Mechanics of Time-Dependent Materials

, Volume 16, Issue 3, pp 275–286 | Cite as

Uniaxial nonlinear viscoelastic viscoplastic modeling of polypropylene

  • Daniel TscharnuterEmail author
  • Michael Jerabek
  • Zoltan Major
  • Gerald Pinter


This paper presents the application of the Schapery viscoelastic and the Perzyna viscoplastic models to strain recovery data of polypropylene. In a previous study, the recovery of strain after monotonic uniaxial tensile loading was measured to gather information on the viscoelasticity and viscoplasticity. The viscoplastic strains from several load histories were determined and are used to calibrate the viscoplastic model. The parameters of the one-dimensional Schapery model are then found by nonlinear optimization using the strain recovery history. The prediction of stress relaxation and creep behavior is investigated.


Nonlinear viscoelasticity Viscoplasticity Schapery model Perzyna model Strain recovery Polypropylene 


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  1. Arenz, R.J.: Nonlinear shear behavior of poly(vinyl acetate) material. Mech. Time-Depend. Mater. 2, 287–305 (1999) CrossRefGoogle Scholar
  2. Crochon, T., Schönherr, T., Li, C., Lévesque, M.: On finite-element implementation strategies of Schapery-type constitutive theories. Mech. Time-Depend. Mater. 14, 359–387 (2010) CrossRefGoogle Scholar
  3. Fasce, L.A., Pettarin, V., Marano, C., Rink, M., Frontini, P.M.: Biaxial yielding of polypropylene/elastomeric polyolefin blends: effect of elastomer content and thermal annealing. Polym. Eng. Sci. 48(7), 1414–1423 (2008) CrossRefGoogle Scholar
  4. Gahleitner, M., Fiebig, J., Wolfschwenger, J., Dreiling, G., Paulik, Ch.: Post-crystallization and physical aging of polypropylene: materials and processing effects. J. Macromol. Sci., Part B B41(4–6), 833–849 (2002) CrossRefGoogle Scholar
  5. Haj-Ali, R.M., Muliana, A.H.: Numerical finite element formulation of the Schapery non-linear viscoelastic material model. Int. J. Numer. Methods Eng. 59(1), 25–45 (2004) zbMATHCrossRefGoogle Scholar
  6. Heeres, O.M., Suiker, A.S.J., de Borst, R.: A comparison between the Perzyna viscoplastic model and the consistency viscoplastic model. Eur. J. Mech. A, Solids 21(1), 1–12 (2002) zbMATHCrossRefGoogle Scholar
  7. Henriksen, M.: Nonlinear viscoelastic stress analysis—a finite element approach. Comput. Struct. 18(1), 133–139 (1984) zbMATHCrossRefGoogle Scholar
  8. Jerabek, M., Major, Z., Lang, R.W.: Strain determination of polymeric materials using digital image correlation. Polym. Test. 29(3), 407–416 (2010) CrossRefGoogle Scholar
  9. Kim, J.S., Muliana, A.H.: A time-integration method for the viscoelastic viscoplastic analyses of polymers and finite element implementation. Int. J. Numer. Methods Eng. 79(5), 550–575 (2009) MathSciNetzbMATHCrossRefGoogle Scholar
  10. Kolařík, J., Pegoretti, A.: Non-linear tensile creep of polypropylene: time-strain superposition and creep prediction. Polymer 47(1), 346–356 (2006) CrossRefGoogle Scholar
  11. Lai, J., Bakker, A.: Analysis of the non-linear creep of high-density polyethylene. Polymer 36(1), 93–99 (1995) CrossRefGoogle Scholar
  12. Lai, J., Bakker, A.: 3D Schapery representation for non-linear viscoelasticity and finite element implementation. Comput. Mech. 18(3), 182–191 (1996) zbMATHCrossRefGoogle Scholar
  13. Lévesque, M., Derrien, K., Baptiste, D., Gilchrist, M.D.: On the development and parameter identification of Schapery-type constitutive theories. Mech. Time-Depend. Mater. 12(2), 95–127 (2008) CrossRefGoogle Scholar
  14. Marano, C., Rink, M.: Shear yielding threshold and viscoelasticity in an amorphous glassy polymer: a study on a styrene-acrylonitrile polymer. Polymer 42(5), 2113–2119 (2001) CrossRefGoogle Scholar
  15. Marano, C., Rink, M.: Viscoelasticity and shear yielding onset in amorphous glassy polymers. Mech. Time-Depend. Mater. 10(3), 173–184 (2006) CrossRefGoogle Scholar
  16. Nordin, L.-O., Varna, J.: Nonlinear viscoplastic and nonlinear viscoelastic material model for paper fiber composites in compression. Composites, Part A 37(2), 344–355 (2006) CrossRefGoogle Scholar
  17. Perzyna, P.: Fundamental problems in viscoplasticity. Adv. Appl. Mech. 9, 243–377 (1966) CrossRefGoogle Scholar
  18. Quinson, R., Perez, J., Rink, M., Pavan, A.: Components of non-elastic deformation in amorphous glassy polymers. J. Mater. Sci. 31(16), 4387–4394 (1996) CrossRefGoogle Scholar
  19. Schapery, R.A.: On the characterization of nonlinear viscoelastic materials. Polym. Eng. Sci. 9(4), 295–310 (1969) CrossRefGoogle Scholar
  20. Sorvari, J., Malinen, M., Hämäläinen, J.: Finite ramp time correction method for nonlinear viscoelastic material model. Int. J. Non-Linear Mech. 41(9), 1050–1056 (2006) CrossRefGoogle Scholar
  21. Tscharnuter, D., Jerabek, M., Major, Z., Pinter, G.: Irreversible deformation of isotactic polypropylene in the pre-yield regime. Eur. Polym. J. 47(5), 989–996 (2011a) CrossRefGoogle Scholar
  22. Tscharnuter, D., Jerabek, M., Major, Z., Lang, R.W.: On the determination of the relaxation modulus of PP compounds from arbitrary strain histories. Mech. Time-Depend. Mater. 15(1), 1–14 (2011b) CrossRefGoogle Scholar

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© Springer Science+Business Media, B. V. 2011

Authors and Affiliations

  • Daniel Tscharnuter
    • 1
    Email author
  • Michael Jerabek
    • 2
  • Zoltan Major
    • 3
  • Gerald Pinter
    • 4
  1. 1.Polymer Competence Center Leoben GmbHLeobenAustria
  2. 2.Borealis Polyolefine GmbHLinzAustria
  3. 3.Institute of Polymer Product EngineeringJohannes Kepler University LinzLinzAustria
  4. 4.Chair of Materials Science and Testing of PolymersUniversity of LeobenLeobenAustria

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