Skip to main content
SpringerLink
Log in

On the evolution law for the frozen fraction in linear theories of shape memory polymers

  • Special Issue
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

Shape memory properties of thermally responsive polymeric materials are due mainly to a phase transition from the rubbery phase above the transition temperature (glass transition or melting temperature) to the glassy or semicrystalline phase below this temperature. Within constitutive models of shape memory polymers (SMPs), this phase transition is mathematically accounted for by the frozen volume fraction for which a suitable evolution law must be postulated or derived. In this paper, the evolution laws that have been proposed in the literature are examined both from the experimental and from the theoretical point of view. It is found that the predictive capabilities of the phenomenological laws may be improved by admitting involved material constants to depend on parameters such as pre-strain, rate of heating and cooling, and other quantities characterizing thermomechanical cyclic tests. It is next shown that for a wide class of linear constitutive models of SMPs, the evolution law for the frozen volume fraction may be derived in a systematic way from strain and stress profiles experimentally obtained in the standard thermomechanical test.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Rousseau I.A.: Challenges of shape memory polymers: a review of the progress toward overcoming SMP’s limitations. Polym. Eng. Sci. 48, 2075–2089 (2008)

    Article  Google Scholar 

  2. Mather P.T., Luo X., Rousseau I.A.: Shape memory polymer research. Ann. Rev. Mater. Res. 39, 445–471 (2009)

    Article  Google Scholar 

  3. Wagermaier W., Kratz K., Heuchel M., Lendlein A.: Characterization methods for shape-memory polymers. Adv. Polym. Sci. 226, 97–145 (2010)

    Article  Google Scholar 

  4. Liu, Y., Gall, K., Dunn, M.L., Greenberg, A.R.: Thermomechanics of the shape memory effect in polymers. In: Materials Research Society Symposium Proceedings 855E, Paper: W5.8 (2005)

  5. Liu Y., Gall K., Dunn M.L., Greenberg A.R., Diani J.: Thermomechanics of shape memory polymers: uniaxial experiments and constitutive modeling. Int. J. Plast. 22, 279–313 (2006)

    Article  MATH  Google Scholar 

  6. Chen Y.-C., Lagoudas D.: A constitutive theory for shape memory polymers. Part II: a linearized model for small deformations. J. Mech. Phys. Solids 56, 1766–1778 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Wang Z.D., Li D.F.: Thermomechanical constitution of shape memory polymers. Int. Conf. Comp. Exp. Eng. Sci. 5, 245–253 (2008)

    Google Scholar 

  8. Wang Z.D., Li D.F., Xiong Z.Y., Chang R.N.: Modeling thermomechanical behaviors of shape memory polymer. J. App. Polym. Sci. 113, 651–656 (2009)

    Article  Google Scholar 

  9. Siskind, R.D.: Model development for shape memory polymers. PhD theses, North Caroline State University, (2008)

  10. Böl M., Reese S.: Micromechanical modelling of shape memory polymers. Adv. Sci. Tech. 54, 137–142 (2008)

    Article  Google Scholar 

  11. Qi H.J., Nguyen T.D., Castro F., Yakacki C.M., Shandas R.: Finite deformation thermo-mechanical behavior of thermally induced shape memory polymers. J. Mech. Phys. Solids 56, 1730–1751 (2008)

    Article  MATH  Google Scholar 

  12. Nguyen T.D., Qi H.J., Castro F., Long K.N.: A thermoviscoelastic model for amorphous shape memory polymers: incorporating structural and stress relaxation. J. Mech. Phys. Solids 56, 1730–1751 (2008)

    Article  MATH  Google Scholar 

  13. Volk, B.: Thermomechanical characterization and modeling of shape memory polymers. MS thesis, Texas A&M University, (2009)

  14. Reese S., Böl M., Christ D.: Finite element-based multi-phase modelling of shape memory polymer stents. Comp. Meth. Appl. Mech. Eng. 199, 1276–1286 (2010)

    Article  MATH  Google Scholar 

  15. Xu W., Li G.: Constitutive modelling of shape memory polymers based self-healing syntactic foam. Int. J. Solids Struct. 47, 1306–1316 (2010)

    Article  MATH  Google Scholar 

  16. Volk, B.L., Lagoudas, D.C., Maitland, D.J.: Characterizing and modeling free recovery and constraint recovery behavior of a polyurethane shape memory polymer. In: Proceedings of SMASIS2010, Philadelphia (2010)

  17. Steeb H., Kazakevic̆iūtė-Makovska R.: Quantification of the evolution of shape storage and recovery in thermally responsive shape memory polymers. Proc. Appl. Math. Mech. 10, 333–334 (2010)

    Article  Google Scholar 

  18. Kazakevic̆iūtė-Makovska, R., Steeb, H.: On the universal relationships in linear theories of shape memory polymers. Smart Mater. Struct. (forthcoming)

  19. Kazakevic̆iūtė-Makovska R., Steeb H.: On recoverable strain and stress relationships for shape memory polymer nanocomposites. KGK - Kautschuk Gummi Kunststoffe 6, 24–28 (2011)

    Google Scholar 

  20. Ozawa T.: Kinetics of non-isothermal crystallization. Polymer 3, 150–158 (1971)

    Article  Google Scholar 

  21. Bianchi O., Oliveira R.V.B., Fiorio R., Martins J.D.N., Zattera A.J., Canto L.B.: Assessment of Avrami, Ozawa and Avrami-Ozawa equations for determination of EVA crosslinking kinetics from DSC measurements. Polym. Test. 27, 722–729 (2008)

    Article  Google Scholar 

  22. Trachenko K.: The Vogel-Fulcher-Tammann law in the elastic theory of glass transition. J. Non-Cryst. Solids 354, 3903–3906 (2008)

    Article  Google Scholar 

  23. Aydin, A.O.: Comparative study of constitutive models for shape memory polymers. Master thesis, LKM, Ruhr-Universität Bochum (2010)

  24. Tobushi H., Hashimoto T., Hayashi S., Yamada E.: Thermomechanical constitutive modeling in shape memory polymer of polyurethane series. J. Int. Mater. Syst. Struct. 8, 711–718 (1997)

    Article  Google Scholar 

  25. Liu Y., Gall K., Dunn M.L., Martin L., McCluskey P.: Thermomechanical recovery couplings of shape memory polymers in flexure. Smart Mater. Struct. 12, 947–954 (2003)

    Article  Google Scholar 

  26. Huang, W.M., Yang, B.: Electrical, thermomechanical and shape-memory properties of the PU shape-memory polymer filled with carbon black. In: Leng, J., Du, S. Shape-Memory Polymers and Multifunctional Composites, CRC Press, New York (2010)

Download references

Author information

Authors and Affiliations

  1. Mechanics-Continuum Mechanics, Ruhr-University Bochum, Universitätsstr. 150, 44780, Bochum, Germany

    Rasa Kazakevic̆iūtė-Makovska, Holger Steeb & Aycan Ö. Aydin

Authors
  1. Rasa Kazakevic̆iūtė-Makovska
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Holger Steeb
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Aycan Ö. Aydin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rasa Kazakevic̆iūtė-Makovska.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kazakevic̆iūtė-Makovska, R., Steeb, H. & Aydin, A.Ö. On the evolution law for the frozen fraction in linear theories of shape memory polymers. Arch Appl Mech 82, 1103–1115 (2012). https://doi.org/10.1007/s00419-012-0615-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-012-0615-7

Keywords

Search

Navigation