Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

On the ageing behaviour of NBR: chemomechanical experiments, modelling and simulation of tension set

  • 60 Accesses

  • 1 Citations


Rubber components produced from nitrile butadiene rubber (NBR) are changing their material properties due to environmental influences. This is caused by irreversible changes occurring in the elastomer network which is known as chemical ageing. In this paper, ageing behaviour of NBR is investigated and modelled under the influence of different surrounding media as air and oil. Based on the previous works, in which chemical ageing was also modelled, a continuum mechanical approach is introduced here, whereby the rubber viscoelasticity is taken into account. Simulations using FEM are then carried out under different chemical and mechanical boundary conditions, and the proposed modelling approach is validated by means of tension set measurements.

This is a preview of subscription content, log in to check access.


  1. 1.

    Andrews, R., Tobolsky, A., Hanson, E.: The theory of permanent set at elevated temperatures in natural and synthetic rubber vulcanizates. J. Appl. Phys. 17, 352–361 (1946)

  2. 2.

    Bathe, K.J.: Finite Elemente Procedures, 2nd edn. Prentice-Hall, Englewood Cliffs (1996)

  3. 3.

    Blum, G., Shelton, J., Winn, H.: Rubber oxidation and ageing studies. Ind. Eng. Chem. 43, 464–471 (1951)

  4. 4.

    Budrugeac, P., Segal, E., Ciutacu, S.: Thermooxidative degradation of nitrile-butadiene rubber. J. Therm. Anal. 37, 1179–1191 (1991)

  5. 5.

    Celina, M., Wise, J., Ottesen, D., Gillen, K., Clough, R.: Oxidation profiles of thermally aged nitrile rubber. Polym Degrad Stab 60, 493–504 (1998)

  6. 6.

    Coleman, B.D., Noll, W.: The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Ration. Mech. Anal. 13, 167–178 (1963)

  7. 7.

    Dippel, B.: Experimentelle Charakterisierung, Modellierung und FE-Berechnung thermomechanischer Kopplungen am Beispiel eines rußgefüllten Naturkautschuks. Ph.D. thesis, Universität der Bundeswehr München (2015)

  8. 8.

    Ehrenstein, G., Pongratz, S.: Beständigkeit von Kunststoffen. Carl Hanser Verlag, Munich (2007)

  9. 9.

    Flory, P.J.: Thermodynamic relations for hight elastic materials. Trans. Faraday Soc. 57, 829–838 (1961)

  10. 10.

    Gillen, K.T., Clough, R.L., Wise, J.: Prediction of Elastomer Lifetimes from Accelerated Thermal-Aging Experiments. ACS Publications, Washington (1996)

  11. 11.

    Haupt, P.: Continuum Mechanics and Theory of Materials. Springer, Berlin (2000)

  12. 12.

    Hossain, M., Possart, G., Steinmann, P.: A finite strain framework for the simulation of polymer curing. Part I: elasticity. Comput. Mech. 44, 621–630 (2009)

  13. 13.

    Johlitz, M.: On the representation of ageing phenomena. J. Adhes 88, 620–648 (2012)

  14. 14.

    Johlitz, M., Diercks, N., Lion, A.: Thermo-oxidative aging of elastomers: a modelling approach based on a finite strain theory. Int. J. Plast. 63, 138–151 (2014)

  15. 15.

    Johlitz, M., Dippel, B., Lion, A.: Dissipative heating of elastomers: a new modelling approach based on finite and coupled thermomechanics. Contin. Mech. Thermodyn. 28, 1111–1125 (2016)

  16. 16.

    Johlitz, M., Lion, A.: Chemo-thermomechanical ageing of elastomers based on multiphase continuum mechanics. Contin. Mech. Thermodyn. 25, 605–624 (2012). https://doi.org/10.1007/s00161-012-0255-8

  17. 17.

    Johlitz, M., Retka, J., Lion, A.: Chemical ageing of elastomers: experiments and modelling. In: Jerrams, S., Murphy, N. (eds.) Constitutive Models for Rubber, vol. VII, pp. 113–118. Taylor & Francis, Boca Raton (2011)

  18. 18.

    Lee, E.H.: Elastic–plastic deformation at finite strain. J. Appl. Mech. 36, 1–6 (1969)

  19. 19.

    Lion, A.: Thermomechanik von Elastomeren. Berichte des Instituts für Mechanik der Universität Kassel (Bericht 1/2000) (2000)

  20. 20.

    Lion, A., Dippel, B., Liebl, C.: Thermomechanical material modelling based on a hybrid free energy density depending on pressure, isochoric deformation and temperature. Int. J. Solids Struct. 51, 729–739 (2014)

  21. 21.

    Lion, A., Johlitz, M.: On the representation of chemical ageing of rubber in continuum mechanics. Int. J. Solids Struct. 49, 1227–1240 (2012)

  22. 22.

    Lubliner, J.: A model of rubber viscoelasticity. Mech. Res. Commun. 12, 93–99 (1985)

  23. 23.

    Santoso, M., Torrejon, Y.N., Giese, U., Schuster, R.H.: Untersuchung thermischer und oxidativer alterungsprozesse von elastomeren; verbrauch von p-phenylendiaminen mit der chemilumineszenz. Kaut. Gummi Kunstst. 61, 306–311 (2008)

  24. 24.

    Scheffer, T., Seibert, H., Diebels, S.: Optimisation of a pretreatment method to reach the basic elasticity of filled rubber materials. Arch. Appl. Mech. 83, 1659–1678 (2013)

  25. 25.

    Sedlan, K.: Viskoelastisches Materialverhalten von Elastomerwerkstoffen, Experimentelle Untersuchung und Modellbildung. Dissertation, Berichte des Instituts für Mechanik (2/2001), Universität Gesamthochschule Kassel (2001)

  26. 26.

    Shaw, J., Jones, S., Wineman, A.: Chemorheological response of elastomers at elevated temperatures: experiments and simulations. J. Mech. Phys. Solids 53, 2758–2793 (2005)

  27. 27.

    Simo, J.C., Taylor, R.L.: Penalty function formulations for incompressible nonlinear elastostatics. Comput. Methods Appl. Mech. Eng. 35, 107–118 (1982)

  28. 28.

    Sussman, T., Bathe, K.J.: A finite element formulation for nonlinear incompressible elastic and inelastic analysis. Comput. Struct. 26, 357–409 (1987)

  29. 29.

    Tobolsky, A.V.: Mechanische Eigenschaften und Struktur von Polymeren. Berliner Union, Stuttgart (1967)

  30. 30.

    Williams, M.L., Landel, R.F., Ferry, J.D.: The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. J. Am. Chem. Soc. 77, 3701–3707 (1955)

  31. 31.

    Wise, J., Gillen, K., Clough, R.: An ultrasensitive technique for testing the Arrhenius extrapolation assumption for thermally aged elastomers. Polym. Degrad. Stab. 49, 403–418 (1995)

Download references


The financial support of the project by the Deutsche Forschungsgemeinschaft (DFG) under the Grant Number JO 818/3-1 is gratefully acknowledged.

Author information

Correspondence to Bruno Musil.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Communicated by Johlitz, Laiarinandrasana and Marco.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Musil, B., Johlitz, M. & Lion, A. On the ageing behaviour of NBR: chemomechanical experiments, modelling and simulation of tension set. Continuum Mech. Thermodyn. 32, 369–385 (2020). https://doi.org/10.1007/s00161-018-0728-5

Download citation


  • Chemical ageing
  • NBR
  • Viscoelasticity
  • Tension set