Skip to main content
SpringerLink
Log in

A general network theory for the development of curing stresses in an epoxy/fiber composite

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

In previous works, a model was developed for the transition of an epoxy liquid to a cured solid as a result of the continuous formation of solid epoxy networks by crosslinking. The model accounts for volume decrease during crosslinking, thermal expansion due to heat generation, deformation and stress generation. The networks were assumed to be linear thermo-elastic isotropic solids, material properties were deduced from the literature, and the model was used to determine the stresses generated by curing in a number of examples. The purpose of the present work is to revisit the ideas on which this model is based and incorporate them into a general framework within the context of continuum mechanics. This will show the assumptions that have been made in the existing model because of the lack of experimental results and also provide a proper framework for extending the model as new experimental results are obtained. Each network is now assumed to be a nonlinear thermo-viscoelastic solid with its own properties. The assumption of small deformations is introduced to lead to a simplified model that is linear in the strains.

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. Heinrich, C.: The influence of the curing process on the response of textile composites, Ph.D. Dissertation, University of Michigan (2011)

  2. Heinrich, C., Aldridge, M., Wineman, A.S., Kieffer, J., Waas, A.M.: Generation of heat and stress during the cure of polymers used in fiber composites. Int. J. Eng. Sci. 53, 85–111 (2012)

    Article  Google Scholar 

  3. Heinrich, C., Aldridge, M., Wineman, A.S., Kieffer, J., Waas, A.M., Shahwan, K.: The influence of the representative volume element (RVE) size on the homogenized response of cured fiber composites. Model. Simul. Mater. Sci. Eng. 20, 075007 (2012)

    Article  Google Scholar 

  4. Heinrich, C., Aldridge, M., Wineman, A.S., Kieffer, J., Waas, A.M., Shahwan, K.: The role of curing stresses in subsequent response, damage and failure of textile polymer composites. J. Mech. Phys. Solids 61, 1241–1264 (2013)

    Article  MathSciNet  Google Scholar 

  5. Aldridge, M., Kieffer, J., Waas, A.J., Wineman, A.: In situ analysis of the relationship between cure kinetics and the mechanical modulus of an epoxy resin. Macromolecules 47, 8368–8376 (2014)

    Article  Google Scholar 

  6. Ramakrishnan, B., Zhu, L., Pitchumani, R.: Curing of composites using internal resistive heating. J. Manuf. Sci. Eng. 122, 124–131 (2000)

    Article  Google Scholar 

  7. Shanku, R., Vaughan, J.G., Roux, J.A.: Rheological characteristics and cure kinetics of EPON 862/W epoxy used in pultrusion. Adv. Polym. Technol. 16, 297–311 (1997)

    Article  Google Scholar 

  8. O’Brien, D.J., White, S.R.: Cure kinetics, gelation, and glass transition of bisphenol epoxide. Polym. Eng. Sci. 43, 863–874 (2003)

    Article  Google Scholar 

  9. Kamal, M.: Thermoset characterization for moldability analysis. Polym. Eng. Sci. 14, 231–239 (1974)

    Article  Google Scholar 

  10. Spencer, A.J.M.: Theory of invariants. In: Eringen, A.C. (ed.) Continuum Physics, vol. 1, pp. 239–353. Academic Press, New York (1971)

    Google Scholar 

  11. Wineman, A.: Nonlinear viscoelastic solids: a review. Math. Mech. Solids 14, 300–366 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Gent, A.N.: Article 3: elasticity. In: Gent, A.N., Alan, N. (eds.) Engineering with Rubber: How to Design Rubber Components, 2nd edn. Hanser Publications, Munich (2001)

    Google Scholar 

  13. Coleman, B.D., Noll, W.: An approximation theorem for functionals with applications in continuum mechanics. Arch. Ration. Mech. Anal. 6, 355–370 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  14. Coleman, B.D., Noll, W.: Foundations of linear viscoelasticity. Rev. Mod. Phys. 33, 239–249 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  15. Gurtin, M.E., Sternberg, E.: On the linear theory of viscoelasticity. Arch. Ration. Mech. Anal. 11, 291–356 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  16. Wineman, A., Rajagopal, K.R.: The Mechanical Response of Polymers. Cambridge University Press, New York (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, 48109, USA

    Alan Wineman

  2. Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 48109, USA

    Christian Heinrich

  3. William E. Boeing Department of Aeronautics and Astronautics, University of Washington, Seattle, WA, 98195-2400, USA

    Nhung Nguyen & Anthony Waas

Authors
  1. Alan Wineman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christian Heinrich
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nhung Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Anthony Waas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alan Wineman.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wineman, A., Heinrich, C., Nguyen, N. et al. A general network theory for the development of curing stresses in an epoxy/fiber composite. Acta Mech 227, 3585–3601 (2016). https://doi.org/10.1007/s00707-016-1675-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-016-1675-5

Search

Navigation