Mechanics of Time-Dependent Materials

, Volume 19, Issue 3, pp 397–417 | Cite as

Analyses of viscoelastic solid polymers undergoing degradation

  • Bentolhoda Davoodi
  • Anastasia MulianaEmail author
  • Daniel Tscharnuter
  • Gerald Pinter


In this paper we study the three-dimensional response of isotropic viscoelastic solid-like polymers undergoing degradation due to mechanical stimuli. A single integral model is used to describe the time-dependent behaviors of polymers under general loading histories. The degradation is associated to excessive deformations in the polymers as strains continuously increase when the mechanical stimuli are prescribed, and therefore we consider a degradation threshold in terms of strains. The degradation part of the deformations is unrecoverable, and upon removal of the prescribed external stimuli, the accumulation of the degradation strains lead to residual strains. We also systematically present material parameter characterization from available experimental data under various loading histories, i.e., ramp loading with different constant rates, creep–recovery under different stresses, and relaxation under several strains. We analyze viscoelastic-degradation response of two polymers, namely polyethylene and polyoxymethylene under uniaxial tensile tests. Longer duration of loading can lead to increase in the degradation of materials due to the substantial increase in the deformations. The single integral model is capable in predicting the time-dependent responses of the polymers under various loading histories and capturing the recovery and residual strains at different stages of degradations.


Viscoelastic Polymers Degradation 



Texas A&M University would like to thank National Science Foundation (CMMI-1266037) and Office of Naval Research (N00014-13-1-0604). Part of this work was performed at the Polymer Competence Center Leoben GmbH (PCCL, Austria) within the framework of the COMET-program of the Federal Ministry for Transport, Innovation and Technology and Federal Ministry for Economy, Family and Youth with contributions by the Montanuniversitaet Leoben. The PCCL is funded by the Austrian Government and the State Governments of Styria, Lower Austria and Upper Austria


  1. Chadwick, P.: Continuum Mechanics: Concise Theory and Problems. Dover, New York (1998) Google Scholar
  2. Chailleux, E., Davis, P.: Modeling the nonlinear viscoelastic–viscoplastic behavior of aramid fiber yarns. Mech. Time-Depend. Mater. 7, 291–301 (2003) CrossRefGoogle Scholar
  3. Chailleux, E., Davis, P.: A nonlinear viscoelastic–viscoplastic model for the behavior of polyester fibers. Mech. Time-Depend. Mater. 9, 147–160 (2005) CrossRefGoogle Scholar
  4. Christensen, R.M.: Theory of Viscoelasticity. Dover, New York (2002) Google Scholar
  5. Christensen, R.M.: A probabilistic treatment of creep rupture behavior for polymers and other materials. Mech. Time-Depend. Mater. 8, 1–15 (2004) CrossRefGoogle Scholar
  6. De Pascalis, R., Abrahams, I.D., Parnell, W.J.: On nonlinear viscoelastic deformations: a reappraisal of Fung’s quasi-linear viscoelastic model. Proc. R. Soc. A 470, 20140058 (2014) CrossRefGoogle Scholar
  7. Drozdov, A.D.: Creep rupture and viscoelastoplasticity of polypropylene. Eng. Fract. Mech. 77, 2277–2293 (2010) CrossRefGoogle Scholar
  8. Drozdov, A.D.: Multi-cycle viscoplastic deformation of polypropylene. Comput. Mater. Sci. 50, 1991–2000 (2011) CrossRefGoogle Scholar
  9. Ferry, J.D.: Viscoelastic Properties of Polymers. Wiley, New York (1961) Google Scholar
  10. Findley, W.N.: Effect of Crystallinity and Crazing, Aging, and Residual Stress on Creep of Monochlorotrifluoroethylene, Canvas Laminate, and Polyvinylchloride. Proceedings, ASTM, vol. 54, p. 1307 (1954) Google Scholar
  11. Fox, T.G., Flory, P.J.: Viscosity-molecular weight and viscosity-temperature relationships for polystyrene and polyisobutylene. J. Am. Chem. Soc. 70, 2384–2395 (1948) CrossRefGoogle Scholar
  12. Freed, A.D.: Soft Solid. Springer, Basel (2014) CrossRefGoogle Scholar
  13. Fung, Y.C.: Biomechanics: Mechanical Properties of Living Tissues. Springer, New York (1981) CrossRefGoogle Scholar
  14. Hin, T.S., Cherry, B.W.: Creep rupture of a linear polyethylene: 1. Rupture and pre-rupture phenomena. Polymer 25, 727–734 (1984) CrossRefGoogle Scholar
  15. Kim, J.S., Muliana, A.: A time integration method for the viscoelastic–viscoplastic analyses of polymers and finite element implementation. Int. J. Numer. Methods Eng. 79, 550–575 (2009) MathSciNetCrossRefzbMATHGoogle Scholar
  16. Lai, J., Bakker, A.: An integral constitutive equation for nonlinear plasto-viscoelastic behavior of high-density polyethylene. Polym. Eng. Sci. 35, 1339–1347 (1995) CrossRefGoogle Scholar
  17. Melo, J.D.D., de Medeiros, A.M.: Long-term creep rupture failure envelope of epoxy. Mech. Time-Depend. Mater. 18, 113–121 (2014) CrossRefGoogle Scholar
  18. Miled, B., Doghri, I., Delannay, L.: Coupled viscoelastic–viscoplastic modeling of homogeneous and isotropic polymers: Numerical algorithm and analytical solutions. Comput. Methods Appl. Mech. Eng. 200, 3381–3394 (2011) MathSciNetCrossRefzbMATHGoogle Scholar
  19. Muliana, A.H., Rajagopal, K.R., Wineman, A.: A new class of quasi-linear models for describing the non-linear viscoelastic response of materials. Acta Mech. 224, 2169–2183 (2013) MathSciNetCrossRefzbMATHGoogle Scholar
  20. Muliana, A., Rajagopal, K.R., Tscharnuter, D.: A nonlinear integral model for describing responses of viscoelastic solids. Int. J. Solids Struct. 58, 146–156 (2015) CrossRefGoogle Scholar
  21. Nolter, K.G., Findley, W.N.: Relationship between the creep of solid and foam polyurethane resulting from combined stress. Trans. ASME J. Basic Eng. 92, 105 (1970) CrossRefGoogle Scholar
  22. O’Connor, D.G., Findley, W.N.: Influence of normal stress on creep in tension and compression. Trans. ASME J. Eng. Ind. 84, 237 (1962) CrossRefGoogle Scholar
  23. Pawlak, A., Galeski, A., Rozanski, A.: Cavitation during deformation of semicrystalline polymers. Prog. Polym. Sci. 39(5), 921–958 (2014) CrossRefGoogle Scholar
  24. Perzyna, P.: Thermodynamic of rehological materials with internal changes. J. Mech. 10, 391–408 (1971) zbMATHGoogle Scholar
  25. Pipkin, A.C.: Lectures on Viscoelasticity Theory, 2nd edn. Springer, Berlin (1986) CrossRefGoogle Scholar
  26. Raghavan, J., Meshii, M.: Creep rupture of polymer composites. Compos. Sci. Technol. 57, 375–388 (1997) CrossRefGoogle Scholar
  27. Regrain, C., Laiarinandrasana, L., Toillon, S.: Experimental and numerical study of creep and creep rupture behavior of PA6. Eng. Fract. Mech. 76, 2656–2665 (2009) CrossRefGoogle Scholar
  28. Schapery, R.A.: On the characterization of nonlinear viscoelastic materials. Polym. Eng. Sci. 9(4), 295–310 (1969) CrossRefGoogle Scholar
  29. Tajima, Y., Itoh, T.: Creep rupture properties of homopolymer, copolymer, and terpolymer based on polyoxymethylene. J. Appl. Polym. Sci. 116, 3242–3248 (2010) Google Scholar
  30. Tscharnuter, D., Muliana: Nonlinear response of viscoelastic polyoxymethylene (POM) at elevated temperatures. Polymer 54, 1208–1217 (2013) CrossRefGoogle Scholar
  31. Tscharnuter, D., Jerabek, M., Major, Z., Pinter, G.: Uniaxial nonlinear viscoelastic–viscoplastic modeling of polypropylene. Mech. Time-Depend. Mater. 16, 275–286 (2012) CrossRefGoogle Scholar
  32. Vujosevic, M., Krajcinovic, D.: Creep rupture of polymers – a statistical model. Int. J. Solids Struct. 34, 1105–1122 (1997) CrossRefzbMATHGoogle Scholar
  33. Wineman, A.: Branching of strain histories for nonlinear viscoelastic solids with a strain clock. Acta Mech. 153, 15–21 (2002) CrossRefzbMATHGoogle Scholar
  34. Wineman, A., Rajagopal, K.R.: Mechanical Responses of Polymers, An Introduction. Cambridge University Press, Cambridge (2001) Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Bentolhoda Davoodi
    • 1
  • Anastasia Muliana
    • 1
    Email author
  • Daniel Tscharnuter
    • 2
  • Gerald Pinter
    • 3
  1. 1.Department of Mechanical EngineeringTexas A&M UniversityCollege StationUSA
  2. 2.Polymer Competence Center Leoben GmbHLeobenAustria
  3. 3.Institute of Materials Science and Testing of PolymersMontanuniversitaet LeobenAustria

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