Mechanical Deformation Behavior

  • Günther Hartwig
Part of the The International Cryogenics Monograph Series book series (ICMS)


The correlation between applied mechanical load and resulting deformation is described by moduli. The basic component of moduli is controlled by binding forces, originating from deformations of the electron configurations. The load acts against the binding forces. This component reacts nearly immediately and is responsible for the elastic behavior. At very low temperatures most polymers behave elastically. Below 20K, the moduli of amorphous, semicrystalline and cross-linked polymers, respectively are rather similar which suggests similar binding forces. Above 30K the asymmetry of binding potentials causes a small decrease of the moduli owing to thermal expansion of the chain distances. The response, however, is strictly elastic. In the vicinity of a glass transition temperature (dispersion region) viscoelastic processes decrease the moduli owing to unfreezing of molecular motions. Only secondary or tertiary transitions are considered here. The deformation behavior in a dispersion region depends on temperature and time. The typical deformation characteristic is plotted schematically for the Young’s modulus E in Figure 7.1 with three characteristic regions:
  1. (a)

    constant elastic modulus (symmetric potential),

  2. (b)

    temperature-dependent elastic modulus (asymmetric potential),

  3. (c)

    time- and temperature-dependent viscoelastic modulus near a glass transition temperature Tg. The latter is time-dependent, for example, a function of the strain rate \( \dot \varepsilon \) or the frequency ω.



Relaxation Modulus Load Amplitude Secant Modulus Dispersion Region Initial Modulus 
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  1. 7.1
    Schwarzl, F.R.; Mechanik der Polymere; p. 136; Springer Press; Berlin-Heidelberg (1990)Google Scholar
  2. 7.2
    Pauling, L. and E.B. Wilson; Introduction to Quantum Physics; McGraw Hill-Verlag (1935).Google Scholar
  3. 7.3
    McCrum, N.G., B.E. Read and G. Williams; Anelastic and Dielectric Effects in Polymeric Solids, John Wiley and Sons; p. 130.Google Scholar
  4. 7.4
    Ref. 7.3; p.137Google Scholar
  5. 7.5
    Ref. 7.3; p.234Google Scholar
  6. 7.6
    Döll, W.; in: Advances in Polymer Sci. 52/53,p. 106; Springer Press; Berlin-Heidelberg (1983).Google Scholar
  7. 7.7
    Hartwig, G.; B. Kneifel and K. Pohlmann; in Advances in Cryogenic Engineering (Materials), Vol. 32; p. 169; Plenum Press, New York, (1986)Google Scholar
  8. 7.8
    Hartwig, G.; Habilitationthesis, University Erlangen (1989).Google Scholar
  9. 7.9
    Haward, R.N. in: The Physics of Glassy Polymers; p. 330 and p. 375; Applied Science Publishers Ltd, London (1973)Google Scholar
  10. 7.10
    Perepechko, J.; Low-Temperatures Properties of Polymers; p. 241 Pergamon Press, MIR Publishers, Moscow (1980).Google Scholar
  11. 7.11
    Hartwig, G.;Cryogenics, Vol. 28; p. 220.Google Scholar

General Reading

  1. 1.
    Ferry, J.D.; Viscoelastic Properties of Polymers; ( 3. Edition); John Wiley and Sons, New York (1980).Google Scholar
  2. 2.
    Advances in Polymer Science 52/53); Crazing in Polymers; Editor: H. H. Kausch; Springer Press; Berlin-Heidelberg (1983).Google Scholar
  3. 3.
    Advances in Polymer Science 91/92, Vol. 2; Crazing in Polymers; Springer Press; Berlin-Heidelberg (1990).Google Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Günther Hartwig
    • 1
    • 2
  1. 1.Kernforschungszentrum KarlsruheKarlsruheGermany
  2. 2.Universität Erlangen-NürnbergErlangenGermany

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