A Study on Existing Rubber Elasticity Theories for Stress-Strain Behavior of Rubber-like Networks

  • Meissner, B. (Institute of Macromolecular Chemistry, Academy of Sciences of the Czech Republic)
  • Published : 2003.06.30

Abstract

The Edwards-Vilgis slip-link theory and the Kaliske-Heinrich extended tube theory were tested experimentally using published experimental data on networks of natural and isoprene rubber and on polysiloxane networks. All parameters were adjusted to achieve an optimum fit. The data description obtained with the EV theory is not satisfactory and the parameter values tend to lie outside their reasonably expected range. But for the region of low strains, the Kaliske-Heinrich theory offers a satisfactorily accurate data description which is able to serve for practical purposes. Its crosslink term, however, is based on approximations which lead to a questionable prediction and values determined for the exponent in the entanglement term lie outside the range expected by the KH model. Thus, the title question cannot be given a positive answer. Conclusions published earlier that the trapped entanglements contribute both to the crosslink and constraint (entanglement) term are supported by the present data analysis. Experimental equibiaxial data on hydrocarbon networks do not show any maximum on their stretch ratio dependence, contrary to the predictions of molecular theories. The stretch ratio dependences of relative reduced stresses do not sensitively reflect differences in the chemical nature of the chain backbone (hydrocarbon vs. siloxane) and in the crosslinking method (end-linking vs. random crosslinking).

Keywords

References

  1. Treloar LRG. The Physics of Rubber Elasticity. 3rd ed. Oxford: Clarendon Press, 1975
  2. Erman B, Mark JE. Structure and Properties of Rubberlike Networks. New York: Oxford University Press, 1997
  3. Edwards SF, Vilgis TA. Polymer 1986;27:483
  4. An Extended Tube-Model for Rubber Elasticity: Statistical-Mechanical Theory and Finite Element Implementation / Kaliske, M ; Heinrich, G. (Rubber chemistry and technology, v.72 no.4, 1999, pp.602-632)
  5. Constitutive Models of Rubber Elasticity: A Review / Boyce, Me.; Arruda, E. M (Rubber chemistry and technology, v.73 no.3, 2000, pp.504-523)
  6. A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials/ Arruda, E.M. ; Boyce, M.C. (Journal of the mechanics and physics of solids, v.41 no.2, 1993, pp.389-412)
  7. Theory of elasticity of polymer networks. 3 / Paul J. Flory, Burak Erman (Macromolecules ; 1982; 15(3); 800-806)
  8. Thirion P, Weil T. Polymer 1984;25:609
  9. Brereton MG, Klein PG. Polymer 1988;29:970
  10. Tensile stress-strain behaviour of rubberlike networks up to break. Theory and experimental comparison/ Meissner, B. (Polymer, v.41 no.21, 2000, pp.7827-7841)
  11. DeformationofElastomeric Ethylene-OcteneCopolymers / Bensason, S. ; Stepanov, E. V. ; Churn, S. ; Hiltner, A. ; Baer, E. (Macromolecules, v.30 no.8, 1997, pp.2436-2444)
  12. Multiaxial Deformations of End-linked Poly(dimethylsiloxane) Networks. 2. Experimental Tests of Molecular Entanglement Models of Rubber Elasticity / Urayama, K. ; Kawamura, T. ; Kohjiya, S. (Macromolecules, v.34 no.23, 2001, pp.8261-8269)
  13. Comparison of recent rubber-elasticity theories with biaxial stress-strain data: the slip-link theory of Edwards and Vilgis / Meissner, B. ; Matejka, L. (Polymer, v.43 no.13, 2002, pp.3803-3809) https://doi.org/10.1016/S0032-3861(02)00150-7
  14. Ball RC, Doi M, Edwards SF, Wamer M. Polymer 1981;22:1010
  15. Xu P, Mark JE. Rubber Chem Technol 1990;63:276
  16. Pak H, Flory PJ. J Polym Sci Polym Phys Ed 1979;17:1845
  17. Rivlin RS, Saunders DW. Philos Trans R Soc London, Ser A 1951;243:251
  18. Treloar LRG. Trans Faraday Soc 1944;40:59 https://doi.org/10.1039/tf9444000059
  19. Experimental survey of the strain energy density function of isoprene rubber vulcanizate / S. Kawabata, M. Matsuda, K. Tei, H. Kawai (Macromolecules; 1981; 14(1); 154-162)
  20. James AG, Green A, Simpson GM. J Appl Polym Sci 1975;19:2033
  21. Meissner B, Klier I, Kucharik S. J Polym Sci, Part C, 1967;16:793
  22. Nonaffine Deformation and Elasticity of Polymer Networks / Rubinstein, M. ; Panyukov, S. (Macromolecules, v.30 no.25, 1997, pp.8036-8044)
  23. Gaylord RJ, Douglas JF. Polym Bull 1987;18:347 and 1990;23:529
  24. Description of the tensile stress-strain behavior of filler-reinforced rubber-like networks using a Langevin-theory-based approach. Part I / Meissner, B. ; Matejka, L. (Polymer, v.41 no.21, 2000, pp.7749-7760)
  25. Description of the tensile stress-strain behaviour of filler-reinforced rubber-like networks using a Langevin-theory-based approach. Part II / Meissner, B. ; Matejka, L. (Polymer, v.42 no.3, 2001, pp.1143-1156)
  26. Meissner B, Spirkov3 L. Macromol Symp. 2002;181:289 https://doi.org/10.1002/1521-3900(200205)181:1<289::AID-MASY289>3.0.CO;2-W
  27. Mooney M. J Appl Phys 1940;11:582. Rivlin RS. Phil Trans R Soc Lond. Ser A 1948;241:379