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

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Abstract

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.

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References

  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.

    Article  ADS  MathSciNet  Google Scholar 

  2. J.P. Berry, J. Scanlan and W.F. Watson, Cross-link formation in stretched rubber networks. Trans. Faraday Soc. 52 (1956) 1137–1151.

    Article  Google Scholar 

  3. L.E. Dickson, First Course in the Theory of Equations. Wiley, New York (1922).

    MATH  Google Scholar 

  4. A.E. Green and J.E. Adkins, Large Elastic Deformations and Non-Linear Continuum Mechanics. Oxford University Press, Oxford (1960).

    MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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).

  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.

    Article  MATH  Google Scholar 

  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.

    Article  Google Scholar 

  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.

  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.

    Article  ADS  Google Scholar 

  11. A.V. Tobolsky, Properties and Structures of Polymers, Chapter V, pp. 223–265, Wiley, New York (1960).

    Google Scholar 

  12. A. Wineman and K.R. Rajagopal, On a constitutive theory for materials undergoing microstructural changes. Arch. Mech. 42 (1990) 53–74.

    MATH  MathSciNet  Google Scholar 

  13. M. Zimmermann and A. Wineman, On the elastic range of scission materials. Math. Mech. Solids 10 (2005) 63–88.

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Alan Wineman.

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Wineman, A., Shaw, J. Influence of Thermally Induced Chemorheological Changes on the Inflation of Spherical Elastomeric Membranes. J Elasticity 80, 73–95 (2005). https://doi.org/10.1007/s10659-005-9020-6

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  • DOI: https://doi.org/10.1007/s10659-005-9020-6

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