Establishment of Constitutive Model of Silicone Rubber Foams Based on Statistical Theory of Rubber Elasticity

  • Cheng-Sha Wei
  • Ai Lu
  • Su-Ming Sun
  • Xing-Wen Wei
  • Xiao-Yu Zho
  • Jie Sun
Article
  • 2 Downloads

Abstract

In this study, a constitutive model based on microscopic physical mechanism of silicone rubber foams was established. A theoretical statistical model of rubber elasticity considering the effect of dangling chains was modified to build this model. When a strain amplification factor (X) was introduced, the theoretical model could fit the tensile stress-strain data of mono- and bi-modal foam matrix well (Adj. R-Square = 0.9989, 0.9983). Parameters related to the polymer network, namely, average molecular weight (Mc) and volume fraction (ϕ) of chain segments between adjacent cross-linking points (network strands), were calculated by probabilistic method from the number-average molecular weight (Mn), vinyl content (wVi) of the primary polysiloxanes and percent conversion (q) of vinyl groups. The primary and infinite strain amplification factors (X0, X) and decay exponent (z), introduced by X and related to the nanoparticles, were obtained by fitting. Inspired by the fact that the actual strain of matrix was lower than that of the foams’, we introduced another item, strain hysteresis item (H, related with the foam porosity and cell structure), into the statistical model as well. With the same above values of Mc, ϕ, X0 and X, the model could also fit the compressive stress-strain data of mono- and bi-modal foams well (Adj. R-Square = 0.9948, 0.9985). Interestingly, the strain hysteresis items of the mono- and bi-modal foams almost completely coincided under all experimental strains, which may be attributed to the almost equal porosity and similar cell structure of the two foams. This constitutive model may connect the macroscopic stress-strain behaviour to the parameters of microscopic molecular structures, promisingly providing a basis for the performance improvement and optimization of silicone rubber foams.

Keywords

Silicone rubber foams Constitutive model Statistical theory of rubber elasticity Strain amplification factor Strain hysteresis item 

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Notes

Acknowledgments

This work was financially supported by the National Natural Science Foundation of China (Nos. 51473151 and 51703210).

References

  1. 1.
    Song, L.; Lu, A.; Feng, P.; Lu, Z. Preparation of silicone rubber foam using supercritical carbon dioxide. Mater. Lett. 2014, 121, 126–128CrossRefGoogle Scholar
  2. 2.
    Chen, H. B.; Liu, B.; Huang, W.; Wu, W. H. Gamma radiation induced effects of compressed silicone foam. Polym. Degrad. Stab. 2015, 114, 89–93CrossRefGoogle Scholar
  3. 3.
    Kumar, A.; Mollah, A. A.; Keshri, A. K.; Kumar, M.; Singh, K.; Rallabhandi, K. D. V. S.; Seelaboyina, R. Development of macroporous silicone rubber for acoustic applications. Ind. Eng. Chem. Res. 2016, 55(32), 8751–8760CrossRefGoogle Scholar
  4. 4.
    Liao, X.; Xu, H.; Li, S.; Zhou, C.; Li, G.; Park, C. B. The effects of viscoelastic properties on the cellular morphology of silicone rubber foams generated by supercritical carbon dioxide. RSC Adv. 2015, 5(129), 106981–106988CrossRefGoogle Scholar
  5. 5.
    Liu, P.; Liu, D.; Zou, H.; Fan, P.; Xu, W. Structure and properties of closed-cell foam prepared from irradiation crosslinked silicone rubber. J. Appl. Polym. Sci. 2009, 113(6), 3590–3595CrossRefGoogle Scholar
  6. 6.
    Yang, Q.; Yu, H.; Song, L.; Lei, Y.; Zhang, F.; Lu, A.; Liu, T.; Luo, S. Solid-state microcellular high temperature vulcanized (HTV) silicone rubber foam with carbon dioxide. J. Appl. Polym. Sci. 2017, 134(20), 44807CrossRefGoogle Scholar
  7. 7.
    Labouriau, A.; Robison, T.; Meincke, L.; Wrobleski, D.; Taylor, D.; Gill, J. Aging mechanisms in RTV polysiloxane foams. Polym. Degrad. Stabil. 2015, 121, 60–68CrossRefGoogle Scholar
  8. 8.
    Rusch, K. C. Energy-absorbing characteristics of foamed polymers. J. Appl. Polym. Sci. 1970, 14(6), 1433–1447CrossRefGoogle Scholar
  9. 9.
    Avalle, M.; Belingardi, G.; Ibba, A. Mechanical models of cellular solids: Parameters identification from experimental tests. Int. J. Impact. Eng. 2007, 34(1), 3–27CrossRefGoogle Scholar
  10. 10.
    Gibson, L. J. Modelling the mechanical behavior of cellular materials. Mat. Sci. Eng A-Struct. 1989, 110, 1–36CrossRefGoogle Scholar
  11. 11.
    Itskov, M.; Knyazeva, A. A rubber elasticity and softening model based on chain length statistics. Int. J. Solids. Struct. 2016, 80, 512–519CrossRefGoogle Scholar
  12. 12.
    Schlögl, S.; Trutschel, M. L.; Chassé, W.; Riess, G.; Saalwächter, K. Correction to entanglement effects in elastomers: macroscopic vs microscopic properties. Macromolecules 2015, 48(8), 2855–2855CrossRefGoogle Scholar
  13. 13.
    Guth, E.; James, H. M. Elastic and thermoelastic properties of rubber like materials. Ind. Eng. Chem. Res. 1941, 33(5), 624–629CrossRefGoogle Scholar
  14. 14.
    Rubinstein, M.; Panyukov, S. Elasticity of polymer networks. Macromolecules 2002, 35(17), 6670–6686CrossRefGoogle Scholar
  15. 15.
    Vega, D. A.; Villar, M. A.; Alessandrini, J. L.; Vallés, E. M. Terminal relaxation of model poly(dimethylsiloxane) networks with pendant chains. Macromolecules 2001, 34(13), 4591–4596CrossRefGoogle Scholar
  16. 16.
    Tsenoglou, C. Rubber elasticity of cross-linked networks with trapped entanglements and dangling chains. Macromolecules 1989, 22(1), 284–289CrossRefGoogle Scholar
  17. 17.
    Lorenz, H.; Klüppel, M.; Heinrich, G. Microstructure-based modelling and FE implementation of filler-induced stress softening and hysteresis of reinforced rubbers. ZAMM-Z. Angew. Math. Me. 2012, 92(8), 608–631CrossRefGoogle Scholar
  18. 18.
    Klüppel, M.; Schramm, J. A generalized tube model of rubber elasticity and stress softening of filler reinforced elastomer systems. Macromol. Theor. Simul. 2000, 9(9), 742–754CrossRefGoogle Scholar
  19. 19.
    Marrucci, G. A mechanical model for rubbers containing entanglements. Rheo. Acta 1979, 18(2), 193–198CrossRefGoogle Scholar
  20. 20.
    Curro, J. G.; Pincus, P. A theoretical basis for viscoelastic relaxation of elastomers in the long-time limit. Macromolecules 1983, 16(4), 559–562CrossRefGoogle Scholar
  21. 21.
    Xu, Q.; Pang, M.; Zhu, L.; Zhang, Y.; Feng, S. Mechanical properties of silicone rubber composed of diverse vinyl content silicone gums blending. Mater. Design 2010, 31(9), 4083–4087CrossRefGoogle Scholar
  22. 22.
    Urayama, K. Network topology-mechanical properties relationships of model elastomers. Polym. J. 2008, 40(8), 669–678CrossRefGoogle Scholar

Copyright information

© Chinese Chemical Society, Institute of Chemistry, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Cheng-Sha Wei
    • 1
  • Ai Lu
    • 1
  • Su-Ming Sun
    • 1
  • Xing-Wen Wei
    • 1
  • Xiao-Yu Zho
    • 1
  • Jie Sun
    • 1
  1. 1.Institute of Chemical MaterialsChina Academy of Engineering PhysicsMianyangChina

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