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Mechanics of Time-Dependent Materials

, Volume 15, Issue 3, pp 255–275 | Cite as

Two features of the uniaxial compression of a glassy epoxy resin: the yield stress rate-dependence and the volumetric instability

  • Lorenzo Bardella
  • Andrea Belleri
Article

Abstract

We report the results of uniaxial compressive tests on a DGEBA epoxy resin at room temperature, well below its glass transition. We first focus on the strength, defined as the stress value corresponding to either a maximum or a flattening of the stress-strain curve, which, for this polymer, may be taken to be coincident with the yield stress, as often assumed for many thermosets. Within the strain rate range (1.E−6 s−1, 2.E−3 s−1) we confirm the linear trend relating the logarithm of the strain rate to the yield stress, as already been observed by other investigators even for the same epoxy resin; instead, at strain rates below \(\dot{\varepsilon} _{0} \approx 1.\mathrm{E}{-}6~\mathrm{s}^{-1}\), we found a negligible rate-dependence, as our data indicate a lowest limit of the yield stress, of about 87 MPa. On the basis of these results, we propose how to extend to the viscoplastic regime of deformation a nonlinear viscoelastic model previously put forward.

Secondarily, within the viscoelastic range, at a stress level significantly lower than the yield stress, our measurements show a mild volumetric instability, allowed by the free lateral expansion, not ascribable to any macroscopic structural effect; such a behaviour has never been reported in the literature, to the best of our knowledge.

Keywords

Mechanical characterization Epoxy resins Strength Viscoelasticity Viscoplasticity Instability 

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References

  1. Argon, A.S.: A theory for the low-temperature plastic deformation of glassy polymers. Philos. Mag. 28, 839–865 (1973) CrossRefGoogle Scholar
  2. Bardella, L.: Mechanical behavior of glass-filled epoxy resins: experiments, homogenization methods for syntactic foams, and applications. PhD thesis, University of Brescia, Italy (2000). http://dicata.ing.unibs.it/bardella/b-thesis.pdf
  3. Bardella, L.: A phenomenological constitutive law for the nonlinear viscoelastic behaviour of epoxy resins in the glassy state. Eur. J. Mech. A, Solids 20(6), 907–934 (2001) zbMATHCrossRefGoogle Scholar
  4. Bardella, L.: On the modeling of the nonlinear viscoelastic behavior of epoxy resins. In: Applied Mechanics in the Americas. Proceedings of the Seventh Pan American Congress of Applied Mechanics (PACAM VII), Temuco, Chile, pp. 229–232 (2002) Google Scholar
  5. Bardenhagen, S.G., Stout, M.G., Gray, G.T.: Three-dimensional, finite deformation, viscoplastic constitutive models for polymeric materials. Mech. Mater. 25, 235–253 (1997) CrossRefGoogle Scholar
  6. Bauwens-Crowet, C.: The compression yield behaviour of polymethyl methacrylate over a wide range of temperatures and strain-rates. J. Mater. Sci. 8, 968–979 (1973) CrossRefGoogle Scholar
  7. Boyce, M.C., Parks, D.M., Argon, A.S.: Large inelastic deformation of glassy polymers. Part I: Rate dependent constitutive model. Mech. Mater. 7, 15–33 (1988) CrossRefGoogle Scholar
  8. Cherry, B.W., Thomson, K.W.: The fracture of highly crosslinked polymers. Part 1: Characterization and fracture toughness. J. Mater. Sci. 16, 1913–1924 (1981) CrossRefGoogle Scholar
  9. Cook, W.D., Mayr, A.E., Edward, G.H.: Yielding behaviour in model epoxy thermosets—II. Temperature dependence. Polymer 39(16), 3725–3733 (1998) CrossRefGoogle Scholar
  10. Del Piero, G., Rizzoni, R.: Weak local minimizers in finite elasticity. J. Elast. 93, 203–244 (2008) zbMATHCrossRefGoogle Scholar
  11. Duckett, R.A., Rabinowitz, A., Ward, I.M.: The strain-rate, temperature and pressure dependence of yield of isotropic poly(methyl methacrylate) and poly(ethylene terephthalate). J. Mater. Sci. 5, 909–915 (1970) CrossRefGoogle Scholar
  12. Eyring, H.: Viscosity, plasticity and diffusion as examples of absolute reaction rates. J. Chem. Phys. 4, 283–291 (1936) CrossRefGoogle Scholar
  13. Frank, G.J., Brockman, R.A.: A viscoelastic-viscoplastic constitutive model for glassy polymers. Int. J. Solids Struct. 38, 5149–5164 (2001) zbMATHCrossRefGoogle Scholar
  14. Hasan, D.A., Boyce, M.C.: A constitutive model for the nonlinear viscoelastic viscoplastic behavior of glassy polymers. Polym. Eng. Sci. 35, 331–344 (1995) CrossRefGoogle Scholar
  15. Haward, R.N., Thackray, G.: The use of a mathematical model to describe isothermal stress-strain curves in glassy thermoplastics. Proc. R. Soc. Lond. A A302, 453–472 (1968) Google Scholar
  16. Hilton, H.H.: The elusive and fickle viscoelastic Poisson’s ratio and its relation to the elastic-viscoelastic correspondence principle. J. Mech. Mater. Struct. 4(7–8), 1341–1364 (2009) CrossRefGoogle Scholar
  17. Hu, Y., Xia, Z., Ellyin, F.: Mechanical behaviour of an epoxy resin under multiaxial loadings. Part I: Experimental study. Polym. Polym. Compos. 8(1), 11–18 (2000) Google Scholar
  18. Iwamoto, T., Nagai, T., Sawa, T.: Experimental and computational investigations on strain rate sensitivity and deformation behavior of bulk materials made of epoxy resin structural adhesive. Int. J. Solids Struct. 47, 175–185 (2010) zbMATHCrossRefGoogle Scholar
  19. Lakes, R.S., Wineman, A.: On Poisson’s ration in linearly viscoelastic solids. J. Elast. 85, 45–63 (2006) MathSciNetzbMATHCrossRefGoogle Scholar
  20. Lee, S.M.: Plastic deformations in epoxy resins. In: Cross-Linked Polymers: Chemistry, Properties, and Applications. ACS Symposium series, vol. 367, pp. 136–144. American Chemical Society, Washington (1988) CrossRefGoogle Scholar
  21. Lesser, A.J., Kody, R.S.: A generalized model for the yield behavior of epoxy networks in multiaxial stress states. J. Polym. Sci., Polym. Phys. 35, 1611–1619 (1997) CrossRefGoogle Scholar
  22. Liang, Y.-M., Liechti, K.M.: On the large deformation and localization behavior of an epoxy resin under multiaxial stress states. Int. J. Solids Struct. 33(10), 1479–1500 (1996) CrossRefGoogle Scholar
  23. Losi, G.U., Knauss, W.G.: Free volume theory and nonlinear thermoviscoelasticity. Polym. Eng. Sci. 32(8), 542–557 (1992) CrossRefGoogle Scholar
  24. Mayr, A.E., Cook, W.D., Edward, G.H.: Yielding behaviour in model epoxy thermosets—I. Effect of strain and composition. Polymer 39(16), 3719–3724 (1998) CrossRefGoogle Scholar
  25. Oleinik, E.F.: Epoxy-aromatic amine networks in the glassy state: structures and properties. Adv. Polym. Sci. 80, 49–99 (1986) MathSciNetGoogle Scholar
  26. Prandini, M., Bardella, L.: Identification of a constitutive model for epoxy resins. In: Proceedings of the XIII Italian Congress on Computational Mechanics (GIMC 2000), Brescia, Italy, pp. 125–131 (2000) Google Scholar
  27. Robertson, R.E.: Theory of the plasticity of glassy polymers. J. Chem. Phys. 44(10), 3950–3956 (1966) CrossRefGoogle Scholar
  28. Schapery, R.A.: On the characterization of nonlinear viscoelastic materials. Polym. Eng. Sci. 9, 295–310 (1969) CrossRefGoogle Scholar
  29. Schapery, R.A.: Nonlinear viscoelastic and viscoplastic constitutive equations based on thermodynamics. Mech. Time-Depend. Mater. 1, 209–240 (1997) CrossRefGoogle Scholar
  30. Sternstein, S.S., Ongchin, L.: Yield criteria for plastic deformation of glassy high polymers in general stress fields. Am. Chem. Soc. Polym. Prepr. 10, 1117–1124 (1969) Google Scholar
  31. Swadener, J.G., Liechti, K.M.: Asymmetric shielding mechanism in the mixed-mode fracture of glass/epoxy interface. J. Appl. Mech.-T. ASME 65, 25–29 (1998) CrossRefGoogle Scholar
  32. Sweeney, J., Ward, I.M.: A unified model of stress relaxation and creep applied to oriented polyethylene. J. Mater. Sci. 25, 697–705 (1990) CrossRefGoogle Scholar
  33. Tcharkhtchi, A., Faivre, S., Roy, L.E., Trotignon, J.P., Verdu, J.: Mechanical properties of thermosets. Part 1: Tensile properties of an anhydride cured epoxy. J. Mater. Sci. 31, 2687–2692 (1996) CrossRefGoogle Scholar
  34. Tschoegl, N.W., Knauss, W.G., Emri, I.: Poisson’s ratio in linear viscoelasticity—a critical review. Mech. Time-Depend. Mater. 6, 3–51 (2002) CrossRefGoogle Scholar
  35. Ward, I.M.: Mechanical Properties of Solid Polymers, 2nd edn. Wiley, New York (1990) Google Scholar
  36. Wronsky, A.S., Pick, M.: Pyramidal yield criteria for epoxides. J. Mater. Sci. 12, 28–34 (1977) CrossRefGoogle Scholar
  37. Xia, Z., Shen, X., Hellyin, F.: An assessment of nonlinear viscoelastic constitutive models for cyclic loading: the effect of a general loading/unloading rule. Mech. Time-Depend. Mater. 9, 281–300 (2006) Google Scholar

Copyright information

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

Authors and Affiliations

  1. 1.DICATAUniversity of BresciaBresciaItaly
  2. 2.Department of Design and TechnologyUniversity of BergamoDalmine (BG)Italy

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