Skip to main content
SpringerLink
Log in

Main Problems in the Creation of Thermal-Protection Systems Based on Structurally Heterogeneous Materials and the Methods of Their Solution

  • REVIEW
  • Published:
High Temperature Aims and scope

Abstract

The review summarizes the advances of Russian and international science in the development and improvement of the properties of carbon–carbon and carbon–ceramic composites, focusing on mechanical, oxidative, and ablative properties. The most in-demand methods at present to modify composite matrices and to apply protective coatings to obtain heterophase compositions based on ultra-high-temperature ceramics are considered. Analysis of the fracture mechanisms of widely used engineering solutions makes it possible to identify promising concepts for the coating architecture. The mathematical formulations of nonlinear heat-transfer problems considering various physicochemical phenomena that occur in structurally heterogeneous materials are presented. The attention is focused on the asymmetry effects, finite speed, and wave nature of the heat propagation within the heat transfer in anisotropic materials. The current methods to assess the stress–strain state of thermally loaded composites and the methods to calculate the effective properties of the composite properties are analyzed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. Yang, Y.Z., Yang, J.L., and Fang, D.N., Appl. Math. Mech. (Engl. Ed.), 2008, vol. 29, no. 1, p. 51.

  2. Sziroczak, D. and Smith, H., Prog. Aeronaut. Sci., 2016, vol. 84, p. 1929.

    Article  Google Scholar 

  3. Zhu., Y., Peng, W., Xu, R., and Jiand, P., Chin. J. Aeronaut., 2018, vol. 31, no. 10, p. 1929.

  4. Dong, Y., Wang, E., You, Y., et al., Energies, 2019, vol. 12, no. 240, p. 240.

    Article  Google Scholar 

  5. Kostikov, V.I. and Varenkov, A.N., Sverkhvysokotemperaturnye kompozitsionnye materialy (Ultrahigh-Temperature Composite Materials), Moscow: Intermet Inzh., 2003.

  6. Shchurik, A.G., Iskusstvennye uglerodnye materialy (Artificial Carbon Materials), Perm: Permsk. Gos. Univ., 2009.

  7. Shabalin, I.L., Ultra-high Temperature Materials I: Carbon (Graphene/Graphite) and Refractory Metals, Amsterdam: Springer, 2014.

    Book  Google Scholar 

  8. Scarponi, C., Carbon–carbon composites in aerospace engineering, in Advanced Composite Materials for Aerospace Engineering, Rana, S. and Fangueiro, R., Eds., New York: Woodhead, 2016, p. 385.

    Google Scholar 

  9. Astapov, A.N. and Terent’eva, V.S., Russ. J. Non-Ferrous Met., 2016, vol. 57, p. 157.

    Article  Google Scholar 

  10. Tang, S. and Hu, C., J. Mater. Sci. Technol., 2017, vol. 33, no. 2, p. 117.

    Article  Google Scholar 

  11. Jin, X., Fan, X., Lu, C., et al., J. Eur. Ceram. Soc., 2018, vol. 38, no. 1, p. 1.

    Article  Google Scholar 

  12. Kumar, V. and Kandasubramanian, B., Ind. Eng. Chem. Res., 2019, vol. 58, no. 51, p. 22663.

    Article  Google Scholar 

  13. Bouchez, M., Beyer, S., and Schmidt, S., Proc. 17th AIAA Int. Space Planes and Hypersonic Systems and Technologies Conf., San Francisco, 2011.

  14. Reimer, T., Kuhn, M., Gulhan, A., Esser, B., Sippel, M., and Foreest, A., Proc. 17th AIAA Int. Space Planes and Hypersonic Systems and Technologies Conf., San Francisco, 2011.

  15. Fialkov, A.S., Uglerod, mezhsloevye soedineniya i kompozity na ego osnove (Carbon, Interlayer Compounds and Composites Based on It), Moscow: Aspekt, 1997.

  16. Zhang, S., et al., Carbon Composites, Singapore: Springer, 2017, p. 531.

    Google Scholar 

  17. Sheehan, J.E., Buesking, K.W., and Sullivan, B.J., Ann. Rev. Mater. Sci., 1994, vol. 24, p. 19.

    Article  ADS  Google Scholar 

  18. Westwood, M.E., et al., J. Mater. Sci., 1996, vol. 31, no. 6, p. 1389.

    Article  ADS  Google Scholar 

  19. Windhorst, T. and Blount, G., Mater. Des., 1997, vol. 18, no. 1, p. 11.

    Article  Google Scholar 

  20. Oku, T., Carbon/carbon composites and their properties, in Carbon Alloys, Yasuda, E., et al., Oxford: Elsevier, 2003, p. 523.

  21. Vil’deman, V.E., Sokolkin, Yu.V., and Tashkinov, A.A., Mekhanika neuprugogo deformirovaniya i razrusheniya kompozitsionnykh materialov (Mechanics of Inelastic Deformation and Fracture of Composite Materials), Moscow: Fizmatlit, 1997.

  22. Aly-Hassan, M.S., et al., Carbon, 2003, vol. 41, no. 5, p. 1069.

    Article  Google Scholar 

  23. Vasil’ev, V.V., Mekhanika konstruktsii iz kompozitsionnykh materialov (Mechanics of Composite Structures), Moscow: Mashinostroenie, 1988, p. 272.

  24. Zhigun, I.G. and Polyakov, V.A., Mater. 6 Vsesoyuzn. s”ezda po teoreticheskoi i prikladnoi mekhanike (Proc. 6th All-Union Conf. on Theoretical and Applied Mechanics), Tashkent, 1986, p. 277.

  25. Mal’ko, D.B. and Ostrovskii, V.S., Mekh. Kompoz. Mater. Konstr., 1997, vol. 3, no. 4, p. 29.

    Google Scholar 

  26. Skoropanov, A.S., et al., Mekh. Kompoz. Mater., 1990, no. 1, p. 13.

  27. Sokolkin, Yu.V., Tashkinov, A.A., and Votinov, A.M., Tekhnologiya i proektirovanie uglerod-uglerodnykh kompozitov i konstruktsii (Technology and Design of Carbon–Carbon Composites and Structures), Moscow: Fizmatlit, 1996, p. 239.

  28. Vasil’ev V.V., and Egorchenkov, A.N., Mekh. Kompoz. Mater., 1989, vol. 3, p. 547.

    Google Scholar 

  29. Prokhorov, V.Yu., D’yakonov, A.Yu., and Kostogorova, O.Ya., Nadezhnost’ i kachestvo: Tr. Mezhdun. simp. (Reliability and Quality: Proc. Int. Symp.), Penza, 2006, vol. 2, p. 82.

  30. Manocha, L.M., Warrier, A., and Manocha, S., Proc. 5th Int. Conf. on High-Temperature Ceramic Matrix Composites, 2004, p. 217.

  31. Zhang, S., Li, H., and Sun, J., J. Xi’an Jiaotong Univ., 2001, vol. 35, no. 11, p. 1157.

    Google Scholar 

  32. Tatarnikov, O.V., Mater. 4-go Mezhdun. simp. “Dinamicheskie i tekhnologicheskie problemy mekhaniki konstruktsii i sploshnykh sred” (Proc. 4th Int. Symp. on Dynamic and Technological Problems of Mechanics of Structures and Continuous Media), Yaropolets, 1998, p. 62.

  33. Aleksyuk, M.M., Probl. Prochn., 1996, no. 5, p. 77.

  34. Jain, P.K., Bahl, O.P., and Manocha, L.M., SAMPE Q., 1992, vol. 23, no. 3, p. 43.

    Google Scholar 

  35. Tanabe, Y. and Yasuda, E., Rep. Res. Lab. Eng. Mater., 1992, vol. 17, p. 137.

    Google Scholar 

  36. Joo Hyeok-Jong, High Temp.—High Pressure, 1990, vol. 22, no. 6, p. 649.

    Google Scholar 

  37. Zaldivar, R.J., Rellick, G.S., and Yang, J.M., Proc., 20th Bienn. Conf. Carbon, Santa Barbara, 1991, p. 400.

  38. Dariel, M.S., et al., Res. Lab. Annu. Rep. Israel At. Energy Commun., 1988, p. 93.

    Google Scholar 

  39. Yasuda, E., et al., High Temp.—High Pressure, 1990, vol. 22, no. 3, p. 329.

    Google Scholar 

  40. Orlov, L.G., et al., in Granitsa razdela, prochnost’ i razrushenie kompozitsionnykh materialov (Interface, Strength, and Fracture of Composite Materials), Leningrad: Fiz.-Tekh. Inst., 1989, p. 113.

  41. Oh, S.-M. and Lee, J.-Y., Carbon, 1988, vol. 26, no. 6, p. 769.

    Article  Google Scholar 

  42. Kaluderovic, B. and Lausevic, Z., Chem. Ind., 1989, vol. 43, no. 10, p. 367.

    Google Scholar 

  43. Thomas, C.R. and Walker, E.J., Mater. Aerosp. Proc., London, 1986, vol. 1, p. 138.

  44. Goto, K., et al., J. Am. Ceram. Soc., 2003, vol. 12, p. 2129.

    Article  Google Scholar 

  45. Dzyuba, V.S. and Oksiyuk, S.V., Probl. Prochn., 2005, no. 1, p. 136.

  46. Sato, S., et al., J. Jpn. Soc. Strength Fract. Mater., 1986, vol. 3, p. 99.

    Google Scholar 

  47. Gu, Z., Qunyao, G., and Weibo, Z., J. Compos. Mater., 1989, vol. 23, no. 10, p. 988.

    Article  ADS  Google Scholar 

  48. Negovskii, A.N., et al., Probl. Prochn., 1999, no. 3, p. 130.

  49. Dzyuba, V.S., Vysotskii, A.V., and Zubik, S.V., Probl. Prochn., 1994, no. 9, p. 86.

  50. Rehmer, B., et al., Proc. 5th Int. Conf. on High-Temperature Ceramic Matrix Composites (HTCMC-5), 2004, p. 575.

  51. Yasuda, J., Noguchi, Y., Hirokawa, T., and Tanamura, T., Reinf. Plast., 1988, vol. 34, no. 1, p. 10.

    Google Scholar 

  52. Oku, T., Ota, S., and Tada, M., Proc., 20th Bienn. Conf. Carbon, Santa Barbara, 1991, p. 608.

  53. Kanari, M., et al., Carbon, 1997, vol. 35, nos. 10–11, p. 1429.

    Article  Google Scholar 

  54. Oku, T., et al., An evaluation of mechanical properties of carbon materials by hardness test, Ibaraki daigaku kogakubu kenkyu hokoku, 1992, vol. 40, p. 205.

  55. Kline, R.A., et al., Proc. IEEE Ultrason. Symp., Montreal, 1989, vol. 2, p. 1171.

  56. Yudin, V.E., et al., in Granitsa razdela, prochnost’ i razrushenie kompozitsionnykh materialov (Interface, Strength, and Fracture of Composite Materials), Leningrad: Fiz.-Tekh. Inst., 1989, p. 156.

  57. Hosten, B., Tittmann, B.R., and Abdel-Gawad, M., Proc. IEEE Ultrason. Symp., Williamsburg, 1986, p. 1061.

  58. Deom, A., et al., Mater. Sci. Eng., B, 1990, vol. 5, no. 2, p. 135.

    Article  Google Scholar 

  59. Zhao, J., Din, K., and Wei, J., ICCM and ECCM: Proc. 6th Int. Conf. Compos. Mater. Combined 2nd Eur. Conf. Compos. Mater., London, 1987, vol. 4, p. 394.

  60. Oliver, W.C. and Pharr, G.M., J. Mater. Res., 1992, vol. 7, p. 1564.

    Article  ADS  Google Scholar 

  61. Golovin, Yu.I., Phys. Solid State, 2008, vol. 50, no. 12, p. 2205.

    Article  ADS  Google Scholar 

  62. Molev, G.V. and Mirzabekyants, N.S., Khim. Tverd. Topliva, 1998, vol. 1, p. 89.

    Google Scholar 

  63. Astapov, A.N., Int. J. Nanomech. Sci. Technol., 2014, vol. 5, no. 4, p. 267.

    Article  Google Scholar 

  64. Arai, Y., et al., Ceram. Int., 2019, vol. 45, no. 12, p. 14481.

    Article  Google Scholar 

  65. Langlais, F. and Vignoles, G.L., Chemical vapor infiltration processing of ceramic matrix composites, in Comprehensive Composite Materials II, Beaumont P.W.R. and Zweben, C.H., Eds., Oxford: Elsevier, 2018, p. 86.

    Google Scholar 

  66. Fahrenholtz, W.G., et al., J. Am. Ceram. Soc., 2007, vol. 90, no. 5, p. 1347.

    Article  Google Scholar 

  67. Naslain, R., et al., The CVI-process: State of the art and perspective, in Mechanical Properties and Performance of Engineering Ceramics II: Ceramic Engineering and Science Proceedings, New York: Wiley, 2008, p. 373.

    Google Scholar 

  68. Xie, C., et al., J. Am. Ceram. Soc., 2012, vol. 95, no. 3, p. 866.

    Google Scholar 

  69. Suresh Kumar, et al., Ceram. Int., 2017, vol. 43, no. 3, p. 3414.

    Article  Google Scholar 

  70. Motz., G. and Schmidt, S., The pip-process: precursor properties and applications, in Ceramic Matrix Composites, New York: Wiley, 2008, p. 165.

  71. Paul, A., Binner, J., and Vaidhyanathan, B., UHTC composites for hypersonic applications, in Ultra-High Temperature Ceramics, New York: Wiley, 2014, part 7, p. 144.

  72. Nannetti, C.A., et al., J. Am. Ceram. Soc., 2004, vol. 87, no. 7, p. 1205.

    Article  Google Scholar 

  73. Magnant, J., Pailer, R., le Petitcorps, Y., et al., J. Eur. Ceram. Soc., 2013, vol. 33, no. 1, p. 181.

    Article  Google Scholar 

  74. Yin, J., et al., Solid State Sci., 2011, vol. 13, no. 11, p. 2055.

    Article  ADS  Google Scholar 

  75. Shen, X.-T., et al., Corros. Sci., 2011, vol. 53, no. 1, p. 105.

    Article  Google Scholar 

  76. Zhu, Y., et al., Mater. Charact., 2008, vol. 59, no. 7, p. 975.

    Article  Google Scholar 

  77. Liu, L., et al., Corros. Sci., 2013, vol. 74, p. 159.

    Article  ADS  Google Scholar 

  78. Liu, L., et al., J. Mater. Sci. Technol., 2015, vol. 31, no. 4, p. 345.

    Article  Google Scholar 

  79. Xie, J., et al., Ceram. Int., 2013, vol. 39, no. 4, p. 4171.

    Article  Google Scholar 

  80. Li, K., et al., J. Mater. Sci. Technol., 2015, vol. 31, no. 1, p. 77.

    Article  Google Scholar 

  81. Yan, C., et al., Corros. Sci., 2014, vol. 86, p. 131.

    Article  Google Scholar 

  82. Li, C., et al., Corros. Sci., 2014, vol. 85, p. 160.

    Article  ADS  Google Scholar 

  83. Li, C., et al., Corros. Sci., 2013, vol. 75, p. 169.

    Article  Google Scholar 

  84. Li, S.-P., et al., Mater. Sci. Eng., A, 2009, vol. 517, no. 1, p. 61.

    Article  Google Scholar 

  85. Xue, L., et al., Corros. Sci., 2015, vol. 94, p. 165.

    Article  Google Scholar 

  86. Wang, Y., et al., Ceram. Int., 2011, vol. 37, no. 4, p. 1277.

    Article  Google Scholar 

  87. Chen, S., et al., Mater. Des., 2014, vol. 58, p. 570.

    Article  Google Scholar 

  88. Zhu, Y., et al., Mater. Lett., 2013, vol. 108, p. 204.

    Article  Google Scholar 

  89. Shen, X., et al., Carbon, 2010, vol. 48, no. 2, p. 344.

    Article  Google Scholar 

  90. Djugum, R. and Sharp, K., Carbon, 2017, vol. 115, p. 105.

    Article  Google Scholar 

  91. Li, K., et al., J. Mater. Sci. Technol., 2017, vol. 33, no. 1, p. 71.

    Article  Google Scholar 

  92. Yan, C., Liu, R., Zhang, C., et al., J. Eur. Ceram. Soc., 2017, vol. 37, no. 6, p. 2343.

    Article  Google Scholar 

  93. Feng, B., et al., Corros. Sci., 2014, vol. 82, p. 27.

    Article  Google Scholar 

  94. Li, K., et al., Carbon, 2013, vol. 57, p. 161.

    Article  Google Scholar 

  95. Li, Q., et al., Mater. Sci. Eng., B, 2013, vol. 178, no. 18, p. 1186.

    Article  Google Scholar 

  96. Li, Q., et al., J. Am. Ceram. Soc., 2012, vol. 95, no. 4, p. 1216.

    Article  Google Scholar 

  97. Yan, C., et al., Mater. Sci. Eng., A, 2014, vol. 591, p. 105.

    Article  Google Scholar 

  98. Li, J., et al., Trans. Nonferr. Metal. Soc., 2016, vol. 26, no. 10, p. 2653.

    ADS  Google Scholar 

  99. Jia, Y., et al., Mater. Des., 2017, vol. 129, p. 15.

    Article  Google Scholar 

  100. Li, H.-J., et al., Corros. Sci., 2013, vol. 74, p. 265.

    Article  Google Scholar 

  101. Liu, L., et al., Corros. Sci., 2013, vol. 67, p. 60.

    Article  Google Scholar 

  102. Liu, L., et al., Ceram. Int., 2014, vol. 40, no. 1, p. 541.

    Article  Google Scholar 

  103. Huang, D., et al., Corros. Sci., 2015, vol. 98, p. 551.

    Article  ADS  Google Scholar 

  104. Li, Q., et al., Ceram. Int., 2013, vol. 39, no. 5, p. 5937.

    Article  Google Scholar 

  105. Yang, X., et al., Ceram. Int., 2016, vol. 42, no. 16, p. 19195.

    Article  Google Scholar 

  106. Uhlmann, F., Wilhelmi, C., Schmidt-Wimmer, S., et al., J. Eur. Ceram. Soc., 2017, vol. 37, no. 5, p. 1955.

    Article  Google Scholar 

  107. Wang, Y., et al., Ceram. Int., 2012, vol. 38, no. 5, p. 4337.

    Article  Google Scholar 

  108. Li, Z., et al., Ceram. Int., 2012, vol. 38, no. 4, p. 3419.

    Article  Google Scholar 

  109. Li, Z., et al., Ceram. Int., 2013, vol. 39, no. 7, p. 8173.

    Article  Google Scholar 

  110. Li, Z., et al., Corros. Sci., 2012, vol. 58, p. 12.

    Article  Google Scholar 

  111. Chang, Y., et al., Ceram. Int., 2016, vol. 42, no. 15, p. 16906.

    Article  Google Scholar 

  112. Phylis, M., Monteverde, F., and Sigalas, I., J. Eur. Ceram. Soc., 2017, vol. 37, no. 10, p. 3227.

    Article  Google Scholar 

  113. Zeng, Y., Wang, D., Xiong, X., et al., J. Eur. Ceram. Soc., 2020, vol. 40, no. 3, p. 651.

    Article  Google Scholar 

  114. Cao, L., et al., Ceram. Int., 2016, vol. 42, no. 10, p. 12289.

    Article  Google Scholar 

  115. Cao, L., et al., J. Alloys Compd., 2017, vol. 703, p. 45.

    Article  Google Scholar 

  116. Paul, A., et al., J. Eur. Ceram. Soc., 2013, vol. 33, no. 2, p. 423.

    Article  Google Scholar 

  117. Chen, S., et al., Composites, Part B, 2014, vol. 60, p. 222.

    Article  Google Scholar 

  118. Astapov, A.N., Lifanov, I.P., et al., Mater. XXV Mezhdun. simp. “Dinamicheskie i tekhnologicheskie problemy mekhaniki konstruktsii i sploshnykh sred” (Mater. XXV Int. Symp. on Dynamic and Technological Problems of Mechanics of Structures and Continuous Media), 2019, vol. 1, p. 16.

  119. Corral, E.L. and Walker, L.S., J. Eur. Ceram. Soc., 2010, vol. 30, p. 2357.

    Article  Google Scholar 

  120. Jayaseelan, D.D., et al., J. Eur. Ceram. Soc., 2011, vol. 31, no. 3, p. 361.

    Article  Google Scholar 

  121. Yan, Ch., et al., RSC Adv., 2015, no. 46, p. 36520.

  122. Kannan, R. and Rangaraj, L., Ceram. Int., 2017, vol. 43, no. 2, p. 2625.

    Article  Google Scholar 

  123. Opeka, M.M., Talmy, I.G., and Zaykoski, J.A., J. Mater. Sci., 2004, vol. 39, no. 19, p. 5887.

    Article  ADS  Google Scholar 

  124. Heuer, A.H. and Lou, V.L.K., J. Am. Ceram. Soc., 1990, vol. 73, no. 10, p. 2789.

    Article  Google Scholar 

  125. Fahrenholtz, W.G., J. Am. Ceram. Soc., 2005, vol. 88, no. 12, p. 3509.

    Article  Google Scholar 

  126. Shabalin, I.L., Ultra-High Temperature Materials II: Refractory Carbides I (Ta, Hf, Nb and Zr Carbides), Amsterdam: Springer, 2019.

    Book  Google Scholar 

  127. Balat-Pichelin, M., et al., Proc. 6th Eur. Symp. Aerothermodynamics for Space Vehicles, Versailles, 2009, vol. 659.

  128. Balat-Pichelin, M., Passarelli, M., and Vesel, A., Mater. Chem. Phys., 2010, vol. 123, no. 1, p. 40.

    Article  Google Scholar 

  129. Vaganov, A.V., et al., AIP Conf. Proc., 2016, vol. 1770, no. 1, 030097.

    Article  Google Scholar 

  130. Kablov, E.N., Zhestkov, B.E., Grashchenkov, D.V., et al., High Temp., 2017, vol. 55, no. 6, p. 873.

    Article  Google Scholar 

  131. Appen, A.A., Temperaturoustoichivye neorganicheskie pokrytiya (Temperature Resistant Inorganic Coatings), Leningrad: Khimiya, 1976.

  132. Sazonova, M.V., Ban’kovskaya, I.B., et al., Neorg. Mater., 1995, vol. 31, no. 8, p. 1072.

    Google Scholar 

  133. Ban’kovskaya, I.B. and Kolovertnov, D.V., Glass Phys. Chem., 2017, vol. 43, no. 2, p. 125.

    Article  Google Scholar 

  134. Kiryukhantsev-Korneev, Ph.V., Iatsyuk, I.V., Shvindina, N.V., et al., Corros. Sci., 2017, vol. 123, p. 319.

    Article  Google Scholar 

  135. Kiryukhantsev-Korneev, Ph.V. and Potanin, A.Y., Russ. J. Non-Ferrous Met., 2018, vol. 59, no. 6, p. 698.

    Article  Google Scholar 

  136. Terentieva, V.S. and Astapov, A.N., Russ. J. Non-Ferrous Met., 2018, vol. 59, no. 6, p. 709.

    Article  Google Scholar 

  137. Astapov, A.N. and Rabinskiy, L.N., Solid State Phenom., 2017, vol. 269, p. 14.

    Article  Google Scholar 

  138. Yurishcheva, A.A., et al., Key Eng. Mater., 2018, vol. 771, p. 103.

    Article  Google Scholar 

  139. Lifanov, I.P., Yurishcheva, A.A., and Astapov, A.N., Russ. Eng. Res., 2019, vol. 39, no. 9, p. 804.

    Article  Google Scholar 

  140. Huang, J.-F., et al., Carbon, 2004, vol. 42, no. 8, p. 1517.

    Article  Google Scholar 

  141. Wang, Y.J., et al., Appl. Surf. Sci., 2011, vol. 257, no. 10, p. 4760.

    Article  ADS  Google Scholar 

  142. Wang, Y., et al., Surf. Coat. Technol., 2012, vol. 206, p. 3883.

    Article  ADS  Google Scholar 

  143. Liu, Q., et al., J. Am. Ceram. Soc., 2010, vol. 93, p. 3990.

    Article  Google Scholar 

  144. Wu, H., et al., J. Eur. Ceram. Soc., 2010, vol. 30, no. 15, p. 3267.

    Article  Google Scholar 

  145. Wang, Y.-J., et al., Ceram. Int., 2013, vol. 39, no. 1, p. 359.

    Article  Google Scholar 

  146. Wu, H., et al., J. Therm. Spray Technol., 2011, vol. 20, p. 1286.

    Article  ADS  Google Scholar 

  147. Yang, Y., et al., Ceram. Int., 2016, vol. 42, no. 4, p. 4768.

    Article  Google Scholar 

  148. Yang, Y., et al., Ceram. Int., 2017, vol. 43, no. 1, p. 1495.

    Article  Google Scholar 

  149. Yang, Y., et al., J. Mater. Sci. Technol., 2017, vol. 33, no. 10, p. 1195.

    Article  Google Scholar 

  150. Yang, Y., et al., J. Ceram. Sci. Technol., 2015, vol. 7, no. 4, p. 379.

    Google Scholar 

  151. Pan, X., et al., Corros. Sci., 2020, vol. 170, 108645.

    Article  Google Scholar 

  152. Liu, T., et al., Corros. Sci., 2018, vol. 145, p. 239.

    Article  Google Scholar 

  153. Wang, P., et al., J. Alloys Compd., 2017, vol. 722, p. 69.

    Article  Google Scholar 

  154. Pan, X., et al., Corros. Sci., 2020, vol. 168, 108560.

    Article  Google Scholar 

  155. Jia, Y., et al., Corros. Sci., 2016, vol. 104, p. 61.

    Article  Google Scholar 

  156. Jia, Y., et al., Ceram. Int., 2017, vol. 43, no. 4, p. 3601.

    Article  Google Scholar 

  157. Jia, Y., et al., Ceram. Int., 2016, vol. 42, no. 12, p. 14236.

    Article  Google Scholar 

  158. Wang, S., et al., Surf. Coat. Technol., 2016, vol. 302, p. 383.

    Article  Google Scholar 

  159. Astapov, A.N., et al., Ceram. Int., 2019, vol. 45, no. 5, p. 6392.

    Article  Google Scholar 

  160. Wang, L., et al., Surf. Eng., 2016, vol. 32, no. 7, p. 508.

    Article  Google Scholar 

  161. Kaiser, A., Lobert, M., and Telle, R., J. Eur. Ceram. Soc., 2008, vol. 28, no. 11, p. 2199.

    Article  Google Scholar 

  162. Jia, Y., et al., Ceram. Int., 2017, vol. 43, no. 4, p. 3601.

    Article  Google Scholar 

  163. Zhang, Y., et al., Surf. Coat. Technol., 2016, vol. 300, p. 1.

    Article  Google Scholar 

  164. Yao, X., et al., J. Mater. Sci. Technol., 2014, vol. 30, no. 2, p. 123.

    Article  Google Scholar 

  165. Ren, X., et al., J. Eur. Ceram. Soc., 2013, vol. 33, no. 15, p. 2953.

    Article  Google Scholar 

  166. Feng, T., et al., J. Alloys Compd., 2016, vol. 662, p. 302.

    Article  Google Scholar 

  167. Ren, X., et al., Surf. Coat. Technol., 2013, vol. 232, p. 821.

    Article  Google Scholar 

  168. Jia, Y., et al., Surf. Coat. Technol., 2017, vol. 309, p. 545.

    Article  Google Scholar 

  169. Zou, B., et al., J. Eur. Ceram. Soc., 2015, vol. 35, no. 7, p. 2017.

    Article  Google Scholar 

  170. Feng, T., et al., Corros. Sci., 2013, vol. 67, p. 292.

    Article  Google Scholar 

  171. Tkachenko, L.A., Shaulov, A.Yu., and Berlin, A.A., Inorg. Mater., 2012, vol. 48, no. 3, p. 213.

    Article  Google Scholar 

  172. Yang, X., Chen, Z.-H., and Feng, C., J. Asian Ceram. Soc., 2014, vol. 2, no. 4, p. 305.

    Article  Google Scholar 

  173. Astapov, A.N., Lifanov, I.P., and Rabinskiy, L.N., High Temp., 2019, vol. 57, no. 5, p. 744.

    Article  Google Scholar 

  174. Carney, C.M. and Key, T.S., in Developments in Strategic Materials and Computational Design, Proc. 38th Int. Conf. on Advanced Ceramics and Composites (ICACC), Daytona Beach, FL: Am. Ceram. Soc., 2015, p. 261.

  175. Terauds, K., PhD Thesis, Boulder: Univ. Colorado, 2014.

  176. Potanin, A.Yu., et al., Corros. Sci., 2019, vol. 158, 108074.

    Article  Google Scholar 

  177. Silvestroni, L., et al., Acta Mater., 2018, vol. 151, p. 216.

    Article  ADS  Google Scholar 

  178. Guo, W.-M. and Zhang, G.-J., J. Eur. Ceram. Soc., 2010, vol. 30, no. 11, p. 2387.

    Article  Google Scholar 

  179. Gao, B., et al., Appl. Catal., A, 2010, vol. 375, no. 1, p. 107.

  180. Oluwabi, A.T., et al., Proc. 17th Baltic Polymer Symp., Tallinn: Tallinn Univ. Technol., Innovations & Business, 2017; Proc. Estonian Acad. Sci., 2018, vol. 67, no. 2, p. 147.

  181. Gild, J., et al., Sci. Rep., 2016, vol. 6, p. 37946.

    Article  ADS  Google Scholar 

  182. Mayrhofer, P.H., et al., Scr. Mater., 2018, vol. 149, p. 93.

    Article  Google Scholar 

  183. Jiang, Y., et al., Appl. Surf. Sci., 2018, vol. 459, no. 30, p. 527.

    Article  ADS  Google Scholar 

  184. Lipke, D.W., et al., Corros. Sci., 2014, vol. 80, p. 402.

    Article  Google Scholar 

  185. Wang, H., et al., Ceram. Int., 2020, vol. 46, no. 8. Pt. A, p. 11160.

  186. Shan, J., et al., Ceram. Int., 2020, vol. 46, no. 10, p. 15104.

    Article  Google Scholar 

  187. Liu, D., et al., J. Eur. Ceram. Soc., 2020, vol. 40, no. 8, p. 2746.

    Article  Google Scholar 

  188. Gild, J., et al., J. Materiomics, 2019, vol. 5, no. 3, p. 337.

    Article  Google Scholar 

  189. Huang, P.-K. and Yeh, J.-W., J. Phys. D: Appl. Phys., 2009, vol. 42, no. 11, 115401.

    Article  ADS  Google Scholar 

  190. Shen, W.J., et al., J. Electrochem. Soc., 2013, vol. 160, no. 11, p. 531.

    Article  Google Scholar 

  191. Zeng, Y., et al., Nat. Commun., 2017, vol. 8, p. 15836.

    Article  ADS  Google Scholar 

  192. Alyamovskii, S.I., Zainulin, Yu.G., and Shveikin, G.P., Oksikarbidy i oksinitridy metallov IVA i VA podgrupp (Oxycarbides and Oxynitrides of IVA and VA Subgroup Metals), Moscow: Nauka, 1981.

  193. Wang, Y.-L., et al., Corros. Sci., 2012, vol. 61, p. 156.

    Article  Google Scholar 

  194. Xu, J., et al., Corros. Sci., 2018, vol. 132, p. 161.

    Article  ADS  Google Scholar 

  195. Gasparrini, C., et al., J. Am. Ceram. Soc., 2018, vol. 101, no. 6, p. 2638.

    Article  Google Scholar 

  196. Wu, W., et al., Appl. Surf. Sci., 2011, vol. 257, no. 16, p. 7295.

    Article  ADS  Google Scholar 

  197. Zhu, L., Bai, Sh., Zhang, H., Ye, Y, and Tong, Y., Phys. Proc., 2013, vol. 50, p. 238.

    Article  ADS  Google Scholar 

  198. Baklanova, N.I., Lozanov, V.V.,Kul’kov, A.A., et al., Inorg. Mater., 2019, vol. 55, no. 3, p. 231.

    Article  Google Scholar 

  199. Formalev, V.F. and Kolesnik, S.A.,Matematicheskoe modelirovanie sopryazhennogo teploperenosa mezhdu vyazkimi gazodinamicheskimi techeniyami i anizotropnymi telami (Mathematical Simulation of Conjugate Heat Transfer between Viscous Gas-Dynamic Flows and Anisotropic Bodies), Moscow: URSS, 2019.

  200. Formalev, V.F., Teploperenos v anizotropnykh tverdykh telakh (Heat Transfer in Anisotropic Solids), Moscow: Fizmatlit, 2015.

  201. Roberts, N.A. and Walker, D.G., Int. J. Therm. Sci., 2011, vol. 50, p. 648.

    Article  Google Scholar 

  202. Wehmeyer, G., et al., Appl. Phys. Rev., 2017, vol. 4, 041304.

    Article  ADS  Google Scholar 

  203. Walker, D.G., Proc. of the Joint ASME, ISHMT Heat Transfer Conf. IIT, Guwahati, India, 2006.

  204. Lo, W., Wang, B., and Li, B., J. Phys. Soc. Jpn., 2008, vol. 77, 054402.

    Article  ADS  Google Scholar 

  205. Cuansing, E.C. and Wang, J.C., Phys. Rev. B: Condens. Matter Mater. Phys., 2010, vol. 81, 052302.

    Article  ADS  Google Scholar 

  206. Starr, C., J. Appl. Phys., 1935, vol. 7, p. 15.

    ADS  Google Scholar 

  207. dos Santos Bernardes, M.A., US Patent 2009/0194263, 2009.

  208. dos Santos Bernardes, M.A., Thermal Conductivity 30: Thermal Expansion 18: Joint Conf., Pittsburgh: DEStech, 2010, p. 354.

  209. dos Santos Bernardes, M.A., Int. J. Heat Mass Transfer, 2014, vol. 73, p. 354.

    Article  Google Scholar 

  210. Kobayashi, W., Teraoka, Y., and Terasaki, I., Appl. Phys. Lett., 2009, vol. 95, 171905.

    Article  ADS  Google Scholar 

  211. Rogolino, P. and Cimmelli, V.A., Math. Comput. Simul., 2020, vol. 176, p. 279.

    Article  Google Scholar 

  212. Maldovan, M., Nature, 2013, vol. 503, p. 209.

    Article  ADS  Google Scholar 

  213. Carlomagno, I., Cimmelli, V., and Jou, D., Phys. E (Amsterdam, Neth.), 2017, vol. 90, p. 149.

    Google Scholar 

  214. Jou, D., Carlomagno, I., and Cimmelli, V.A., Phys. E (Amsterdam, Neth.), 2015, vol. 73, p. 242.

    Google Scholar 

  215. Jou, D., Carlomagno, I., and Cimmelli, V.A., Phys. Lett. A, 2016, vol. 380, p. 1824.

    Article  ADS  Google Scholar 

  216. Cooper, M.Q., Mikic, B., and Yovanovich, M.M., Int. J. Heat Mass Transfer, 1969, vol. 12, p. 279.

    Article  Google Scholar 

  217. Chumak, K. and Martynyak, R., Int. J. Heat Mass Transfer, 2012, vol. 55, p. 5603.

    Article  Google Scholar 

  218. Chang, C.W., et al., Science, 2006, vol. 314, p. 1121.

    Article  ADS  Google Scholar 

  219. Zhao, J., et al., Appl. Therm. Eng., 2020, vol. 176, 115410.

    Article  Google Scholar 

  220. Sadat, H. and le Dez, V., Mech. Res. Commun., 2016, vol. 76, p. 48.

    Article  Google Scholar 

  221. Pereira, E., Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2011, vol. 83, 031106.

    Article  ADS  Google Scholar 

  222. Wang, J., Pereira, E., and Casati, G., Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2012, vol. 86, 010101.

    Article  Google Scholar 

  223. Shih, T.M., et al., Sci. Rep., 2015, vol. 5, no. 1, p. 12677.

    Article  ADS  Google Scholar 

  224. Zhang, Z., et al., Appl. Therm. Eng., 2016, vol. 102, p. 1075.

    Article  ADS  Google Scholar 

  225. Yang, N., Zheng, G., and Li, B., Appl. Phys. Lett., 2008, vol. 93, 243111.

    Article  ADS  Google Scholar 

  226. Sawaki, D., et al., Appl. Phys. Lett., 2011, vol. 98, 081915.

    Article  ADS  Google Scholar 

  227. Majumdar, A. and Reddy, P., Appl. Phys. Lett., 2004, vol. 84, no. 23, p. 4768.

    Article  ADS  Google Scholar 

  228. Terraneo, M., Peyrard, M., and Casati, G., Phys. Rev. Lett., 2002, vol. 88, no. 9, p. 4302.

    Article  Google Scholar 

  229. Li, B., Lan, J., and Wang, L., Phys. Rev. Lett., 2005, vol. 95, 104302.

    Article  ADS  Google Scholar 

  230. Hu, B., Yang, L., and Zhang, Y., Phys. Rev. Lett., 2006, vol. 97, 124302.

    Article  ADS  Google Scholar 

  231. Li, B., Wang, L., and Casati, G., Phys. Rev. Lett., 2004, vol. 93, 184301.

    Article  ADS  Google Scholar 

  232. Yang, N., et al., Phys. Rev. B: Condens. Matter Mater. Phys., 2007, vol. 76, 020301.

    Article  ADS  Google Scholar 

  233. Zhang, C., Guo, Z., and Chen, S., Int. J. Heat Mass Transfer, 2020, vol. 153, 119665.

    Article  Google Scholar 

  234. Sgouros, A.P., et al., Int. J. Heat Mass Transfer, 2019, vol. 140, p. 579.

    Article  Google Scholar 

  235. Criado-Sancho, M., et al., Phys. Lett. A, 2012, vol. 376, no. 19, p. 1641.

    Article  ADS  Google Scholar 

  236. Criado-Sancho, M., Alvarez, F.X., and Jou, D., J. Appl. Phys., 2013, vol. 114, 053512.

    Article  ADS  Google Scholar 

  237. Yosefi, F., Khoeini, F., and Rajabpour, A., Int. J. Heat Mass Transfer, 2020, vol. 146, 118884.

    Article  Google Scholar 

  238. Cao, H.Y., Xiang, H., and Gong, X.G., Solid State Commun., 2012, vol. 152, p. 1807.

    Article  ADS  Google Scholar 

  239. Olatuni-Ojo, A., Boetcher, S.K.S., and Cundari, T.R., Comput. Mater. Sci., 2012, vol. 54, p. 329.

    Article  Google Scholar 

  240. Carlomagno, I., Cimmelli, V.A., and Jou, D., Phys. B (Amsterdam, Neth.), 2016, vol. 481, p. 244.

    Google Scholar 

  241. Maxwell, J.C., Philos. Trans. R. Soc. London, 1867, vol. 157, p. 49.

    Article  ADS  Google Scholar 

  242. Nernst, W., Die Theoretische Gründlagen des Warmestatzes, Halle: Knapp, 1917.

    Google Scholar 

  243. Onsager, L., Phys. Rev., 1931, vol. 37, p. 405.

    Article  ADS  Google Scholar 

  244. Landau, L., J. Phys., 1941, vol. 5, p. 71.

    Google Scholar 

  245. Tisza, L., C. R. Acad. Sci., 1938, vol. 207, no. 22, p. 1035.

    Google Scholar 

  246. Peshkov, V., J. Phys., 1944, vol. 8, p. 381.

    Google Scholar 

  247. Band, W. and Meyer, L., Phys. Rev., 1948, vol. 73, p. 226.

    Article  ADS  Google Scholar 

  248. Osborne, D.T.V., Propagation of second sound below 1k, Low Temp. Phys. NBS (US) Circular, 1950, vol. 519.

    Google Scholar 

  249. Peshkov, V., Int. Conf. in Fund. Particles and Low Temperatures. Cavendish Laboratory, Cambridge: Taylor & Francis, 1946.

  250. Joseph, D.T.D. and Preziosi, L., Rev. Mod. Phys., 1989, vol. 61, p. 41.

    Article  ADS  Google Scholar 

  251. Cattaneo, C., Atti del Semin. Mat. Fiz., Modena: Univ. Modena, 1948, vol. 3, p. 3.

    Google Scholar 

  252. Grad, H., Handbuch der physic, Flügge, S., Ed., Berlin: Springer, 1958, vol. 12.

    Google Scholar 

  253. Bubnov, V.A., Int. J. Heat Mass Transfer, 1974, vol. 19, p. 175.

    Article  ADS  Google Scholar 

  254. Vernotte, P., C. R. Acad. Sci., 1958, vol. 246, p. 3154.

    Google Scholar 

  255. Vernotte, P., C. R. Acad. Sci., 1958, vol. 247, p. 2103.

    MathSciNet  Google Scholar 

  256. Morse, P.M. and Feschbach, H., Methods of Theoretical Physics, New York: McGraw Hill, 1953, vol. 1.

    Google Scholar 

  257. Goldstein, S., Q. J. Mech. Appl. Math., 1951, vol. 4, no. 2, p. 129.

    Article  Google Scholar 

  258. Kaliski, S., Bull. Acad. Pol. Sci., 1965, vol. 4, no. 13, p. 211.

    Google Scholar 

  259. Guyer, R.A. and Krumhansl, J.A., Phys. Rev., 1964, vol. 133, p. A1411.

    Article  ADS  Google Scholar 

  260. Guyer, R.A. and Krumhansl, J.A., Phys. Rev., 1966, vol. 148, p. 766.

    Article  ADS  Google Scholar 

  261. Kwok, P., Physics, 1967, vol. 3, p. 221.

    Article  Google Scholar 

  262. Maurer, M.J., J. Appl. Phys., 1969, vol. 40, p. 5123.

    Article  ADS  Google Scholar 

  263. Beck, H., Dynamical Proerties of Solids, Horton, K. and Maraudin, A.A., Eds., Amsterdam: North-Holland, 1975, vol. 2, p. 205.

    Google Scholar 

  264. Gurtin, M.A. and Pipkin, A.C., Arch. Ration Mech. Anal., 1968, vol. 31, p. 113.

    Article  Google Scholar 

  265. Joseph, D.D., Narain, A., and Riccius, O., Fluid Mech., 1986, vol. 171, p. 289.

    Article  ADS  Google Scholar 

  266. Nunziato, J.W., Q. Appl. Math., 1971, vol. 29, p. 187.

    Article  Google Scholar 

  267. Cattaneo, C., C. R. Acad. Sci., 1958, vol. 247, no. 4, p. 431.

    Google Scholar 

  268. Vernotte, P., C. R. Acad. Sci., 1961, vol. 252, p. 2190.

    Google Scholar 

  269. Narayan, A. and Joseph, D.D., Rheol. Acta, 1982, vol. 21, p. 228.

    Article  MathSciNet  Google Scholar 

  270. Coleman, B.D. and Noll, W., Arch. Ration Mech. Anal., 1960, vol. 6, p. 355.

    Article  Google Scholar 

  271. Saut, J.C. and Joseph, D.D., Arch. Ration Mech. Anal., 1983, vol. 81, p. 53.

    Article  Google Scholar 

  272. Domenico, M.D., Jou, D., and Sellitto, A., Int. J. Heat Mass Transfer, 2020, vol. 156, 119888.

    Article  Google Scholar 

  273. Joseph, D.D. and Preziosi, L., Rev. Mod. Phys., 1990, vol. 62, p. 375.

    Article  ADS  Google Scholar 

  274. Ozisik, M.N. and Tzou, D.Y., J. Heat Transfer, 1994, vol. 116, no. 3, p. 526.

    Article  Google Scholar 

  275. Tzou, D.Y., Int. J. Heat Mass Transfer, 1995, vol. 38, no. 17, p. 3231.

    Article  Google Scholar 

  276. Qiu, T.Q. and Tien, C.L., J. Heat Transfer, 1993, vol. 115, p. 835.

    Article  Google Scholar 

  277. Tzou, D.Y., Int. J. Heat Mass Transfer, 1993, vol. 36, p. 1845.

    Article  Google Scholar 

  278. Ismagilov, R.S., Rautian, N.A., and Vlasov, V.V., arXiv:1402.4107, 2014.

  279. Liouville, I., J. Math. Pure Appl., 1837, vol. 2, p. 16.

    Google Scholar 

  280. Horn, J., Math. Ann., 1899, vol. 52, p. 340.

    Article  MathSciNet  Google Scholar 

  281. Prandtl, L., Proc. III Int. Math. Congress 1904, Heidelberg: Teubner, 1905, p. 484.

  282. Schlesinger, L., Math. Ann., 1907, vol. 63, p. 277.

    Article  MathSciNet  Google Scholar 

  283. Birkhoff, G.D., Trans. Am. Math. Soc., 1908, vol. 9, p. 219.

    Article  Google Scholar 

  284. Tzou, D.Y., in Annual Review of Heat Transfer, Tien, C.-L., Ed., Washington, DC: Hemisphere, 1992, p. 111.

    Google Scholar 

  285. Zel’dovich, Ya.B. and Kompaneets, A.S., Sbornik, posvyashchennyi semidesyatiletiyu akad. A.F. Ioffe (Collection of Papers, Dedicated to the 17th Anniversary of Academician A.F. Ioffe), Lukirskii, P.I., Ed., Moscow: Akad. Nauk SSSR, 1950.

    Google Scholar 

  286. Shashkov, A.G., Bubnov, A.V., and Yanovskii, S.Yu., Volnovye yavleniya teploprovodnosti (Wave Phenomena of Thermal Conductivity), Moscow: URSS, 2004.

  287. Zel’dovich, Ya.V. and Raizer, Yu.P., Fizika udarnykh voln i vysokotemperaturnykh gidrodinamicheskikh yavlenii (Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena), Moscow: Fizmatlit, 1966, 2nd ed.

  288. Formalev, V.F. and Rabinskiy, L.N., High Temp., 2014, vol. 52, no. 5, p. 675.

    Article  Google Scholar 

  289. Formalev, V.F., Kuznetsova, E.L., and Rabinskiy, L.N., High Temp., 2015, vol. 53, no. 4, p. 548.

    Article  Google Scholar 

  290. Formalev, V.F. and Kolesnik, S.A., J. Eng. Phys. Thermophys., 2016, vol. 89, no. 4, p. 975.

    Article  Google Scholar 

  291. Formalev, V.F., Kolesnik, S.A., Kuznetsova, E.L., and Rabinskiy, L.N., High Temp., 2016, vol. 54, no. 3, p. 390.

    Article  Google Scholar 

  292. Formalev, V.F., Kolesnik, S.A., and Kuznetsova, E.L., High Temp., 2016, vol. 54, no. 6, p. 824.

    Article  Google Scholar 

  293. Formalev, V.F., et al., Int. J. Pure Appl. Math., 2016, vol. 111, no. 2, p. 303.

    Google Scholar 

  294. Formalev, V.F. and Kolesnik, S.A., J. Eng. Phys. Thermophys., 2017, vol. 90, no. 6, p. 1302.

    Article  Google Scholar 

  295. Formalev, V.F., Kolesnik, S.A., and Kuznetsova, E.L., High Temp., 2017, vol. 55, no. 5, p. 761.

    Article  Google Scholar 

  296. Formalev, V.F., Kolesnik, S.A., and Kuznetsova, E.L., Period. Tche Quim., 2018, vol. 15, p. 426.

    Google Scholar 

  297. Formalev, V.F. and Kolesnik, S.A., Int. J. Heat Mass Transfer, 2018, vol. 123, p. 994.

    Article  Google Scholar 

  298. Formalev, V.F., Kolesnik, S.A., and Kuznetsova, E.L., High Temp., 2018, vol. 56, no. 5, p. 727.

    Article  Google Scholar 

  299. Formalev, V.F. and Kolesnik, S.A., J. Eng. Phys. Thermophys., 2019, vol. 92, no. 1, p. 52.

    Article  Google Scholar 

  300. Wang, B.L. and Han, J.C., Int. J. Heat Mass Transfer, 2012, vol. 55, p. 4631.

    Article  Google Scholar 

  301. Chang, D.M. and Wang, B.L., Eng. Fract. Mech., 2012, vol. 94, p. 29.

    Article  Google Scholar 

  302. Guo, S.L. and Wang, B.L., Int. J. Heat Mass Transfer, 2015, vol. 91, p. 235.

    Article  Google Scholar 

  303. Hu, K.Q. and Chen, Z.T., Int. J. Heat Mass Transfer, 2013, vol. 62, p. 445.

    Article  Google Scholar 

  304. Fu, J., et al., Eng. Fract. Mech., 2014, vol. 128, p. 103.

    Article  Google Scholar 

  305. Zhang, X.Y. and Li, X.F., Eng. Fract. Mech., 2017, vol. 171, p. 22.

    Article  Google Scholar 

  306. Ramadan, K. and Al-Nimr, M.A., Int. J. Therm. Sci., 2009, vol. 48, p. 1718.

    Article  Google Scholar 

  307. Ciarletta, M., Sellitto, A., and Tibullo, B., Int. J. Eng. Sci., 2017, vol. 119, p. 78.

    Article  Google Scholar 

  308. Kales, I. and Conker, C., Eur. J. Mech. A, 2011, vol. 30, p. 449.

    Article  Google Scholar 

  309. Ivanov, D.S., et al., Mater. Vseros. s”ezda po teoreticheskoi i prikladnoi mekhanike (Proc. All-Russian Conf. on Theoretical and Applied Mechanics) Nizhny Novgorod, 2006, p. 98.

  310. Ivanov, S.G. and Rochev, I.N., Abstracts of Papers, 28 Nauch.-tekh. konf. Permsk. gos. tekh. univ. po rezul’tatam NIR (28th Sci. Tech. conf. of the Perm State Univ. on the Results of Research Works), Perm, 1995, p. 22.

  311. Gu, Z. and Chen, J., J. Compos. Mater., 1990, vol. 24, no. 9, p. 957.

    Article  ADS  Google Scholar 

  312. Ivanov, S.G., Solov’ev, Yu.V., and Tokareva, N.V., Mater. Vseross. s”ezda po teoreticheskoi i prikladnoi mekhanike (Proc. All-Russian Conf. on Theoretical and Applied Mechanics), Perm’, 2001, p. 289.

  313. Akbarov, S.D., Kosker, R., and Simsek, K., Mekh. Kompoz. Mater., 2005, vol. 41, no. 4, p. 433.

    Google Scholar 

  314. Tatarnikov, O.V., et al., Mekh. Kompoz. Mater., 1992, vol. 5, p. 627.

    Google Scholar 

  315. Dimitrienko, Yu.I., Mekh. Kompoz. Mater., 1991, vol. 6, p. 1030.

    Google Scholar 

  316. Berestova, S.A., Mekh. Kompoz. Mater. Konstr., 2005, vol. 11, no. 2, p. 169.

    Google Scholar 

  317. Volokhovskaya, O.A. and Podalkov, V.V., Vestn. Mosk. Energ. Inst., 2002, no. 3, p. 12.

  318. Chekalkin, A.A., Kotov, A.G., and Sokolkin, Y.V., Proc. 19th Int. Congr. on Theoretical and Applied Mechanics, Kyoto, 1996, p. 264.

  319. Shagivaleev, R.F. and Yarullin R.R., Tr. Akademenergo, 2006, no. 4, p. 87.

  320. Liu, X., et al., Composites, Part B, 2019, vol. 172, p. 649.

    Article  Google Scholar 

  321. Rouf, Khizar., Liu, X., and Yu, W., Int. J. Solids Struct., 2018, vol. 136-137, p. 89.

    Article  Google Scholar 

  322. Orzuri, R., et al., Composites, Part B, 2020, vol. 184, 107726.

    Article  Google Scholar 

  323. Malekimoghadam, R. and Icardi, U., Composites, Part B, 2019, vol. 177, 107405.

    Article  Google Scholar 

  324. Pourasghar, A. and Chen, Z., Int. J. Solids Struct., 2019, vol. 163, p. 117.

    Article  Google Scholar 

  325. Alibeigloo, A., Composites, Part B, 2018, vol. 153, p. 445.

    Article  Google Scholar 

  326. Safaei, B., et al., Compos. Struct., vol. 226, 111209.

  327. Krysko, A.V., et al., Composites, Part B, 2019, vol. 158, p. 319.

    Article  Google Scholar 

  328. Belardi, V.G., Fanelli, P., and Vivio, F., Composites, Part B, 2018, vol. 150, p. 184.

    Article  Google Scholar 

  329. Zhilin, P.A., Prikladnaya mekhanika. Osnovy teorii obolochek (Applied Mechanics: Fundamentals of the Shell Theory), St. Petersburg: St. Petersburg. Politekh. Univ., 2006, p. 167.

  330. Ambartsumyan, S.A., Obshchaya teoriya anizotropnykh obolochek (General Theory of Anisotropic Shells), Moscow: Nauka, 1974.

  331. Korolev, V.I., Sloistye anizotropnye plastinki i obolochki izarmirovannykh plastmass (Laminated Anisotropic Plates and Shells of Reinforced Plastics), Moscow: Mashinostroenie, 1965.

  332. Korolev, V.I., Uprugoplasticheskie deformatsii obolochek (Elastoplastic Deformations of Shells), Moscow: Mashinostroenie, 1971.

  333. Bolotin, V.V. and Novichkov, Yu.N., Mekhanika mnogosloinykh konstruktsii (Mechanics of Multilayer Structures), Moscow: Mashinostroenie, 1980.

  334. Bolotin, V.V., Izv. Akad. Nauk SSSR, Mekh. Mashinostr., 1963, no. 3, p. 65.

  335. Rzhanitsyn, A.R., Proekt Standart, 1938, no. 2, p. 29.

  336. Fankhanel, J., Arash, B., and Rolfes, R., Composites, Part B, 2019, vol. 176, 107211.

    Article  Google Scholar 

  337. Tatar, J., Taylor, C.R., and Hamilton, H.R., Composites, Part B, 2019, vol. 172, p. 679.

    Article  Google Scholar 

  338. Kim, B., et al., Composites, Part B, 2017, vol. 120, p. 128.

    Article  Google Scholar 

  339. Johnston, J.P., et al., Composites, Part B, 2017, vol. 111, p. 27.

    Article  Google Scholar 

  340. Trevor, S., et al., Composites, Part B, 2016, vol. 100, p. 31.

    Article  Google Scholar 

  341. Andreev, V., Tsybin, N., and Turusov, R., Struct. Mech. Eng. Construct. Build., 2018, vol. 14, p. 180.

    Article  Google Scholar 

  342. Andreev, V.I., Turusov, R.A., and Tsybin, N.Yu., Vestn. Mosk. Gos. Strioit. Univ., 2016, no. 4, p. 17.

  343. Volkov-Bogorodskii, D.B., Vestn. Nizhegorodsk. Univ. im. N.I Lobachevskogo, 2011, no. 4(2), p. 407.

  344. Buznik V.M., et al., Vestn. Permsk. Nats. Issled. Politekh. Univ., Mekh., 2015, no. 4, p. 36.

  345. Zhang, Y.-F., et al., Composites, Part B, 2016, vol. 106, p. 324.

    Article  Google Scholar 

  346. Li, X., et al., Comput. Mater. Sci., 2012, vol. 63, p. 207.

    Article  ADS  Google Scholar 

  347. Rajeshwari, P. and Dey, T.K., Thermochim. Acta, 2016, vol. 638, p. 103.

    Article  Google Scholar 

  348. Gong, J., et al., Compos. Struct., 2019, vol. 224, 111071.

    Article  Google Scholar 

  349. Voigt, W., Lehrbuch der kristallphysik (Textbook of Crystal Physics), Berlin: Teubner, 1928.

  350. Reuss, A., Z. Angew. Math. Mech., 1929, vol. 9, no. 4, p. 49.

    Article  Google Scholar 

  351. Lifshits, I.M. and Rozentsveig, L.N., Zh. Eksp. Teor. Fiz., 1946, vol. 16, no. 11, p. 967.

    Google Scholar 

  352. Volkov, S.D. and Stavrov, V.P., Statisticheskaya mekhanika kompozitnykh materialov (Statistical Mechanics of Composite Materials), Minsk: Beloruss. Gos. Univ., 1978.

  353. Composite Materials, 8 vols., Sendeckyj, G.P., Ed., vol. 2: Mechanics of Composite Materials, New York: Academic, 1974.

  354. Lomakin, V.A., Statisticheskie zadachi mekhaniki tverdykh deformiruemykh tel (Statistical Problems of Solid Mechanics), Moscow: Nauka, 1970.

  355. Guz’, A.N., Khoroshun, L.P., and Vanin, G.A., Mekhanika kompozitnykh materialov i elementov konstruktsii (Mechanics of Composite Materials and Structural Elements), Kiev: Naukova Dumka, 1982, vol. 1.

  356. Beran, I., Statistical Continuum Theories, New York: Interscience, 1968.

    Book  MATH  Google Scholar 

  357. Hashin, Z. and Rosen, W.B., J. Appl. Mech., 1964, vol. 31, p. 223.

    Article  ADS  Google Scholar 

  358. Hashin, Z. and Strikman, S., J. Mech. Phys. Solids, 1963, vol. 11, no. 2, p. 127.

    Article  MathSciNet  ADS  Google Scholar 

  359. Hill, R., J. Mech. Phys. Solids, 1963, vol. 11, no. 5, p. 357.

    Article  ADS  Google Scholar 

  360. Aizicovici, S. and Aron, M., Acta Mech., 1977, vol. 27, p. 275.

    Article  MathSciNet  Google Scholar 

  361. Yeh, R.H.T., J. Appl. Phys., 1973, vol. 44, no. 2, p. 662.

    Article  ADS  Google Scholar 

  362. Bakhvalov, N.S., Dokl. Akad. Nauk SSSR, 1975, vol. 221, no. 3, p. 516.

    MathSciNet  Google Scholar 

  363. Bakhvalov, N.S., Dokl. Akad. Nauk SSSR, 1975, vol. 225, no. 2, p. 249.

    MathSciNet  Google Scholar 

  364. Kalamkarov, A.L., Kudryavtsev, B.A., and Parton, V.Z., Itogi Nauki Tekh., 1987, no. 19, p. 78.

  365. Pobedrya, B.E., Mekhanika kompozitsionnykh materialov (Mechanics of Composite Materials), Moscow: Mosk. Gos. Univ., 1984.

  366. Gorbachev, V.I., Effektivnye mekhanicheskie kharakteristiki mikroneodnorodnykh tel s periodicheskoi strukturoi. Uprugost’ i neuprugost’ (Effective Mechanical Characteristics of Microheterogeneous Bodies with a Periodic Structure: Elasticity and Inelasticity), Moscow: Mosk. Gos. Univ., 1978, no. 5.

  367. Karalyunas, R.I., Vestn. Mosk. Univ., Ser. 1: Mat., M-ekh., 1984, no. 2, p. 77.

  368. Pin, L. and Lee, K.H., Int. J. Solids Struct., 2020, vol. 39, no. 3, p. 649.

    Google Scholar 

  369. Alekhin, V.V., Annin, B.D., and Kolpakov, A.G., Sintez sloistykh materialov i konstruktsii (Synthesis of Layered Materials and Structures), Novosibirsk: Sib. Otd. Akad. Nauk SSSR, 1988.

  370. Annin, B.D., et al., Raschet i proektirovanie kompozitsionnykh materialov i elementov konstruktsii (Calculation and Design of Composite Materials and Structural Elements), Novosibirsk: Nauka, 1993.

  371. Antsiferov, V.N., Sokolkin, Yu.V., and Tashkinov, A.A., Voloknistye kompozitsionnye materialy na osnove titana (Fiber Composites Based on Titanium), Moscow: Nauka, 1990.

  372. Bolotin, V.V. and Novichkov, Yu.N., Mekhanika mnogosloinykh konstruktsii (Mechanics of Multilayer Structures), Moscow: Nauka, 1980.

  373. Vanin, G.A., Mikromekhanika kompozitsionnykh materialov (Micromechanics of Composite Materials), Kiev: Naukova Dumka, 1985.

  374. Karpinos, D.M., Kompozitsionnye materialy (Composite Materials) Kiev: Naukova Dumka, 1985.

  375. Vasil’ev, V.V., Kompozitsionnye materialy. Spravochnik (Composite Materials: Handbook), Moscow: Nauka, 1990.

  376. Kravchuk, A.S., Maiboroda, V.P., and Urzhumtsev, Yu.S., Mekhanika polimernykh i kompozitsionnykh materialov (Mechanics of Polymer and Composite Materials), Moscow: Nauka, 1985.

  377. Kunin, I.A., Teoriya uprugikh sred s mikrostrukturoi (Theory of Elastic Media with Microstructure), Moscow: Nauka, 1975.

  378. Lagedin’, A.Zh., et al., Metod orientatsionnogo usredneniya v mekhanike materialov (Orientational Averaging Method in Material Mechanics), Riga: Zinatne, 1989.

  379. Malmeister, A.K., Tamuzh, V.P., and Teters, G.A., Soprotivlenie polimernykh i kompozitnykh materialov (Resistance of Polymer and Composite Materials), Riga: Zinatne, 1980.

  380. Nemirovskii, Yu.V. and Reznikov, B.S., Prochnost’ elementov konstruktsii iz kompozitnykh materialov (Strength of Composite Structural Elements), Novosibirsk: Nauka, 1986.

  381. Nigmatulin, R.I., Osnovy mekhaniki geterogennykh sred (Fundamentals of Mechanics of Heterogeneous Media), Moscow: Nauka, 1978.

  382. Obraztsov, I.F., Vasil’ev, V.V., and Bunakov, V.A., Optimal’noe armirovanie obolochek vrashcheniya iz kompozitsionnykh materialov (Optimal Reinforcement of Shells of Revolution Made of Composite Materials), Moscow: Mashinostroenie, 1977.

  383. Oviinskii, A.S., Protsessy razrusheniya kompozitsionnykh materialov. Imitatsiya mikro- i makromekhanizmov na EVM (Fracture Processes of Composite Materials: Computer Simulation of Micro- and Macromechanisms), Moscow: Nauka, 1988.

  384. Berlin, A.A., et al., Printsipy sozdaniya kompozitsion-nykh polimernykh materialov (Principles of Creating Composite Polymer Materials), Moscow: Khimiya, 1990.

  385. Karpinos, D.M., et al., Prochnost’ kompozitsionnykh materialov (Strength of Composite Materials), Kiev: Naukova Dumka, 1978.

  386. Grushetskii, I.V., Dimitrienko, I.P., and Ermolenko, A.F., Razrushenie konstruktsii iz kompozitnykh materialov (Failure of a Composite Structure), Riga: Zinatne, 1986.

  387. Romalis, N.B. and Tamuzh, V.P., Razrushenie strukturno neodnorodnykh tel (Destruction of Structurally Heterogeneous Bodies), Riga: Zinatne, 1989.

  388. Skudra, A.M. and Bulave, F.Ya., Prochnost’ armirovannykh plastikov (Strength of Reinforced Plastics), Moscow: Khimiya, 1982.

  389. Sokolkin, Yu.V., and Tashkinov, A.A., Mekhanika deformirovaniya i razrusheniya strukturno-neodnorodnykh tel (Mechanics of Deformation and Fracture of Structurally Inhomogeneous Bodies), Moscow: Nauka, 1984.

  390. Tamuzh, V.P. and Kuksenko, B.C., Mikromekhanika razrusheniya polimernykh materialov (Fracture Micromechanics of Polymeric Materials), Riga: Zinatne, 1978.

  391. Fujii, T. and Zako, M., Fracture and Mechanics of Composite Materials, Tokyo: Jikkyo Shuppan, 1978.

    Google Scholar 

  392. Cherepanov, G.P., Mekhanika razrusheniya kompozitsionnykh materialov (Fracture Mechanics of Composite Materials), Moscow: Nauka, 1983.

  393. Shermegor, T.D., Teoriya uprugosti mikroneodnorodnykh sred (Theory of Elasticity of Microinhomogeneous Media), Moscow: Nauka, 1977.

  394. Postnykh, A.M., Sokolkin, Yu.V., and Tashkinov, A.A., Mater. 7 Vses. s”ezda s”ezda po teoreticheskoi i prikladnoi mekhanike (Proc. 7th All-Union Conf. on Theoretical and Applied Mechanics), Moscow, 1991.

  395. Svistkov, A.L. and Evlampieva, S.E., Appl. Mech. Tech. Phys., 2003, vol. 44, no. 5, p. 727.

    Article  MathSciNet  ADS  Google Scholar 

  396. Trapeznikov, D.A., et al., in Uglerodnye materialy (Carbon Materials), Moscow: Nauchno-Issed. Inst. Grafita, 1991, p. 67.

  397. Romanova, V.A., Balokhonov, R.R., and Karpenko, N.I., Fiz. Mezomekh., 2004, vol. 7, no. 2, p. 71.

    Google Scholar 

  398. Nemirovskii, Yu.V. and Yankovskii, A.P., Izv. Vyssh. Uchebn. Zaved., Stroit., 2006, no. 5(569), p. 16.

  399. Hashin, Z., Mech. Mater., 1990, vol. 4, p. 293.

    Article  Google Scholar 

  400. Grediac, M., Pierron, F., and Zhavoronok, S.I., Int. J. Solids Struct., 2000, vol. 37, no. 32, p. 4437.

    Article  Google Scholar 

  401. Takano, N. and Zako, M., Trans. Jpn. Soc. Mech. Eng., 2001, vol. 67, no. 656, p. 603.

    Article  Google Scholar 

  402. Vorobey, V.V., et al., Mater. 5-go Mezhdun. simp. “Dinamicheskie i tekhnologicheskie problemy mekhaniki konstruktsii i sploshnykh sred” (Proc. 5th Int. Symp. on Dynamic and Technological Problems of Mechanics of Structures and Continuous Media), Yaropolets, 1999, p. 56.

  403. Reznichenko, A.I., Computation and nondestructive testing of reduced elastic characteristics of products made of composite materials, Novocherkassk: Novocherk. Polytechn. Institute, 1991.

    Google Scholar 

  404. Rikards, D. B., et al., Prochnost, zhestkost I technologichnost izdeliy iz kompozitsionnykh materialov. Tez. dokl. 3 Vsesoyuz. Konf. (Strength, Stiffness and Manufacturability of Industrial Products made from Composite Materials, Proc. of the 3rd All-Union Conference), 1989, p. 173.

  405. Borovkov, A.I. Effective physic and mechanic properties of fibrous composites. Moscow: VINITI, 1985.

    Google Scholar 

  406. Borovkov, A.I. and Palmov, V.A., Nauchno-Tecn. Vedomosti of StPetersbourg. Gos. Univ. (Sci. and Technol. Bull. of the St Petersb. State Univ.), 2008, No. 4 (63), p. 27.

Download references

Funding

This paper was supported by the Russian Science Foundation under the activity Research Conducted by Scientific Teams Led by Young Scientists within the Presidential Program of Research Projects, project no. 19-79-10 258 dated August 8, 2019.

Author information

Authors and Affiliations

  1. Moscow Aviation Institute (National Research University), 125993, Moscow, Russia

    A. N. Astapov, S. I. Zhavoronok, A. S. Kurbatov, L. N. Rabinskiy & O. V. Tushavina

  2. Institute of Applied Mechanics of Russian Academy of Sciences, 125040, Moscow, Russia

    S. I. Zhavoronok

Authors
  1. A. N. Astapov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. I. Zhavoronok
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. S. Kurbatov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. L. N. Rabinskiy
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. O. V. Tushavina
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. N. Astapov.

Additional information

Translated by N. Semenova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Astapov, A.N., Zhavoronok, S.I., Kurbatov, A.S. et al. Main Problems in the Creation of Thermal-Protection Systems Based on Structurally Heterogeneous Materials and the Methods of Their Solution. High Temp 59, 346–372 (2021). https://doi.org/10.1134/S0018151X21020012

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0018151X21020012

Search

Navigation