Skip to main content

Constitutive Modelling of the Glass Transition and Related Phenomena: Relaxation of Shear Stress Under Pressure

  • Chapter
  • First Online:
Advanced Methods of Continuum Mechanics for Materials and Structures

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 60))

  • 1965 Accesses

Abstract

In industrial fabrication processes as well as in many applications of polymer parts, the glass transition plays a significant role. This is due to high mechanical processing speeds, high temperatures or large cooling rates. The mechanical, the thermomechanical and the caloric properties of polymers differ below and above the glass transition which is a thermoviscoelastic phenomenon. It depends on the ratio between the intrinsic time scale of the polymer and that of the thermomechanical loading process. If both scales are comparable, the material is in the glass transition region. Otherwise it is in the equilibrium or in the glassy region. In the industry, there are increasing demands to simulate fabrication processes in order to estimate the resulting behaviour of the polymer parts before they are manufactured. To this end, constitutive models of finite thermoviscoelasticity are needed which can represent the volumetric as well as the isochoric mechanical behaviour of the polymer in combination with the caloric and the thermomechanical properties. In a recent paper of the authors, the concept of a hybrid free energy has been developed. This approach will be applied in the current essay where the pressure-dependent relaxation behaviour under shear deformations is of interest.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Altenbach, H.: Kontinuumsmechanik: Einführung in die Materialunabhängigen und Materialabhängigen Gleichungen, 3rd edn. Springer, Heidelberg (2015). doi:10.1007/978-3-662-47070-1

    Google Scholar 

  • Altenbach, .H., Altenbach, J.: Einfürung in die Kontinuumsmechanik. Teubner (1994)

    Google Scholar 

  • Doolittle, A.K.: Studies in newtonian flow ii. the dependence of the viscosity of liquids on free-space. J. Appl. Phys. 22(12), 1471–1475 (1951)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Greiner, R., Schwarzl, F.: Thermal contraction and volume relaxation of amorphous polymers. Rheol. Acta 23(4), 378–395 (1984)

    Article  Google Scholar 

  • Haupt, P.: Continuum Mechanics and Theory of Materials. Springer, Heidelberg (2002)

    Google Scholar 

  • Jackle, J.: Models of the glass transition. Rep. Prog. Phys. 49(2), 171 (1986)

    Article  Google Scholar 

  • Johlitz, M., Scharding, D., Diebels, S., Retka, J., Lion, A.: Modelling of thermo-viscoelastic material behaviour of polyurethane close to the glass transition temperature. ZAMM-J. Appl. Math. Mech./Zeitschrift für Angewandte Mathematik und Mechanik 90(5), 387–398 (2010)

    Article  MATH  Google Scholar 

  • Lion, A.: On the large deformation behaviour of reinforced rubber at different temperatures. J. Mech. Phys. Solid 45(11), 1805–1834 (1997)

    Article  Google Scholar 

  • Lion, A., Liebl, C., Kolmeder, S., Peters, J.: Representation of the glass-transition in mechanical and thermal properties of glass-forming materials: a three-dimensional theory based on thermodynamics with internal state variables. J. Mech. Phys. Solid 58(9), 1338–1360 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • Lion, A., Peters, J., Kolmeder, S.: Simulation of temperature history-dependent phenomena of glass-forming materials based on thermodynamics with internal state variables. Thermochim. Acta 522(1), 182–193 (2011)

    Article  Google Scholar 

  • 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. Solid. Struct. 51(3), 729–739 (2014)

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Malvern, L.E.: Introduction to the Mechanics of a Continuous Medium. Prentice-Hall, Upper Saddle River (1969)

    Google Scholar 

  • Naumann, T., Stommel, M.: Simulation of the long term behavior of polymers on the basis of short term data. Tech. Mech. 32, 446–462 (2011)

    Google Scholar 

  • Peters, J., von Estorff, O., Lion, A.: Description of history-dependent phenomena in polymers: the glass transition in modulus, coefficient of thermal expansion and heat capacity. KGK - Kautsch. Gummi Kunstst. 64(5), 40–44 (2011)

    Google Scholar 

  • Reese, S., Govindjee, S.: A theory of finite viscoelasticity and numerical aspects. Int. J. Solid. Struct. 35(26), 3455–3482 (1998)

    Article  MATH  Google Scholar 

  • 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(14), 3701–3707 (1955)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alexander Lion .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media Singapore

About this chapter

Cite this chapter

Lion, A., Johlitz, M., Mittermeier, C. (2016). Constitutive Modelling of the Glass Transition and Related Phenomena: Relaxation of Shear Stress Under Pressure. In: Naumenko, K., Aßmus, M. (eds) Advanced Methods of Continuum Mechanics for Materials and Structures. Advanced Structured Materials, vol 60. Springer, Singapore. https://doi.org/10.1007/978-981-10-0959-4_6

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-0959-4_6

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-0958-7

  • Online ISBN: 978-981-10-0959-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics