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Nonlinear analysis for propellant solids

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Abstract

This research paper aims to develop a mathematical model for the interpretation of experimental data for propellant solids. A simple model is constructed by assuming a spherical unit cell. Equations are written with respect to the volume fraction of the filler particles as well as the fraction of the area that is unbonded. A sphere of a finite radius is assumed, containing a rubber matrix inside of which is a rigid filler particle of a smaller radius. A parameter is assigned for the porosity of the material while effective expressions for the shear and the bulk modulus and the strain energy function are written for the composite material. Based on the proposed strain energy function, the stress–strain relations are defined for the propellant solids. The model is based on four material parameters that were evaluated using Farris’s experimental data.

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References

  1. Shen, L.-L., Shen, Z.-B., Xie, Y., Li, H.-Y.: effective mechanical property estimation of composite solid propellants based on VCFEM. Int. J. Aerospace Eng. 2018, 2050876 (2018)

    Google Scholar 

  2. Adel, W.M., Liang, G.-Z.: Analysis of mechanical properties for AP/HTPB solid propellant under different loading conditions. World Acad. Sci. Eng. Technol. Int. J. Aerospace Mech. Eng. 11(12), 1915–1919 (2017)

    Google Scholar 

  3. Kakavas, P.A.: Mechanical properties of propellant composite materials reinforced with ammonium perchlorate particles. Int. J. Solids Struct. 51(10), 2019–2026 (2014)

    Article  Google Scholar 

  4. Fareghi, A.R., Moosavi Nadooshan, S.A., Zekri, N., Mohammadi-Vala, M.: Mechanical properties and burning rate studies of double-base propellants with Akarditeii, Centralite, or 2-Ndpa as stabilizers. J. Energ. Mater. 11(1), 55–60 (2016)

    Google Scholar 

  5. Rao, N.P., Solanke, C., Bihari, B.K., Singh, P.P., Bhattacharya, B.: evaluation of mechanical properties of solid propellants in rocket motors by indentation technique. Propellants Explos. Pyrotech. 41(2), 281–285 (2016)

    Article  Google Scholar 

  6. Mason, B.P., Roland, C.M.: Solid propellants. Rubber Chem. Technol. 92(1), 1–24 (2019)

    Article  Google Scholar 

  7. Eirich, F.R.Q.: Failure modes of elastomers. Eng. Fract. Mech. 5(3), 555–562 (1973)

    Article  Google Scholar 

  8. Bueche, F.: Physical Properties of Polymers, p. 49. Wiley, New York (1962)

    Google Scholar 

  9. Farris, R.J.: The influence of vacuole formation on the response and failure of filled elastomers. J. Rheol. 12(2), 315–334 (1968)

    ADS  Google Scholar 

  10. Farris, R.J.: The character of the stress-strain function for highly filled elastomers. J. Rheol. 12(2), 303–314 (1968)

    ADS  Google Scholar 

  11. Farris, R.J., Falabella, R., Tsai, Y.D.: influence of vacuole formation and growth on the mechanical behavior of polymers. ACS Symp. Ser. 95, 233–243 (1978)

    Article  Google Scholar 

  12. Dong, S., Herrmann, L., Pister, K., Taylor, R.: Studies relating to structural analysis of solid propellants. Final Report to Aerojet-General Corporation, Department of Civil Engineering, UCB (1962)

  13. Ogden, R.W.: Large deformation isotropic elasticity - On the correlation of theory and experiment for incompressible rubberlike solids. Rubber Chem. Technol. 46(2), 398–416 (1973)

    Article  Google Scholar 

  14. Lepie, A., Adicoff, A.: Dynamic mechanical behavior of highly filled polymers: Dewetting effect. J. Appl. Polym. Sci. 16(5), 1155–1166 (1972)

    Article  Google Scholar 

  15. Mullins, L.: Effects of stretching on the properties of rubber. Rubber Chem. Technol. 21(2), 281–300 (1948)

    Article  Google Scholar 

  16. Lion, A.: A constitutive model for carbon black filled rubber: experimental investigations and mathematical representation. Continuum Mech. Thermodyn. 8(3), 153–169 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  17. Kakavas, P.A., Chang, W.V.: Acoustic emission in bonded elastomer discs subjected to uniform tension. J. Appl. Polym. Sci. 42(6), 1997–2004 (1991)

    Article  Google Scholar 

  18. Kakavas, P.A.: New development of the strain energy function for hyperelastic materials using a logarithmic strain approach. J. Appl. Polym. Sci. 77(3), 660–672 (2000)

    Article  Google Scholar 

  19. Kasner, A.I., Meinecke, E.A.: Porosity in rubber, a review. Rubber Chem. Technol. 69(3), 424–443 (1996)

    Article  Google Scholar 

  20. Kasner, A.I., Meinecke, E.A.: Effect of porosity on dynamic mechanical properties of rubber in compression. Rubber Chem. Technol. 69(2), 223–233 (1996)

    Article  Google Scholar 

  21. Griffith, A.A.: The phenomena of rupture and flow in solids. Philos. Trans. R. Soc. A 221, 163–198 (1921)

    ADS  MATH  Google Scholar 

  22. Stoll, R.D., Freudenthal, A.M., Heller, R.A.: Effects of mean pressure on the behavior of a filled elastomer. Exp. Mech. 7(9), 339–345 (1967)

    Article  Google Scholar 

  23. Buswell, H.J.: The effect of pressure on the flow properties of filled polyisobutylene. Rheol. Acta 13(3), 571–576 (1974)

    Article  Google Scholar 

  24. Oberth, A.E.: Principle of strength reinforcement in filled polymers. Rubber Chem. Technol. 40, 1337–1362 (1967)

    Article  Google Scholar 

  25. Blatz, P.J., Sharda, S.C., Tschoegl, N.W.: Strain energy function for rubberlike materials based on a generalized measure of strain. Trans. Soc. Rheol. 18(1), 145–161 (1974)

    Article  Google Scholar 

  26. Beatty, M.F.: Topics in finite elasticity: hyperelasticity of rubber, elastomers, and biological tissues-with examples. Appl. Mech. Rev. 40(12), 1699–1734 (1987)

    Article  ADS  Google Scholar 

  27. Boyce, M.C., Arruda, E.M.: Constitutive models of rubber elasticity: a review. Rubber Chem. Technol. 73(3), 504–523 (2000)

    Article  Google Scholar 

  28. Warren, N.: Theoretical calculation of the compressibility of porous media. J. Geophys. Res. 78(2), 352–362 (1973)

    Article  ADS  Google Scholar 

  29. Tobolsky, A.V., Shen, M.C.: Thermoelasticity, chain conformation, and the equation of state for rubber networks. J. Appl. Phys. 37(5), 1952–1955 (1966)

    Article  ADS  Google Scholar 

  30. Misra, A., Singh, V.: Thermomechanics-based nonlinear rate-dependent coupled damage-plasticity granular micromechanics model. Continuum Mech. Thermodyn. 27(4–5), 787–817 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  31. Jia, H., Misra, A., Poorsolhjouy, P., Liu, C.: Optimal structural topology of materials with micro-scale tension-compression asymmetry simulated using granular micromechanics. Mater. Des. 115, 422–432 (2017)

    Article  Google Scholar 

  32. Timofeev, D., Barchiesi, E., Misra, A., Placidi, L.: Hemivariational continuum approach for granular solids with damage-induced anisotropy evolution. Math. Mech. Solids 26(5), 738–770 (2021)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, School of Engineering, University of Peloponnese, 1 M Alexandrou Str, 26334, Patras, Greece

    Panayiotis A. Kakavas-Papaniaros

  2. Department of Mechanical Engineering, School of Engineering, University of Peloponnese, 1 M Alexandrou Str, 26334, Patras, Greece

    Georgios I. Giannopoulos

Authors
  1. Panayiotis A. Kakavas-Papaniaros
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  2. Georgios I. Giannopoulos
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Correspondence to Panayiotis A. Kakavas-Papaniaros.

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Communicated by Andreas Öchsner.

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This research was performed along the graduate studies of the author at the University of Southern California, LA, USA, under the supervision of professor P.J. Blatz (passed away on May 2010).

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Kakavas-Papaniaros, P.A., Giannopoulos, G.I. Nonlinear analysis for propellant solids. Continuum Mech. Thermodyn. 34, 1159–1171 (2022). https://doi.org/10.1007/s00161-022-01111-w

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