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Rheologica Acta

, Volume 32, Issue 4, pp 370–379 | Cite as

The determination of a general time creep compliance relation of linear viscoelastic materials under constant load and its extension to nonlinear viscoelastic behavior for the Burger model

  • B. Möginger
Original Contributions

Abstract

Linear viscoelastic materials yield a creep function which only depends on time if creep experiments are performed under constant stress σ0. In practice, this condition is very difficult to realize, and as a consequence, the experiments are performed under constant force. For small strains the difference between the conditions of constant stress and constant force is negligible. Otherwise, the decrease in cross-section has to be taken into account and leads to increasing stress in the course of time for creep experiments under constant load. The Boltzmann superposition principle is solved under the condition of constant load and for strains \(\varepsilon (t) = \frac{{l(t)}}{{l_0 }} < 0.2\). The creep complicance C(t; σ0) defined by the ratio \(\frac{{\varepsilon (t)}}{{\sigma _0 }}\) becomes, in principle, dependent on the initial stress σ0. As a consequence, a set of creep compliance curves cannot be approximated with a simple parameter fit. Already the application of the solution on the Burger model yields a creep compliance curve with all three creep ranges. Furthermore, the mathematical structure of the time creep compliance relation of the Burger model allows nonlinear viscoelastic extension via the introduction of the yield strength σmax and a nonlinearity parameter n l . The creep behavior of PBT and PC can be described in the range of long times up to initial stresses σ0, being 75% for PBT and 60% for PC of the yield stress σmax with only two or one free fit parameter, respectively.

Key words

Linear viscoelasticity Laplace transformation creep complicance Burger model 

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References

  1. Bronstein IN, Semendjajew KA (1979) Taschenbuch der Mathematik. Verlag Harry Deutsch Thun, FrankfurtGoogle Scholar
  2. Gross B (1953) Mathematical structure of the theories of viscoelasticity. Libraire scientifique Hermann et Cie, ParisGoogle Scholar
  3. Honerkamp J, Weese J (1990) Tikhonov's regularization method for ill-posed problems. Continuum Mech Thermodyn 2:17–30Google Scholar
  4. Möginger B, Fritz U, Rammhofer T (1991) Determination of stress strain relations for thermoplastic polymers with a linear viscoelastic approach. Stuttgarter Kunststoff Kolloquium 1991Google Scholar
  5. Nowacki W (1965) Theorie des Kriechens, lineare Viskoelastizität. Franz Deuticke, WienGoogle Scholar
  6. Roberts J (1988) Stress-strain property reference points for non-linear materials. Plastic and Rubber Processing and Applications 9:17–21Google Scholar
  7. Pöllet P (1985) Automatisierte Zeitstandsmessung — Verfahren mit berührungsloser Dehnungsmessung. Kunststoffe 75:829–834Google Scholar
  8. Schwarzl RF (1990) Polymermechanik. Springer, BerlinGoogle Scholar
  9. Spiegel MR (1977) Schaum's outline “Laplace Transformationen”. Theorie und Anwendung, McGraw Hill Book Company, 112–113Google Scholar
  10. Tobolsky AV (1966) Properties and structure of polymers. Wiley, New YorkGoogle Scholar

Copyright information

© Steinkopff-Verlag 1993

Authors and Affiliations

  • B. Möginger
    • 1
  1. 1.Institute of Polymer Testing and Polymer Science (IKP)University of StuttgartStuttgartGermany

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