Journal of Materials Science

, Volume 42, Issue 12, pp 4609–4623 | Cite as

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

  • Mica GrujicicEmail author
  • D. C. Angstadt
  • Y.  P. Sun
  • K.  L. Koudela


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.


Load Transfer Orientation Distribution Function Covalent Functionalization Reinforcement Volume Fraction Composite Armor 



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.


  1. 1.
    Zhu J, Kim J, Peng H, Margrave JL, Khabashesku VN, Barrera EV (2003) Nano Lett 3:1107CrossRefGoogle Scholar
  2. 2.
    Berber S, Kwon YK, Tomanek D (2000) Phys Rev Lett 84:4613CrossRefGoogle Scholar
  3. 3.
    Lourie O, Wagner HD (1998) J Mater Res 13:2418CrossRefGoogle Scholar
  4. 4.
    Walters DA, Ericson LM, Casavant MJ, Liu J, Colbert DT, Smith KA, Smalley RE (1999) Appl Phys Lett 74:3803CrossRefGoogle Scholar
  5. 5.
    Andrews R, Jacques D, Rao AM, Rantell T, Derbyshire F, Chen Y, Chen J, Haddon RC (1999) Appl Phys Lett 75:1329CrossRefGoogle Scholar
  6. 6.
    Mamedov AA, Kotov NA, Prato M, Guldi DM, Wicksted JP, Hirsch A (2002) Nat Mater 1:190CrossRefGoogle Scholar
  7. 7.
    Salvetat JP, Briggs GAD, Bonard JM, Bacsa RR, Kulik AJ, Stockli T, Burnham NA, Forro L (1999) Phys Rev Lett 82:944CrossRefGoogle Scholar
  8. 8.
    Chen J (2001) J Phys Chem B 105:2525CrossRefGoogle Scholar
  9. 9.
    Frankland SJV, Caglar A, Brenner DW, Griebel M (2002) J Phys Chem B 106:3046CrossRefGoogle Scholar
  10. 10.
    Watts PCP, Hsu WK, Chen GZ, Fray DJ, Kroto HW, Walton DRM (2001) J Mater Chem 11:2482CrossRefGoogle Scholar
  11. 11.
    Kis A, Csanyi G, Salvetat J-P, Lee T-N, Couteau E, Kulik AJ, Benoit W, Brugger J, Forro L (2004) Nat Mater 3:153CrossRefGoogle Scholar
  12. 12.
    Thess A (1996) Science 273:483CrossRefGoogle Scholar
  13. 13.
    Dalton AB, Collins S, Munoz E, Razal JM, Ebron VH, Ferraris JP, Coleman JN, Kim BG, Baughman RH (2003) Nature 423:703CrossRefGoogle Scholar
  14. 14.
    Zhu HW, Xu CL, Wu DH, Wei BQ, Vajtai R, Ajayan PM (2002) Science 296:884CrossRefGoogle Scholar
  15. 15.
    Ausman KD, Piner R, Lourie O, Rouff RS, Korobov M (2000) J Phys Chem B 104:8911CrossRefGoogle Scholar
  16. 16.
    Shaffer MS, Windle AH (1999) Adv Mater 11:937CrossRefGoogle Scholar
  17. 17.
    Qian D, Dickey EC, Andrews R, Rantell T (2000) Appl Phys Lett 76:2868CrossRefGoogle Scholar
  18. 18.
    Qian D, Dickey EC (2001) J Microsc 204:39CrossRefGoogle Scholar
  19. 19.
    Grimes CA, Dickey EC, Mungle C, Ong KG, Qian D (2001) J Appl Phys 90:4134CrossRefGoogle Scholar
  20. 20.
    Safadi B, Andrews R, Grulke EA (2002) J Appl Polym Sci 84:2660CrossRefGoogle Scholar
  21. 21.
    Pirlot C, Willems I, Fonseca A, Nagy JB, Delhalle J (2002) Adv Eng Mater 4:109CrossRefGoogle Scholar
  22. 22.
    Andrews R, Jacques D, Minot M, Randell T (2002) Macromol Mater Eng 287:395CrossRefGoogle Scholar
  23. 23.
    Potschke P, Fornes TD, Paul DR (2002) Polymer 43:3247CrossRefGoogle Scholar
  24. 24.
    Gong X, Liu J, Baskaran S, Voise RD, Young JS (2000) Chem Mater 12:1049CrossRefGoogle Scholar
  25. 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 40:1721CrossRefGoogle Scholar
  26. 26.
    Viswanathan G, Chakrapani N, Yang H, Wei B, Chung H, Cho K, Ryu CY, Ajayan PM (2003) J Am Chem Soc 125:9258CrossRefGoogle Scholar
  27. 27.
    Wu W, Zhang S, Li Y, Li J, Liu L, Qin Y, Guo ZX, Dai L, Ye C, Zhu DB (2003) Macromolecules 36:6286CrossRefGoogle Scholar
  28. 28.
    Penumadu D, Dutta A, Pharr GM, Files B (2003) J Mater Res 18:1849CrossRefGoogle Scholar
  29. 29.
    Dutta AK, Penumadu D, Files B (2004) J Mater Res 19:158CrossRefGoogle Scholar
  30. 30.
    Grujicic M, Cao G, Roy WN (2004) Appl Surf Sci 227:349CrossRefGoogle Scholar
  31. 31.
    Grujicic M, Cao G, Roy WN (2004) J Mater Sci 39:2315CrossRefGoogle Scholar
  32. 32.
    Grujicic M, Sun Y-P, Koudela KL (2006) Appl Surf Sci (accepted for publication, March)Google Scholar
  33. 33.
    Grujicic M (2006) Unpublished work. Clemson UniversityGoogle Scholar
  34. 34.
    Ashby MF (1992) Material selection in mechanical design, 3rd edn. Butterworth-Heinemann Oxford, United KingdomGoogle Scholar
  35. 35.
    Haque A, Hossain MK (2003) J Compos Mater 37:647Google Scholar
  36. 36.
    Mori T, Tanaka K (1973) Acta Metall 21:571CrossRefGoogle Scholar
  37. 37.
    Mura T (1982) Micromechanics of defects in solids. Martinus Nijhoff, The HagueCrossRefGoogle Scholar
  38. 38.
    Qui YP, Weng GJ (1990) Inter J Eng Sci 28:1121CrossRefGoogle Scholar
  39. 39.
    Benveniste Y (1987) Mech Mater 6:147CrossRefGoogle Scholar
  40. 40.
    Eshelby JD (1957) Proc R Soc London Ser A 241A:376Google Scholar
  41. 41.
    Odegard GM, Gates TS, Wise KE, Park C, Siochi EJ (2003) Compos Sci Technol 63:1671CrossRefGoogle Scholar
  42. 42.
    Gruneisen E (1926) Handbuch der Physik. Springer-Verlag, BerlinGoogle Scholar
  43. 43.
    AUTODYN-2D and 3D, Version 6.1. (2006) User documentation. Century Dynamics IncGoogle Scholar
  44. 44.
    Pandurangan B (2006) Ph.D. work in progress. Clemson University, April 2006Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Mica Grujicic
    • 1
    Email author
  • D. C. Angstadt
    • 1
  • Y.  P. Sun
    • 2
  • K.  L. Koudela
    • 3
  1. 1.Department of Mechanical EngineeringClemson UniversityClemsonUSA
  2. 2.Department of ChemistryClemson UniversityClemsonUSA
  3. 3.Applied Research LaboratoryPennsylvania State UniversityUniversity ParkUSA

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