Mechanics of Time-Dependent Materials

, Volume 14, Issue 3, pp 219–241 | Cite as

Effects of thermal rates on the thermomechanical behaviors of amorphous shape memory polymers

  • Francisco Castro
  • Kristofer K. Westbrook
  • Kevin N. Long
  • Robin Shandas
  • H. Jerry Qi


Shape memory polymers (SMPs) are polymers that can recover a large pre-deformed shape in response to environmental stimuli, such as temperature, light, etc. For a thermally triggered (or activated) amorphous SMP, the pre-deformation and recovery of the shape require the temperature of the material to traverse the glass transition temperature T g under constrained or free conditions. In this paper, effects of thermal rates on the thermomechanical behaviors of amorphous SMPs are investigated. Under uniaxial compression, during a temperature cycle (cooling followed by heating), the stress decreases to zero as the temperature decreases to below the glass transition temperature, and increases to a value larger than the initial stress (termed stress overshoot) as the temperature is raised above the glass transition temperature. These observations are examined by a thermoviscoelasticity model that couples the nonequilibrium structural relaxation and temperature dependent viscoelastic behavior of the material. In addition, using this model, stress-temperature behaviors during temperature cycles with various thermal rate conditions and tensile loading conditions are studied.


Shape memory polymers Constitutive models Structural relaxation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bergstrom, J.S., Boyce, M.C.: Constitutive modeling of the large strain time-dependent behavior of elastomers. J. Mech. Phys. Solids 46(5), 931–954 (1998) CrossRefGoogle Scholar
  2. Di Marzio, E.A., Yang, A.J.M.: Configurational entropy approach to the kinetics of glasses. J. Res. Natl. Inst. Stand. Technol. 102(2), 135–157 (1997) Google Scholar
  3. Engels, T.A.P., Govaert, L.E., et al.: Processing-induced properties in glassy polymers: application of structural relaxation to yield stress development. J. Polym. Sci., B, Polym. Phys. 44(8), 1212–1225 (2006) CrossRefGoogle Scholar
  4. Hutchinson, J.M.: Physical aging of polymers. Prog. Polym. Sci. 20(4), 703–760 (1995) CrossRefGoogle Scholar
  5. Kauzmann, W.: The nature of the glassy state and the behavior of liquids at low temperatures. Chem. Rev. 43(2), 219–256 (1948) CrossRefGoogle Scholar
  6. Kovacs, A.J.: Fortschr. Hochpolymer.-Forsch. 3, 394 (1964) CrossRefGoogle Scholar
  7. Kovacs, A.J., Aklonis, J.J., et al.: Isobaric volume and enthalpy recovery of glasses 2: transparent multi-parameter theory. J. Polym. Sci., B, Polym. Phys. 17(7), 1097–1162 (1979) CrossRefGoogle Scholar
  8. Lendlein, A., Kelch, S.: Shape-memory polymers. Angew. Chem. Int. Ed. 41(12), 2034–2057 (2002) CrossRefGoogle Scholar
  9. Lendlein, A., Kelch, S., et al.: Shape memory polymers. In: Encyclopedia of Materials: Science and Technology (2005) Google Scholar
  10. Liu, Y.P., Gall, K., et al.: Thermomechanical recovery couplings of shape memory polymers in flexure. Smart Mater. Struct. 12(6), 947–954 (2003) CrossRefGoogle Scholar
  11. Liu, Y.P., Gall, K., et al.: Thermomechanics of shape memory polymers: uniaxial experiments and constitutive modeling. Int. J. Plast. 22(2), 279–313 (2006) MATHCrossRefGoogle Scholar
  12. Liu, C., Qin, H., et al.: Review of progress in shape-memory polymers. J. Mater. Chem. 17(16), 1543–1558 (2007) CrossRefGoogle Scholar
  13. McKenna, G.B.: Glass formation and glassy behavior. In: Booth, P.C. (ed.) Comprehensive Polymer Science, vol. 2, pp. 311–362. Pergamon, Oxford (1989) Google Scholar
  14. Moynihan, C.T., Easteal, A.J., et al.: Dependence of fictive temperature of glass on cooling rate. J. Am. Ceram. Soc. 59(1–2), 12–16 (1976) CrossRefGoogle Scholar
  15. Narayanaswamy, O.S.: Model of structural relaxation in glass. J. Am. Ceram. Soc. 54(10), 491 (1971) CrossRefGoogle Scholar
  16. Nguyen, T.D., Qi, H.J., et al.: A thermoviscoelastic model for amorphous shape memory polymers: incorporating structural and stress relaxation. J. Mech. Phys. Solids 56(9), 2792–2814 (2008) MATHCrossRefGoogle Scholar
  17. O’Connell, P.A., McKenna, G.B.: Arrhenius-type temperature dependence of the segmental relaxation below T g. J. Chem. Phys. 110(22), 11054–11060 (1999) CrossRefGoogle Scholar
  18. Qi, H.J., Nguyen, T.D., et al.: Finite deformation thermo-mechanical behavior of thermally induced shape memory polymers. J. Mech. Phys. Solids 56(5), 1730–1751 (2008) MATHCrossRefGoogle Scholar
  19. Reese, S., Govindjee, S.: A theory of finite viscoelasticity and numerical aspects. Int. J. Solids Struct. 35(26–27), 3455–3482 (1998) MATHCrossRefGoogle Scholar
  20. Robertson, R.E., Simha, R., et al.: Free-volume and the kinetics of aging of polymer glasses. Macromolecules 17(4), 911–919 (1984) CrossRefGoogle Scholar
  21. Tobushi, H., Hara, H., et al.: Thermomechanical properties in a thin film of shape memory polymer of polyurethane series. Smart Mater. Struct. 5(4), 483–491 (1996a) CrossRefGoogle Scholar
  22. Tobushi, H., Hara, H., et al.: Thermomechanical properties in a thin film of shape memory polymer of polyurethane series. SPIE-Int. Soc. Opt. Eng. (1996b) Google Scholar
  23. Tool, A.Q.: Relation between inelastic deformability and thermal expansion of glass in its annealing range. J. Am. Ceram. Soc. 29(9), 240–253 (1946) CrossRefGoogle Scholar
  24. Tool, A.Q.: Effect of heat-treatment on the density and constitution of high-silica glasses of the borosilicate type. J. Am. Ceram. Soc. 31(7), 177–186 (1948) CrossRefGoogle Scholar
  25. Tool, A.Q., Eichlin, C.G.: Variations caused in the heating curves of glass by heat treatment. J. Am. Ceram. Soc. 14(4), 276–308 (1931) CrossRefGoogle Scholar
  26. Westbrook, K.K., Castro, F., et al.: Improved design for thermo-mechanical experiments on polymers using uniaxial testing equipment (2009, in preparation) Google Scholar
  27. Williams, G., Watts, D.C.: Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function. Trans. Faraday Soc. 66(565P), 80 (1970) CrossRefGoogle Scholar
  28. Williams, M.L., Landel, R.F., et al.: Temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. Phys. Rev. 98(5), 1549–1549 (1955) Google Scholar
  29. Yakacki, C.M., Shandas, R., et al.: Unconstrained recovery characterization of shape-memory polymer networks for cardiovascular applications. Biomaterials 28(14), 2255–2263 (2007) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, B. V. 2010

Authors and Affiliations

  • Francisco Castro
    • 1
  • Kristofer K. Westbrook
    • 1
  • Kevin N. Long
    • 1
  • Robin Shandas
    • 1
  • H. Jerry Qi
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of ColoradoBoulderUSA

Personalised recommendations