko, and V.G. Panchuk, J. Phys. Conf. Ser., 1426, No. 1: 012033 (2020); https://doi.org/10.1088/1742-6596/1426/1/012033
  112. Y.M. Kusyi and A.M. Kuk, J. Phys. Conf. Ser., 1426: 012034 (2020); https://doi.org/10.1088/1742-6596/1426/1/012034
  113. M. Kaseem, S. Fatimah, N. Nashrah, Y.G. Ko, Progress in Materials Science, 117: 100735 (2021); https://doi.org/10.1016/j.pmatsci.2020.100735
  114. M. Bembenek, P. Prysyazhnyuk, T. Shihab, R. Machnik, O. Ivanov, and L. Ropyak, Materials, 15, No.14: 5074 (2022); https://doi.org/10.3390/ma15145074
  115. I.M. Melnyk, T.M. Radchenko, and V.A. Tatarenko, Metallofiz. Noveishie Tekhnol., 32, No. 9: 1191 (2010) (in Ukrainian).
  116. T.M. Radchenko, O.S. Gatsenko, V.V. Lizunov, and V.A. Tatarenko, Prog. Phys. Met., 21, No. 4: 580 (2020); https://doi.org/10.15407/ufm.21.04.580
  117. T. Shihab, P. Prysyazhnyuk, I. Semyanyk, R. Anrusyshyn, O. Ivanov, L. Troshchuk, Manag. Syst. Prod. Eng., 28, No. 2: 84 (2020); https://doi.org/10.2478/mspe-2020-0013
  118. A.G. Solomenko, R.M. Balabai, T.M. Radchenko, and V.A. Tatarenko, Prog. Phys. Met., 23, No. 2: 147 (2022); https://doi.org/10.15407/ufm.23.02.147
  119. P. Prysyazhnyuk, L. Shlapak, I. Semyanyk, V. Kotsyubynsky, L. Troshchuk, S. Korniy, and V. Artym, East-Eur. J. Enterp. Technol., 6, No. 12: 28 (2020); https://doi.org/10.15587/1729-4061.2020.217281
  120. V. Pokhmurskii, H. Nykyforchyn, M. Student, M. Klapkiv, H. Pokhmurska, B. Wielage, T. Grund, A. Wank, Proc. Int. Thermal Spray Conf., 16: 998 (2007); https://doi.org/10.1007/s11666-007-9104-x
  121. M.M. Student, V.M. Posuvailo, H.H. Veselivs’ka, Y.Y. Sirak, and R.A. Yatsyuk, Mater. Sci., 53: 789 (2018); https://doi.org/10.1007/s11003-018-0137-8
  122. M. Shao, W. Wang, H. Yang, X. Zhang, and X. He, Coatings, 11, No. 11: 1288 (2021); https://doi.org/10.3390/coatings11111288
  123. A.H. Pakseresht, M. Saremi, H. Omidvar, and M. Alizadeh, Surf. Coat. Technol., 366: 338 (2019); https://doi.org/10.1016/j.surfcoat.2019.03.059
  124. A.M. Kamalan Kirubaharan and P. Kuppusami, Micro and Nano Technologies. Corrosion Protection at the Nanoscale (Ed. S. Rajendran) (Amsterdam: Elsevier: 2020), p. 295; https://doi.org/10.1016/B978-0-12-819359-4.00016-7
  125. V. Hutsaylyuk, M. Student, V. Posuvailo, O. Student, Y. Sirak, V. Hvozdets'kyi, P. Maruschak, and H. Veselivska, Vacuum, 179: 109514 (2020); https://doi.org/10.1016/j.vacuum.2020.109514
  126. B.-J. Wei, Y.-L. Cheng, Y.-Y. Liu, Z.-D. Zhu, and Y.-L. Cheng, Transactions of Nonferrous Metals Society of China, 31, 2287 (2021); https://doi.org/10.1016/S1003-6326(21)65655-8
  127. H. Barekatain and S.M. Mousavi Khoei, Surf. Coat. Technol., 384: 125339 (2020); https://doi.org/10.1016/j.surfcoat.2020.125339
  128. J. Zhang, Y. Fan, X. Zhao, R. Ma, A. Du, and X. Cao, Surf. Coat. Technol., 337: 141 (2018); https://doi.org/10.1016/j.surfcoat.2017.12.064
  129. A. López-Ortega, J.L. Arana, E. Rodríguez, and R. Bayón, Corrosion Sci., 143: 258 (2018); https://doi.org/10.1016/j.corsci.2018.08.001
  130. L. Lu, D. Shen, J. Zhang, and C. Guo, Applied Mechanics and Materials, 152–154: 40 (2012); https://doi.org/10.4028/www.scientific.net/AMM.152-154.40
  131. L. Lu, J. Zhang, D. Shen, L. Wu, G. Jiang, and L. Li, J. Alloys Compd., 512: 57 (2012); https://doi.org/10.1016/j.jallcom.2011.08.103
  132. J.H. Zhao, G.H. Zhao, T. Li, X. Liu, J.L. Li, and E. Han, Structure and properties of composite ceramic coatings on H13 steel by hot dipping aluminium and plasma electrolytic oxidation. Cailiao Rechuli Xuebao/Trans Mater. Heat Treat., 33: 129 (2012).
  133. W.C. Gu, G.H. Lv, H. Chen, G.L. Chen, W.R. Feng, G.L. Zhang, and S.Z. Yang, J. Alloys Compd., 430: 308 (2007); https://doi.org/10.1016/j.jallcom.2006.05.030
  134. Z. Wu, Y. Xia, G. Li, and F. Xu, Appl. Surf. Sci., 253: 8398 (2007); https://doi.org/10.1016/j.apsusc.2007.04.007
  135. W.C. Gu, D.J. Shen, Y.L. Wang, G.L. Chen, W.R. Feng, G.L. Zhang, S.H. Fan, C.Z. Liu, and S.Z. Yang, Appl. Surf. Sci., 252, No. 8: 2927 (2006); https://doi.org/10.1016/j.apsusc.2005.04.036
  136. B. Wielage, D. Meyer, H. Pokhmurska, G. Alisch, and T. Grund, Materialwissenschaft und Werkstofftechnik, 39: 920 (2008); https://doi.org/10.1002/mawe.200800407
  137. T. Lampke, D. Meyer, G. Alisch, D. Nickel, I. Scharf, L. Wagner, and U. Raab, Surf. Coat. Technol., 206, No. 7: 2012 (2011); https://doi.org/10.1016/j.surfcoat.2011.09.006
  138. T. Lampke, D. Meyer, G. Alisch, B. Wielage, H. Pokhmurska, M. Klapkiv, and M. Student, Materials Science, 46: 591 (2011); https://doi.org/10.1007/s11003-011-9328-2
  139. S. Durdu, S. L. Aktuğ, and K. Korkmaz, Surf. Coat. Technol., 236: 303 (2013); https://doi.org/10.1016/j.surfcoat.2013.10.004
  140. Z. Chen, K. Zhou, X. Lu, and Y. Lam, Acta Mechanica, 225: 431 (2014); https://doi.org/10.1007/s00707-013-0979-y
  141. B.N.J. Persson and M. Scaraggi, J. Chem. Phys., 141, No. 12: 124701 (2014); https://doi.org/10.1063/1.4895789
  142. G. Abadias, E. Chason, J. Keckes, M. Sebastiani, G.B. Thompson, E. Barthel, G.L. Doll, C.E. Murray, C.H. Stoessel, and L. Martinu, J. Vacuum Sci. Technol. A, 36, No. 2: 020801 (2018); https://doi.org/10.1116/1.5011790
  143. Ya.S. Pidstryhach, V.A. Lomakin, and Yu.M. Koliano, Thermoelasticity of Bodies of Inhomogeneous Structure (Moskva: Nauka: 1984) (in Russian).
  144. M. Dutkiewicz, T. Dalyak, I. Shatskyi, T. Venhrynyuk, and A. Velychkovych, Appl. Sci., 11, No. 22: 10676 (2021); https://doi.org/10.3390/app112210676
  145. J. Yang, Theory of Thermal Conductivity (Boston: Springer: 2004); https://doi.org/10.1007/0-387-26017-X_1
  146. E.M. Kartashov, Analytical Methods in the Theory of Thermal Conductivity of Solids (Moskva: Vysshaya Shkola: 1985) (in Russian).
  147. A.I. Lurie, Theory of Elasticity (Berlin: Springer: 2010)
  148. Ya.S. Pidstryhach, Yu.A. Chernukha, and N.I. Voitovich, Doklady AN UkrSSR, Ser. A, 5: 429 (1975).
  149. Ya.S. Pidstryhach, N.I. Voitovich, and Yu.A. Chernukha, Mathematical Methods and Physical-Mechanical Fields, 3: 15 (1976)
  150. Y.S. Podstrigach, Y.A. Chernykha, and N.I. Voitovich, Strength of Materials, 18: 686 (1986); https://doi.org/10.1007/BF01522787
  151. B.A. Boley and J.H. Weiner, Theory of Thermal Stresses (New York: Dover Publications: 2012).
  152. A. Bandura and O. Skaskiv, Rocky Mountain J. Math., 49, No. 4: 1063 (2019); https://doi.org/10.1216/RMJ-2019-49-4-1063
  153. A. Bandura and O. Skaskiv, Demonstration Math., 52, No. 1: 82 (2019); https://doi.org/10.1515/dema-2019-0008
  154. O. Posiko and M. Sheremeta, Integral Transforms Spec. Funct., 18, No. 4: 271 (2007); https://doi.org/10.1080/10652460600935387
  155. M.M. Sheremeta and A.O. Kuryliak, Mat. Stud., 50, No. 1: 22 (2018); https://doi.org/10.15330/ms.50.1.22-35
  156. H. Grauert, The Methods of the Theory of Functions of Several Complex Variables (Berlin–Heidelberg: Springer: 1991); https://doi.org/10.1007/978-3-642-76709-8_8
  157. B. Lepson, Proc. Sympos. Pure Math. 11: 298 (1968).
  158. V. Baksa, A. Bandura, and O. Skaskiv, Constr. Math. Anal., 3, No. 1: 9 (2020); https://doi.org/10.33205/CMA.650977
  159. M. German and P. Grinchuk, J. Eng. Phys. Thermophys., 75: 1301 (2002); https://doi.org/10.1023/A:1022150523156
  160. A.F. Chudnovsky, Thermophysical Characteristics of Dispersed Materials (Moskva: Fizmatgiz: 1962) (in Russian).
  161. P. Jadhav, A. Bongale, S. Kumar, D.Y. Pimenov, K. Giasin, and S. Wojciechowski, Materials, 15, No. 4: 1616 (2022); https://doi.org/10.3390/ma15041616
  162. I.S. Gradshtein and I.M. Ryzhik, Tables of Integrals, Series and Products (Elsevier: 2014); https://doi.org/10.1016/C2010-0-64839-5
  163. A.H. Chokshi and M.A. Meyers, Scr. Metall. Mater., 24, No. 4: 605 (1990); https://doi.org/10.1016/0956-716X(90)90209-Y
  164. A.V. Sergueeva, N.A. Mara, and A.K. Mukherjee, MRS Online Proceedings Library, 821: 336 (2004); https://doi.org/10.1557/PROC-821-P9.8
  165. A.A. Shirzadi, C. Zhang, M.Z. Mughal, and P. Xia, Metals, 12, No. 7: 1193 (2022); https://doi.org/10.3390/met12071193

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