Mechanics of Time-Dependent Materials

, Volume 13, Issue 3, pp 275–299 | Cite as

Constitutive model for cyclic deformation of perfluoroelastomers



Observations are reported in uniaxial cyclic tensile tests with a strain-controlled program on perfluoroelastomer Hyflon MFA. A constitutive model is developed for its viscoplastic response and damage at three-dimensional deformations with finite strains. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. Numerical simulation demonstrates that the constitutive equations adequately describe the mechanical response of perfluoroelastomer in cyclic tests with complicated deformation programs.


Perfluoroelastomer Viscoplasticity Damage Constitutive equations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ameduri, B., Boutevin, B., Kostov, G.: Fluoroelastomers: synthesis, properties and applications. Progr. Polym. Sci. 26, 105–187 (2001) CrossRefGoogle Scholar
  2. Bergstrom, J.S., Kurtz, S.M., Rimnac, C.M., Edidin, A.A.: Constitutive modeling of ultra-high molecular weight polyethylene under large-deformation and cyclic loading conditions. Biomaterials 23, 2329–2343 (2002) CrossRefGoogle Scholar
  3. Bueche, F.: Mullins effect and rubber–filler interaction. J. Appl. Polym. Sci. 5, 271–281 (1961) CrossRefGoogle Scholar
  4. Chagnon, G., Verron, E., Gornet, L., Marckmann, G., Charrier, P.: On the relevance of continuum damage mechanics as applied to the Mullins effect in elastomers. J. Mech. Phys. Solids 52, 1627–1650 (2004) MATHCrossRefGoogle Scholar
  5. Chagnon, G., Verron, E., Marckmann, G., Gornet, L.: Development of new constitutive equations for the Mullins effect in rubber using the network alteration theory. Int. J. Solids Struct. 43, 6817–6831 (2006) MATHCrossRefGoogle Scholar
  6. Chen, J., Asano, M., Maekawa, Y., Yoshida, M.: Suitability of some fluoropolymers used as base films for preparation of polymer electrolyte fuel cell membranes. J. Membr. Sci. 277, 249–257 (2006) CrossRefGoogle Scholar
  7. De Tommasi, D., Puglisi, G., Saccomandi, G.: A micromechanics-based model for the Mullins effect. J. Rheol. 50, 495–512 (2006) CrossRefGoogle Scholar
  8. Diani, J., Brieu, M., Vacherand, J.M.: A damage directional constitutive model for Mullins effect with permanent set and induced anisotropy. Eur. J. Mech. A 25, 483–496 (2006) MATHCrossRefGoogle Scholar
  9. Drozdov, A.D., Christiansen, J.deC.: Cyclic viscoplasticity of thermoplastic elastomers. Acta Mech. 194, 47–65 (2007) MATHCrossRefGoogle Scholar
  10. Drozdov, A.D., Dorfmann, A.: Stress–strain relations in finite viscoelastoplasticity of rigid-rod networks: Applications to the Mullins effect. Continuum Mech. Thermodyn. 13, 183–205 (2001) MATHMathSciNetGoogle Scholar
  11. Erman, B., Flory, P.J.: Theory of elasticity of polymer networks. II. The effect of geometric constraints on junctions. J. Chem. Phys. 68, 5363–5369 (1978) CrossRefGoogle Scholar
  12. Erman, B., Monnerie, L.: Theory of elasticity of amorphous networks: effects of constraints along chains. Macromolecules 22, 3342–3348 (1989) CrossRefGoogle Scholar
  13. Goktepe, S., Miehe, C.: A micro-macro approach to rubber-like materials. III. The micro-sphere model of anisotropic Mullins-type damage. J. Mech. Phys. Solids 53, 2259–2283 (2005) CrossRefMathSciNetGoogle Scholar
  14. Govindjee, S., Simo, J.: Transition from micro-mechanics to computationally efficient phenomenology: Carbon black filled rubbers incorporating Mullins’ effect. J. Mech. Phys. Solids 40, 213–233 (1992) MATHCrossRefGoogle Scholar
  15. Horgan, C.O., Ogden, R.W., Saccomandi, G.: A theory of stress softening of elastomers based on finite chain extensibility. Proc. R. Soc. A 460, 1737–1754 (2004) MATHCrossRefMathSciNetGoogle Scholar
  16. Johnson, M.A., Beatty, M.F.: A constitutive equation for the Mullins effect in stress controlled uniaxial extension experiments. Continuum Mech. Thermodyn. 5, 301–318 (1993) CrossRefMathSciNetGoogle Scholar
  17. Kaliske, M., Nasdala, L., Rothert, H.: On damage modelling for elastic and viscoelastic materials at large strain. Comp. Struct. 79, 2133–2141 (2001) CrossRefGoogle Scholar
  18. Kafka, V., Vokoun, D.: On backstresses, overstresses, and internal stresses represented on the mesoscale. Int. J. Plast. 21, 1461–1480 (2005) MATHCrossRefGoogle Scholar
  19. Kaushiva, B.D., Wilkes, G.L., Comeaux, C., Socha, L.: Structure-property relationships of poly(tetra fluoroethylene)–poly(tetrafluoroethylene-co-vinylidene fluoride-co-hexafluoropropylene) blends. Polymer 42, 4619–4633 (2001) CrossRefGoogle Scholar
  20. Likozar, B., Sebenik, U., Krajnc, M.: Modeling of dynamic mechanical properties of vulcanized fluoroelastomer. Polym. Eng. Sci. 47, 2085–2094 (2007) CrossRefGoogle Scholar
  21. Lin, R.C., Schomburg, U.: A finite elastic-viscoelastic-elastoplastic material law with damage: Theoretical and numerical aspects. Comp. Meth. Appl. Mech. Engng. 192, 1591–1627 (2003) MATHCrossRefGoogle Scholar
  22. Losi, G.U., Knauss, W.G.: Free volume theory and nonlinear thermoviscoelastictity. Polym. Eng. Sci. 32, 542–557 (1992) CrossRefGoogle Scholar
  23. Mullins, L.: Softening of rubber by deformation. Rubber Chem. Technol. 42, 339–362 (1969) Google Scholar
  24. Ogden, R.W., Roxburgh, D.G.: A pseudo-elastic model for the Mullins effect in filled rubber. Proc. R. Soc. A 455, 2861–2877 (1999) MATHMathSciNetCrossRefGoogle Scholar
  25. Popelar, C.F., Liechti, K.M.: A distortion-modified free volume theory for nonlinear viscoelastic behavior. Mech. Time-Depend. Mater. 7, 89–141 (2003) CrossRefGoogle Scholar
  26. Simo, J.C.: On a fully three-dimensional finite-strain viscoelastic damage model: Formulation and computational aspects. Comp. Meth. Appl. Mech. Eng. 60, 153–173 (1987) MATHCrossRefMathSciNetGoogle Scholar
  27. Souzy, R., Ameduri, B.: Functional fluoropolymers for fuel cell membranes. Progr. Polym. Sci. 30, 644–687 (2005) CrossRefGoogle Scholar
  28. Souzy, R., Ameduri, B., Boutevin, B., Gebel, G., Capron, P.: Functional fluoropolymers for fuel cell membranes. Solid State Ionics 176, 2839–2848 (2005) CrossRefGoogle Scholar
  29. Sullivan, R.W.: Development of a viscoelastic continuum damage model for cyclic loading. Mech. Time-Depend. Mater. 12, 329–342 (2008) CrossRefMathSciNetGoogle Scholar
  30. Tan, J., Chao, Y.J., Van Zee, J.W., Li, X., Wang, X., Yang, M.: Assessment of mechanical properties of fluoroelastomer and EPDM in a simulated PEM fuel cell environment by microindentation test. Mater. Sci. Eng. A 496, 464–470 (2008) CrossRefGoogle Scholar
  31. Turri, S., Levi, M., Cristini, M., Sanguineti, A.: Dynamic and thermo-mechanical properties of some specialty fluoroelastomers for low T g seal materials. J. Polym. Res. 14, 141–145 (2007) CrossRefGoogle Scholar
  32. Turri, S., Valsecchi, R., Levi, M., Cristini, M., Sanguineti, A.: Microstructure to property relations in a family of millable polyurethane fluoroelastomers. Eur. Polym. J. 44, 2951–2961 (2008) CrossRefGoogle Scholar
  33. Wang, S., Legare, J.M.: Perfluoroelastomer and fluoroelastomer seals for semiconductor wafer processing equipment. J. Fluorine Chem. 122, 113–119 (2003) CrossRefGoogle Scholar
  34. Xia, Z., Shen, X., Ellyin, F.: An assessment of nonlinearly viscoelastic constitutive models for cyclic loading: The effect of a general loading/unloading rule. Mech. Time-Depend. Mater. 9, 281–300 (2005) CrossRefGoogle Scholar
  35. Yakimets, I., Lai, D., Guigon, M.: Model to predict the viscoelastic response of a semi-crystalline polymer under complex cyclic mechanical loading and unloading conditions. Mech. Time-Depend. Mater. 11, 47–60 (2007) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, B. V. 2009

Authors and Affiliations

  1. 1.Danish Technological InstituteTaastrupDenmark

Personalised recommendations