Journal of Elasticity

, Volume 80, Issue 1–3, pp 73–95 | Cite as

Influence of Thermally Induced Chemorheological Changes on the Inflation of Spherical Elastomeric Membranes

  • Alan Wineman
  • John Shaw


When an elastomeric material is deformed and subjected to temperatures above some chemorheological value T cr (near 100°C for natural rubber), its macromolecular structure undergoes time and temperature dependent chemical changes. The process continues until the temperature decreases below T cr. Compared to the virgin material, the new material system has modified properties (often a reduced stiffness) and permanent set on removal of the applied load. A recently proposed constitutive theory is used to study the influence of chemorheological changes on the inflation of an initially isotropic spherical rubber membrane. The membrane is inflated while at a temperature below T cr. We then look at the pressure response assuming the sphere's radius is held fixed while the temperature is increased above T cr for a period of time and then returned to its original value. The inflation pressure during this process is expressed in terms of the temperature, representing entropic stiffening of the elastomer, and a time dependent property that represents the kinetics of the chemorheological change in the elastomer. When the membrane has been returned to its original temperature, it is shown to have a permanent set and a modified pressure-inflated radius relation. Their dependence on the initial inflated radius, material properties and kinetics of chemorheological change is studied when the underlying elastomeric networks are neo-Hookean or Mooney–Rivlin.

Key words

elastomers membranes scission and crosslinking chemorheology thermal effects. 

Mathematics Subject Classification (2000)

74F05 74F25 74D10 74E94 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J.E. Adkins and R.S. Rivlin, Large elastic deformations of isotropic materials IX. The deformation of thin shells. Philos. Trans.- R. Soc. Lond. A244 (1952) 505–531.CrossRefADSMathSciNetGoogle Scholar
  2. 2.
    J.P. Berry, J. Scanlan and W.F. Watson, Cross-link formation in stretched rubber networks. Trans. Faraday Soc. 52 (1956) 1137–1151.CrossRefGoogle Scholar
  3. 3.
    L.E. Dickson, First Course in the Theory of Equations. Wiley, New York (1922).MATHGoogle Scholar
  4. 4.
    A.E. Green and J.E. Adkins, Large Elastic Deformations and Non-Linear Continuum Mechanics. Oxford University Press, Oxford (1960).MATHGoogle Scholar
  5. 5.
    W.H. Han, F. Horkay and G.B. McKenna, Mechanical and swelling behaviors of rubber: a comparison of some molecular models with experiments. Math. Mech. Solids 4 (1999) 139–167.MATHCrossRefGoogle Scholar
  6. 6.
    A. Jones, An experimental study of the thermo-mechanical response of elastomers undergoing scission and crosslinking at high temperatures. PhD dissertation, University of Michigan (2003).Google Scholar
  7. 7.
    K.R. Rajagopal and A. Wineman, A constitutive equation for non-linear solids which undergo deformation induced microstructural changes, Int. J. Plast. 8 (1992) 385–395.MATHCrossRefGoogle Scholar
  8. 8.
    J. Scanlan and W.F. Watson, The interpretation of stress–relaxation measurements made on rubber during aging. Trans. Faraday Soc. 54 (1958) 740–750.CrossRefGoogle Scholar
  9. 9.
    J.A. Shaw, A. Jones and A.S. Wineman, Chemorheological response in elastomers at elevated temperatures: experiments and simulations. J. Mech. Phys. Solids, in press.Google Scholar
  10. 10.
    A.V. Tobolsky, I.B. Prettyman and J.H. Dillon, Stress relaxation of natural and synthetic stocks. J. Appl. Phys. 15 (1944) 380–395.CrossRefADSGoogle Scholar
  11. 11.
    A.V. Tobolsky, Properties and Structures of Polymers, Chapter V, pp. 223–265, Wiley, New York (1960).Google Scholar
  12. 12.
    A. Wineman and K.R. Rajagopal, On a constitutive theory for materials undergoing microstructural changes. Arch. Mech. 42 (1990) 53–74.MATHMathSciNetGoogle Scholar
  13. 13.
    M. Zimmermann and A. Wineman, On the elastic range of scission materials. Math. Mech. Solids 10 (2005) 63–88.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of MichiganAnn ArborUSA
  2. 2.Department of Aerospace EngineeringUniversity of MichiganAnn ArborUSA

Personalised recommendations