Rheologica Acta

, Volume 33, Issue 6, pp 506–516 | Cite as

Assessment of nonlinear strain measures for extensional and shearing flows of polymer melts

  • M. H. Wagner
  • J. Schaeffer


From stress-strain experiments in extensional and shearing flows, nonlinear strain measures and effective damping functions are derived for a polyisobutylene melt. The strain measures determined in planar extensional flow and in simple shear flow coincide. Experimental results are compared with predictions of two molecular theories, the Doi-Edwards model and the molecular stress function approach of Wagner and Schaeffer. Discrepancies between theories and experiment lead to a reconsideration of the classification of extensional flows. The symmetry of the flow field is identified and quantified as an important parameter influencing the strain measure, and a unifying strain measure for general extensional and shearing flows of polymer melts is presented.

Key words

Strain measure damping function extensional flow transversely isotropic flow planar flow shear flow Doi-Edwards model molecular stress function classification of extensional flows planarity index 


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  1. Brod H, Buggisch H (1992) Ein Rheometer zur Untersuchung von flüssigen Polymermaterialien in einachsiger and zweiachsiger Dehnung. Rheol Acta 31:283 – 293Google Scholar
  2. Demarmels A (1983) Das rheologische Verhalten von Polyisobutylen bei mehrachsigen Dehnstromungen und seine Beschreibung in den Netzwerktheorien. Dissertation ETH Zürich Nr 7345Google Scholar
  3. Demarmels A, Meissner J (1986) Multiaxial elongations of polyisobutylene and the predictions of several network theories. Colloid Polym Sci 264:829 – 846Google Scholar
  4. Doi M, Edwards SF (1978) Dynamics of concentrated polymer systems. Faraday Trans II, 74:1818 – 1832Google Scholar
  5. Geiger K (1986) Bogenspalt-Kapillarrheometer zur Ermittlung viskoser and elastischer Eigenschaften von Kunststoffschmelzen. Dissertation Universität StuttgartGoogle Scholar
  6. Hoppler HU (1990) Die Beschreibung der dehnungsinduzierten Doppelbrechung von geschmolzenem Polystyrol mit einem kinetischen Orientierungs-Modell. Dissertation ETH Zürich Nr 9099Google Scholar
  7. Khan SA, Larson RG (1991) Step planar extension of polymer melts using a lubricated channel. Rheol Acta 30:1–6Google Scholar
  8. Larson RG (1988) Constitutive equations for polymer melts and solutions. Butterworths, LondonGoogle Scholar
  9. Laun HM (1978) Description of the non-linear shear behaviour of a low density polyethylene melt by means of an experimentally determined strain dependent memory function. Rheol Acta 17:1–15Google Scholar
  10. Laun HM (1980) Stresses and recoverable strains of stretched polymer melts and their prediction by means of a single integral constitutive equation. Proc VIIth Int Congress Rheology, Naples p 419–424Google Scholar
  11. Laun HM, Schuch H (1989) Transient elongational viscosities and drawability of polymer melts. J Rheol 33:119–175Google Scholar
  12. Lodge AS (1964) “Elastic liquids”. Academic Press, London New YorkGoogle Scholar
  13. Meissner J (1972) Modifications of the Weissenberg rheogoniometer for measurement of transient rheological properties of molten polyethylene under shear. Comparison with tensile data. J Appl Polym Sci 16:2877–2899Google Scholar
  14. Samurkas T, Larson RG, Dealy JM (1989) Strong extensional and shearing flow of a branched polyethylene. J Rheol 33:559–578Google Scholar
  15. Schaeffer J, Wagner MH (1993) Nonlinear strain measures for extensional and shearing flows of polymer melts. ASME Winter Annual Meeting, developments in nonNewtonian flows. AMD-Vol 175:27 – 34Google Scholar
  16. Schaeffer J (1994) Entwicklung einer rheologischen Zustandsgleichung für biaxiale Dehnungen und Scherung von Polymerschmelzen. Dissertation Universität of StuttgartGoogle Scholar
  17. Soskey P, Winter H (1984) Large step shear strain experiments with parallel-disk rotational rheometers. J Rheol 28:625 – 645Google Scholar
  18. Stephenson S (1980) Biaxial elongational flow of polymer melts and its realization in a newly developed rheometer. Dissertation ETH Zürich No 6664Google Scholar
  19. Stevenson JF, Chung SC-K, Jenkins JT (1975) Evaluation of material functions for steady elongational flow. Trans Soc Rheol 19:397–405Google Scholar
  20. Wagner MH (1976) Analysis of time-dependent non-linear stress-growth data for shear and elongational flow of a low-density branched polyethylene melt. Rheol Acta 17:136–142Google Scholar
  21. Wagner MH (1978) A constitutive analysis of uniaxial elongational flow data of low-density polyethylene melt. J Non-Newtonian Fluid Mech 4:39 – 55Google Scholar
  22. Wagner MH, Laun HM (1978) Nonlinear shear creep and constrained elastic recovery of a LDPE melt. Rheol Acta 17:138–148Google Scholar
  23. Wagner MH (1979) Zur Netzwerktheorie von Polymer-Schmelzen. Rheol Acta 18:33 – 50Google Scholar
  24. Wagner MH (1990) The nonlinear strain measure of polyisobutylene melt in general biaxial flow and its comparison to the Doi-Edwards model. Rheol Acta 29:594 – 603Google Scholar
  25. Wagner MH, Demarmels A (1990) A constitutive analysis of extensional flows of polyisobutylene. J Rheol 34:943 – 958Google Scholar
  26. Wagner MH, Schaeffer J (1992) Nonlinear strain measures for general biaxial extension of polymer melts. J Rheol 36:1–26Google Scholar
  27. Wagner MH, Schaeffer J (1993) Rubbers and polymer melts: universal aspects of nonlinear stress-strain relations. J Rheol 37:643–661Google Scholar

Copyright information

© Steinkopff-Verlag 1994

Authors and Affiliations

  • M. H. Wagner
    • 1
  • J. Schaeffer
    • 1
  1. 1.Institut für KunststofftechnologieUniversität StuttgartStuttgartGermany

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