A shear-lag model for carbon nanotube-reinforced polymer composites

International Journal of Solids and Structures

Volumn 42, Issue 5-6, 2005, Pages 1649-1667

  Gao, X L ^a   Li, K ^b  

^a Texas AandM University   (United States)

^b Michigan Technological University   (United States)

Author keywords

Carbon nanotube; Elasticity; Interfacial stress transfer; Molecular structural mechanics; Multiscale modeling; Nanocomposite; Polymer composite; Shear lag model

Indexed keywords

CARBON NANOTUBES; COMPUTATIONAL METHODS; ELASTIC MODULI; ELASTICITY; INTERFACES (MATERIALS); MATHEMATICAL MODELS; NANOSTRUCTURED MATERIALS; POLYMERS; STRESS ANALYSIS;

INTERFACIAL STRESS TRANSFER; MOLECULAR STRUCTURAL MECHANICS; MULTISCALE MODELING; POLYMER COMPOSITES; SHEAR-LAG MODELS;

COMPOSITE MATERIALS;

EID: 9944229469     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2004.08.020     Document Type: Article

References (45)

1. Ajayan, P.M., Schadler, L.S., Giannaris, C., Rubio, A., 2000. Single-walled carbon nanotube-polymer composites: strength and weakness. Adv. Mater. 12, 750-753.
2. Barber, A.H., Cohen, S.R., Wagner, H.D., 2003. Measurement of carbon nanotube-polymer interfacial strength. Appl. Phys. Lett. 82, 4140-4142.
3. Bower, C., Zhu, W., Jin, S., Zhou, O., 2000. Plasma-induced alignment of carbon nanotubes. Appl. Phys. Lett. 77, 830-832.
4. Chang, T., Gao, H., 2003. Size-dependent elastic properties of a single-walled carbon nanotube via a molecular mechanics model. J. Mech. Phys. Solids 51, 1059-1074.
5. Cooper, C.A., Ravich, D., Lips, D., Mayer, J., Wagner, H.D., 2002. Distribution and alignment of carbon nanotubes and nanofibrils in a polymer matrix. Compos. Sci. Technol. 62, 1105-1112.
6. Cox, H.L., 1952. The elasticity and strength of paper and other fibrous materials. Brit. J. Appl. Phys. 3, 72-79.
7. Frankland, S.J.V., Harik, V. M., 2003 Analysis of carbon nanotube pull-out from a polymer matrix Surf Sci 525, L103-L108.
8. Frankland, S.J.V., Caglar, A., Brenner, D.W., Griebel, M., 2002. Molecular simulation of the influence of chemical cross-links on the shear strength of carbon nanotube-polymer interfaces. J. Phys. Chem. B 106, 3046-3048.
9. Frankland, S.J.V., Harik, V.M., Odegard, G.M., Brenner, D.W., Gates, T.S., 2003. The stress-strain behavior of polymer-nanotube composites from molecular dynamics simulation. Compos. Sci. Technol. 63, 1655-1661.
10. Fujita, M., Saito, R., Dresselhaus, G., Dresselhaus, M.S., 1992. Formation of general fullerenes by their projection on a honeycomb lattice. Phys. Rev. B 45, 13834-13836.
11. Gao, X.-L., Li, K., 2003. Finite deformation continuum model for single-walled carbon nanotubes. Int. J. Solids Struct. 40, 7329-7337.
12. Glukhova, O.E., Zhbanov, A.I., Torgashov, I.G., Sinitsyn, N.I., Torgashov, G.V., 2003. Ponderomotive forces effect on the filed emission of carbon nanotube films. Appl. Surf. Sci. 215, 149-159.
13. Govindjee, S., Sackman, J.L., 1999. On the use of continuum mechanics to estimate the properties of nanotubes. Solid State Commun. 110, 227-230.
14. Haggenmueller, R., Gommans, H.H., Rinzler, A.G., Fischer, J.E., Winey, K.I., 2000. Aligned single-wall carbon nanotubes in composites by melt processing methods. Chem. Phys. Lett. 330, 219-225.
15. Harik, V.M., 2001. Ranges of applicability for the continuum beam model in the mechanics of carbon nanotubes and nanorods. Solid State Commun. 120, 331-335.
16. Harik, V.M., 2002. Mechanics of carbon nanotubes: applicability of the continuum-beam models. Comput. Mater. Sci. 24, 328-342.
17. Harris, P.J.F., 1999. Carbon Nanotubes and Related Structures. Cambridge University Press, Cambridge.
18. Li, C., Chou, T.-W., 2003a. A structural mechanics approach for the analysis of carbon nanotubes. Int. J. Solids Struct. 40, 2487-2499.
19. Li, C., Chou, T.-W., 2003b. Multiscale modeling of carbon nanotube reinforced polymer composites. J. Nanosci. Nanotech. 3, 1-8.
20. Li, K., Gao, X.-L., Roy, A.K., 2003. Micromechanical analysis of three-dimensional open-cell foams using the matrix method for space frame structures. In: Proceedings of the 14th International Conference on Composite Materials (ICCM-14), San Diego, CA, July 14-18, 2003.
21. Liao, K., Li, S., 2001. Interfacial characteristics of a carbon nanotube-polystyrene composite system. Appl. Phys. Lett. 79, 4225-4227.
22. Lilleodden, E.T., Zimmerman, J.A., Foiles, S.M., Nix, W.D., 2003. Atomistic simulations of elastic deformation and dislocation nucleation during nanoindentation. J. Mech. Phys. Solids 51, 901-920.
23. Liu, Y.J., Chen, X.L., 2003. Continuum models of carbon nanotube-based composites using the boundary element method. Electron. J. Bound. Elem. 1, 316-335.
24. Lordi, V., Yao, N., 2000. Molecular mechanics of binding in carbon-nanotube-polymer composites. J. Mater. Res. 15, 2770-2779.
25. Lourie, O., Cox, D.M., Wagner, H.D., 1998. Buckling and collapse of embedded carbon nanotubes. Phys. Rev. Lett. 81, 1638-1641.
26. Maruyama, B., Alam, K., 2002. Carbon nanotubes and nanofibers in composite materials. SAMPE J. 38 (3), 59-68.
27. McCartney, L.N., 1992. Analytical models of stress transfer in unidirectional composites and cross-ply laminates, and their application to the prediction of matrix/transverse cracking. In: Reddy, J.N., Reifsnider, K.L. (Eds.), Local Mechanics Concepts for Composite Material Systems, Proceedings of IUTAM Symposium, Blacksburg, VA, October 28-31, 1991. Springer-Verlag, Berlin, pp. 251-282.
28. Nairn, J.A., 1997. On the use of shear-lag methods for analysis of stress transfer in unidirectional composites. Mech. Mater. 26, 63-80.
29. Odegard, G.M., Gates, T.S., Nicholson, L.M., Wise, K.E., 2002. Equivalent-continuum modeling of nano-structured materials. Compos. Sci. Technol. 62, 1869-1880.
30. Pantano, A., Parks, D.M., Boyce, M.C., 2004. Mechanics of deformation of single- and multi-wall carbon nanotubes. J. Mech. Phys. Solids 52, 789-821.
31. Popov, V.N., Van Doren, V.E., Balkanski, M., 2000. Elastic properties of single-walled carbon nanotubes. Phys. Rev. B 61, 3078-3084.
32. Qian, D., Dickey, E.C., Andrews, R., Rantell, T., 2000. Load transfer and deformation mechanisms in carbon nanotube-polystyrene composites. Appl. Phys. Lett. 76, 2868-2870.
33. Ru, C.Q., 2000. Effective bending stiffness of carbon nanotubes. Phy. Rev. B 62, 9973-9976.
34. Saito, R., Fujita, M., Dresselhaus, G., Dresselhaus, M.S., 1992. Electronic structure of chiral graphene tubules. Appl. Phys. Lett. 60, 2204-2206.
35. Saito, R., Fujita, M., Dresselhaus, G., Dresselhaus, M.S., 1993. Electronic structure and growth mechanism of carbon tubules. Mater. Sci. Eng. B 19, 185-191.
36. Schadler, L.S., Giannaris, S.C., Ajayan, P.M., 1998. Load transfer in carbon nanotube epoxy composites. Appl. Phys. Lett. 73, 3842-3844.
37. Smith, G.E., Spencer, A.J.M., 1970. Interfacial tractions in a fibre-reinforced elastic composite material. J. Mech. Phys. Solids 18, 81-100.
38. Thostenson, E.T., Chou, T.-W., 2002. Aligned multi-walled carbon nanotube-reinforced composites: processing and mechanical characterization. J. Phys. D: Appl. Phys. 35, L77-L80.
39. Thostenson, E.T., Chou, T.-W., 2003. On the elastic properties of carbon nanotube-based composites: modeling and characterization. J. Phys. D: Appl. Phys. 36, 573-582.
40. Thostenson, E.T., Ren, Z., Chou, T.-W., 2001. Advances in the science and technology of carbon nanotubes and their composites: a review, Compos. Sci. Technol. 61, 1899-1912.
41. Wagner, H.D., 2002. Nanotube-polymer adhesion: a mechanics approach. Chem. Phys. Lett. 361, 57-61.
42. Wagner, H.D., Lourie, O., Feldman, Y., Tenne, R., 1998. Stress-induced fragmentation of multiwall carbon nanotubes in a polymer matrix. Appl. Phys. Lett. 72, 188-190.
43. Wu, Z.J., Ye, J.Q., Cabrera, J.G., 2000. 3D analysis of stress transfer in the micromechanics of fiber reinforced composites by using an eigen-function expansion method. J. Mech. Phys. Solids 48, 1037-1063.
44. Yao, N., Lordi, V., 1998. Carbon nanotube caps as springs: molecular dynamics simulations. Phys. Rev. B 58, 12649-12651.
45. Zhang, P., Huang, Y., Geubelle, P.H., Klein, P.A., Hwang, K.C., 2002. The elastic modulus of single-wall carbon nanotubes: a continuum analysis incorporating interatomic potentials. Int. J. Solids Struct. 39, 3893-3906.