Solid-phase combustion in a plane stress state. 1. Stationary combustion wave



A model that describes propagation of the conversion front in a generalized plane stress state typical for technological conditions of coating synthesis on a substrate, with allowance for the coupled character of heat transfer and deformation without external mechanical loading, is proposed. A stationary solution is obtained in the approximation of a narrow combustion front. Ranges of model parameters where the temperature of reaction products and the components of stress and strain tensors behave differently are identified.

Key words

synthesis of coatings on a substrate solid-phase combustion plane stress state 


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  1. 1.
    L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 6: Fluid Mechanics, Pergamon Press, Oxford-Elmsford, New York (1987).Google Scholar
  2. 2.
    A. G. Merzhanov and B. I. Khaikin, Theory of Combustion Waves in Homogeneous Media [in Russian], Inst. of Struct. Macrokinetics, Russian Acad. of Sci., Chernogolovka (1992).Google Scholar
  3. 3.
    I. L. Pobol’, “Processing of structural and industrial materials and obtaining articles under the electron beam action,” Doct. Dissertation in Tech. Sci., Minsk (2007).Google Scholar
  4. 4.
    A. G. Knyazeva, “Effect of rheological properties of the medium on ignition and combustion characteristics,” in: Unsteady Combustion and Interior Ballistics, Proc. Int. Workshop (Saint Petersburg, June 26–30, 2001), Vol. 1, Baltic State Tech. Univ., St. Petersburg (2001), pp. 30–40.Google Scholar
  5. 5.
    A. G. Knyazeva, “The stationary modes of the reaction front and their stability for solid media with regard to chemically induced internal stresses and strains,” in: Combustion of Energetic Materials, Select. Papers of the 5th Int. Symp. on Special Topics in Chemical Propulsion (Stresa, Italy, June 18–22, 2000), Kluwer Acad. Publ., S. 1. (2001), pp. 867–878.Google Scholar
  6. 6.
    B. V. Novozhilov, “Propagation velocity of the exothermic reaction front in the condensed phase,” Dokl. Akad. Nauk SSSR, 141, No. 1, 151–153 (1961).Google Scholar
  7. 7.
    M. G. Makhviladze and B. V. Novozhilov, “Two-dimensional stability of the combustion of condensed systems,” J. Appl. Mech. Tech. Phys., 12, No. 5, 676–682 (1971).CrossRefADSGoogle Scholar
  8. 8.
    K. G. Shkadinskii and B. I. Khaikin, “Effect of heat losses on propagation of the exothermal reaction front in the k-phase,” in: Combustion and Explosion [in Russian], Nauka, Moscow (1972), pp. 104–109.Google Scholar
  9. 9.
    A. G. Knyazeva, “Solution of the thermoelasticity problem in the form of a traveling wave and its application to analysis of possible regimes of solid-phase transformations,” J. Appl. Mech. Tech. Phys., 44, No. 2, 164–173 (2003).CrossRefMathSciNetGoogle Scholar
  10. 10.
    Yu. A. Gordopolov, V. S. Trofimov, and A. G. Merzhanov, “Possibility of gasless detonation of condensed systems,” Dokl. Ross. Akad. Nauk, Fizika, 341, No. 3, 327–329 (1995).Google Scholar
  11. 11.
    S. S. Batsanov and Yu. A. Gordopolov, “Limits of solid-phase detonation velocity,” Dokl. Ross. Akad. Nauk, 341, No. 3, 327–329 (195).Google Scholar
  12. 12.
    L. G. Bolkhovitinov and S. S. Batsanov, “Theory of solid-state detonation,” Combust., Expl., Shock Waves, 43, No. 2, 219–221 (2007).CrossRefGoogle Scholar
  13. 13.
    A. G. Knyazeva, “Combustion wave propagation through deformed solids,” Combust., Expl., Shock Waves, 29, No. 3, 299–303 (1993).MathSciNetGoogle Scholar
  14. 14.
    B. Boley and J. Weiner, Theory of Thermal Stresses, John Wiley and Sons, New York (1960).MATHGoogle Scholar
  15. 15.
    A. G. Knyazeva, “Thermomechanical stability of the reaction front in the technology conditions,” in: Proc. 4th Europ. Combustion Meeting (Vienna, April 14–17, 2009), Vienna Univ. of Technol., Vienna (2009); CD ROM, P811400.Google Scholar
  16. 16.
    A. G. Knyazeva, “Velocity of the solid-phase combustion wave. Asymptotical analysis,” Fiz. Mezomekh., 7, No. 3, 63–70 (2004).Google Scholar

Copyright information

© MAIK/Nauka 2010

Authors and Affiliations

  1. 1.Institute of Strength Physics and Material Science, Siberian DivisionRussian Academy of SciencesTomskRussia

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