Advertisement

Mechanical behavior of amorphous polymers in shear

Article

Abstract

Based on the non-equilibrium thermodynamic theory, a new thermo-viscoelastic constitutive model for an incompressible material is proposed. This model can be considered as a kind of generalization of the non-Gaussian network theory in rubber elasticity to include the viscous and the thermal effects. A set of second rank tensorial internal variables was introduced, and in order to adequately describe the evolution of these internal variables, a new expression of the Helmholtz free energy was suggested. The mechanical behavior of the thermo-viscoelastic material under simple shear deformation was studied, and the “viscous dissipation induced” anisotropy due to the change of orientation distribution of molecular chains was examined. Influences of strain rate and thermal softening produced by the viscous dissipation on the shear stress were also discussed. Finally, the model predictions were compared with the experimental results performed by G' Sell et al., thus the validity of the proposed model is verified.

Key words

thermo-viscoelastic constitutive theory non-Gaussian network model finite deformation simple shear deformation non-equilibrium thermodynamics 

Chinese Library Classification

O343.6 O414.14 

2000 Mathematics Subject Classification

74D10 74C20 74F05 

References

  1. [1]
    Treloar L R G.The Physics of Rubber Elasticity [M], 3rd edition. Oxford: Oxford University Press, 1975.Google Scholar
  2. [2]
    Ward I M.Mechanical Properties of Solid Polymers [M]. 2nd edition. New York: Wiley-Interscience, 1983.Google Scholar
  3. [3]
    James H M, Guth E. Theory of the elastic properties of rubber [J].J Chem Phys, 1943,11(10): 455–481.CrossRefGoogle Scholar
  4. [4]
    Arruda E M, Boyce M C. Evolution of plastic anisotropy in amorphous polymers during finite straining[A]. In: Boehler J-P, Khan A S Eds.Anisotropy and Localization of Plastic Deformation [C]. London: Elsevier Applied Science, 1991, 483–488.Google Scholar
  5. [5]
    Wu P D, Van der Giessen E. On improved 3-D non-Gaussian network models for rubber elasticity [J].Mech Res Comm, 1992,19(5):427–433.CrossRefGoogle Scholar
  6. [6]
    Wu P D, Van der Giessen E. On improved network models for rubber elasticity and their applications to orientation hardening in glassy polymers[J].J Mech Phys Solids, 1993,41(3):427–456.MATHCrossRefGoogle Scholar
  7. [7]
    G'Sell Christian, Boni Serge. Application of the plane simple shear test for determination of the plastic behavior of solid polymers at large strains[J].Journal of Materials Science, 1983,18(3): 903–918.CrossRefGoogle Scholar
  8. [8]
    HUANG Zhu-ping, CHEN Jian-kang, WANG Wen-biao. An internal-variable theory of thermo-viscoelastic constitutive relations at finite strain[J].Science in China, Series A, 2000,43(5):545–551.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Bataille J, Kestin J. Irreversible processes and physical interpretation of rational thermo-dynamics [J].J Non-Equilib Thermodyn, 1979,4(4):229–258.CrossRefGoogle Scholar
  10. [10]
    HUANG Zhu-ping.Fundamentals of Continuum Mechanics [M]. Beijing: Higher Education Publishing House, 2003. (in Chinese)Google Scholar
  11. [11]
    La Mantia F P, Titomanlio G, Acierno D. The viscoelastic behavior of nylon 6/lithium halides mixtures [J].Rheol Acta, 1980,19:88–93.CrossRefGoogle Scholar
  12. [12]
    Aklonis J J, MacKnight W J, Shen M.Introduction to Polymer Viscoelasticity[M]. New York: Wiley-Interscience, 1972.Google Scholar
  13. [13]
    LIU Kuang-hai, Hatakeyama T.Hand Book of Analytical Chemistry. the 8th Fascicule:Heat Analysis[M]. 2nd ed. Beijing: Chemistry Industry Press, 2000. (in Chinese)Google Scholar
  14. [14]
    HE Man-jun, CHEN Wei-xiao, DONG Xi-xia.The Physics of Polymers[M]. Shanghai: Fudan University Press, 1990. (in Chinese)Google Scholar
  15. [15]
    Ashby M F, Jones D R H.Engineering Materials: An Introduction to Their Properties and Applications[M]. Oxford: Pergamon Press, 1980.Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2004

Authors and Affiliations

  1. 1.State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering SciencePeking UniversityBeijingP.R. China

Personalised recommendations