Skip to main content
SpringerLink
Log in

Micro-mechanics based derivation of the materials constitutive relations for carbon-nanotube reinforced poly-vinyl-ester-epoxy based composites

  • Published:
Journal of Materials Science Aims and scope Submit manuscript

Abstract

The atomic-level computational results of the mechanical properties of Multi-Walled Carbon Nanotube (MWCNT) reinforced poly-vinyl-ester-epoxy obtained in our recent work [Grujicic M, Sun Y-P, Koudela KL (2006) Appl Surf Sci (accepted for publication, March)], have been utilized in the present work within a continuum-based micro-mechanics formulation to determine the effective macroscopic mechanical properties of these materials. Since the MWCNT reinforcements and the polymer-matrix molecules are of comparable length scales, the reinforcement/matrix interactions which control the matrix-to-reinforcement load transfer in these materials are accounted for through direct atomic-level modeling of the “effective reinforcement” mechanical properties. The term an “effective reinforcement” is used to denote a MWCNT surrounded by a layer of the polymer matrix whose thickness is comparable to the MWCNT radius and whose conformation is changed as a result of its interactions with the MWCNT. The micro-mechanics procedure yielded the effective continuum mechanical properties for the MWCNT-reinforced poly-vinyl-ester-epoxy matrix composite mats with a random in-plane orientation of the MWCNTs as a function of the following composite microstructural parameters: the volume fraction of the MWCNTs, their aspect ratio, the extent of covalent functionalization of the MWCNT outer walls as well as a function of the mechanical properties of the matrix and the reinforcements.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Zhu J, Kim J, Peng H, Margrave JL, Khabashesku VN, Barrera EV (2003) Nano Lett 3:1107

    Article  CAS  Google Scholar 

  2. Berber S, Kwon YK, Tomanek D (2000) Phys Rev Lett 84:4613

    Article  CAS  Google Scholar 

  3. Lourie O, Wagner HD (1998) J Mater Res 13:2418

    Article  CAS  Google Scholar 

  4. Walters DA, Ericson LM, Casavant MJ, Liu J, Colbert DT, Smith KA, Smalley RE (1999) Appl Phys Lett 74:3803

    Article  CAS  Google Scholar 

  5. Andrews R, Jacques D, Rao AM, Rantell T, Derbyshire F, Chen Y, Chen J, Haddon RC (1999) Appl Phys Lett 75:1329

    Article  CAS  Google Scholar 

  6. Mamedov AA, Kotov NA, Prato M, Guldi DM, Wicksted JP, Hirsch A (2002) Nat Mater 1:190

    Article  CAS  Google Scholar 

  7. Salvetat JP, Briggs GAD, Bonard JM, Bacsa RR, Kulik AJ, Stockli T, Burnham NA, Forro L (1999) Phys Rev Lett 82:944

    Article  CAS  Google Scholar 

  8. Chen J (2001) J Phys Chem B 105:2525

    Article  CAS  Google Scholar 

  9. Frankland SJV, Caglar A, Brenner DW, Griebel M (2002) J Phys Chem B 106:3046

    Article  CAS  Google Scholar 

  10. Watts PCP, Hsu WK, Chen GZ, Fray DJ, Kroto HW, Walton DRM (2001) J Mater Chem 11:2482

    Article  CAS  Google Scholar 

  11. Kis A, Csanyi G, Salvetat J-P, Lee T-N, Couteau E, Kulik AJ, Benoit W, Brugger J, Forro L (2004) Nat Mater 3:153

    Article  CAS  Google Scholar 

  12. Thess A (1996) Science 273:483

    Article  CAS  Google Scholar 

  13. Dalton AB, Collins S, Munoz E, Razal JM, Ebron VH, Ferraris JP, Coleman JN, Kim BG, Baughman RH (2003) Nature 423:703

    Article  CAS  Google Scholar 

  14. Zhu HW, Xu CL, Wu DH, Wei BQ, Vajtai R, Ajayan PM (2002) Science 296:884

    Article  CAS  Google Scholar 

  15. Ausman KD, Piner R, Lourie O, Rouff RS, Korobov M (2000) J Phys Chem B 104:8911

    Article  CAS  Google Scholar 

  16. Shaffer MS, Windle AH (1999) Adv Mater 11:937

    Article  CAS  Google Scholar 

  17. Qian D, Dickey EC, Andrews R, Rantell T (2000) Appl Phys Lett 76:2868

    Article  CAS  Google Scholar 

  18. Qian D, Dickey EC (2001) J Microsc 204:39

    Article  CAS  Google Scholar 

  19. Grimes CA, Dickey EC, Mungle C, Ong KG, Qian D (2001) J Appl Phys 90:4134

    Article  CAS  Google Scholar 

  20. Safadi B, Andrews R, Grulke EA (2002) J Appl Polym Sci 84:2660

    Article  CAS  Google Scholar 

  21. Pirlot C, Willems I, Fonseca A, Nagy JB, Delhalle J (2002) Adv Eng Mater 4:109

    Article  CAS  Google Scholar 

  22. Andrews R, Jacques D, Minot M, Randell T (2002) Macromol Mater Eng 287:395

    Article  CAS  Google Scholar 

  23. Potschke P, Fornes TD, Paul DR (2002) Polymer 43:3247

    Article  CAS  Google Scholar 

  24. Gong X, Liu J, Baskaran S, Voise RD, Young JS (2000) Chem Mater 12:1049

    Article  CAS  Google Scholar 

  25. Star A, Stoddart JF, Steuerman MD, Boukai A, Wong EW, Yang X, Chung S, Choi H, Heath JR (2001) Angew Chem Int Edn Engl 40:1721

    Article  CAS  Google Scholar 

  26. Viswanathan G, Chakrapani N, Yang H, Wei B, Chung H, Cho K, Ryu CY, Ajayan PM (2003) J Am Chem Soc 125:9258

    Article  CAS  Google Scholar 

  27. Wu W, Zhang S, Li Y, Li J, Liu L, Qin Y, Guo ZX, Dai L, Ye C, Zhu DB (2003) Macromolecules 36:6286

    Article  CAS  Google Scholar 

  28. Penumadu D, Dutta A, Pharr GM, Files B (2003) J Mater Res 18:1849

    Article  CAS  Google Scholar 

  29. Dutta AK, Penumadu D, Files B (2004) J Mater Res 19:158

    Article  CAS  Google Scholar 

  30. Grujicic M, Cao G, Roy WN (2004) Appl Surf Sci 227:349

    Article  CAS  Google Scholar 

  31. Grujicic M, Cao G, Roy WN (2004) J Mater Sci 39:2315

    Article  CAS  Google Scholar 

  32. Grujicic M, Sun Y-P, Koudela KL (2006) Appl Surf Sci (accepted for publication, March)

  33. Grujicic M (2006) Unpublished work. Clemson University

  34. Ashby MF (1992) Material selection in mechanical design, 3rd edn. Butterworth-Heinemann Oxford, United Kingdom

    Google Scholar 

  35. Haque A, Hossain MK (2003) J Compos Mater 37:647

    Google Scholar 

  36. Mori T, Tanaka K (1973) Acta Metall 21:571

    Article  Google Scholar 

  37. Mura T (1982) Micromechanics of defects in solids. Martinus Nijhoff, The Hague

    Book  Google Scholar 

  38. Qui YP, Weng GJ (1990) Inter J Eng Sci 28:1121

    Article  Google Scholar 

  39. Benveniste Y (1987) Mech Mater 6:147

    Article  Google Scholar 

  40. Eshelby JD (1957) Proc R Soc London Ser A 241A:376

    Google Scholar 

  41. Odegard GM, Gates TS, Wise KE, Park C, Siochi EJ (2003) Compos Sci Technol 63:1671

    Article  CAS  Google Scholar 

  42. Gruneisen E (1926) Handbuch der Physik. Springer-Verlag, Berlin

  43. AUTODYN-2D and 3D, Version 6.1. (2006) User documentation. Century Dynamics Inc

  44. Pandurangan B (2006) Ph.D. work in progress. Clemson University, April 2006

Download references

Acknowledgements

The material presented in this paper is based on work supported by the Naval Research Office ender the Grant Number N00014-05-1-0844, by the U.S. Army/Clemson University Cooperative Agreement Number W911NF-04-2-0024 and by the U.S. Army Grant Number DAAD19-01-1-0661. The authors are indebted to Dr. Tom Juska of the Naval Research Laboratory and to Drs. Walter Roy, Bryan Cheeseman and Fred Stanton from the Army Research Laboratory.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Clemson University, 241 Engineering Innovation Building, Clemson, SC, 29634-0921, USA

    Mica Grujicic & D. C. Angstadt

  2. Department of Chemistry, Clemson University, Clemson, SC, 29634, USA

    Y. P. Sun

  3. Applied Research Laboratory, Pennsylvania State University, 155, ARL Building, University Park, PA, 16802, USA

    K. L. Koudela

Authors
  1. Mica Grujicic
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. C. Angstadt
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Y. P. Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. K. L. Koudela
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mica Grujicic.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grujicic, M., Angstadt, D.C., Sun, Y.P. et al. Micro-mechanics based derivation of the materials constitutive relations for carbon-nanotube reinforced poly-vinyl-ester-epoxy based composites. J Mater Sci 42, 4609–4623 (2007). https://doi.org/10.1007/s10853-006-0520-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10853-006-0520-y

Keywords

Search

Navigation