A hybrid numerical-analytical method for modeling the viscoelastic properties of polymer nanocomposites

Journal of Applied Mechanics, Transactions ASME

Volumn 73, Issue 5, 2006, Pages 758-768

  Liu, Hua ^a   Catherine Brinson, L ^a  

^a Northwestern University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CERAMIC MATRIX NANOCOMPOSITES; NANOPLATELETS; POLYMER NANOCOMPOSITES; VISCOELASTIC RESPONSE;

COMPOSITE MICROMECHANICS; COSTS; FILLERS; FINITE ELEMENT METHOD; NANOTUBES; POLYMERS; VISCOELASTICITY;

NANOSTRUCTURED MATERIALS;

EID: 33748424008     PISSN: 00218936     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2204961     Document Type: Conference Paper

References (66)

1. Schadler, L. S., 2003, "Polymer-Based and Polymer-Filled Nanocomposites," Nanocomposite Science and Technology, P. M. Ajayan, L. S. Schadler, and P. V. Braun, eds., Wiley, New York, p. 71-153.
2. Ramanathan, T., Liu, H., and Brinson, L. C., 2005, "Functionalized SWNT Polymer Nanocomposites for Dramatic Property Improvement," J. Polym. Sci., Part B: Polym. Phys., 43(17), pp. 2269-2279.
3. Ramanathan, T., Stankovich, S., Dikin, D. A., Liu, H., Shen, H., Nguyen, S. T., and Brinson, L. C., 2006, "An Investigation of Particle Size and Dispersion and Their Influence on Graphite/PMMA Nanocomposites Properties," J. Polym. Sci., Part B: Polym. Phys. (submitted).
4. Kasimatis, K. G., and Torkelson, J. M., 2004, "Well-Exfoliated, Kinetically Stable Polypropylene-Clay Nanocomposites Made by Solid-State Shear Pulverization," Abstracts of Papers of the American Chemical Society, 228 U429-U429 96-PMSE Part 2.
5. Curran, S. A., Coleman, J. N., Dalton, A. B., Davey, A. P., Drury, A., and McCarthy, B., 1998, "A Composite From Poly(m-phenylenevinylene-co-2, 5-dioctoxy-p-phenylenevinylene) and Carbon Nanotubes: A Novel Material for Molecular Optoelectronics," Adv. Mater. (Weinheim, Ger.), 10(14), pp. 1091-1093.
6. Muzny, C. D., Butler, B. D., Hanley, H. J. M., Tsvetkov, F., and Peiffer, D. G., 1996, "Clay Platelet Dispersion in a Polymer Matrix," Mater. Lett., 28(4-6), pp. 379-384.
7. Mack, J. J., Viculus, L. M., Ali, A., Luoh, R., Yang, G., Hahn, H. T., Ko, F. K., and Kaner, R. B., 2005, "Graphite Nanoplatelet Reinforcement of Electrospun Polyacrylonitrile Nanofibers," Adv. Mater. (Weinheim, Ger.), 17(1), pp. 77-80.
8. Sandler, J. K. W., Shaffer, M. S. P., Prasse, T., Bauhofer, W. K., and Windle, A. H., 1999, "Development of a Dispersion Process for Carbon Nanotubes in an Epoxy Matrix and the Resulting Electrical Properties," Polymer, 40(21), pp. 5967-5971.
9. Sandler, J. K. W., Kirk, J. E., Kinloch, I. A., Shaffer, M. S. P., and Windle, A. H., 2003, "Ultra-Low Electrical Percolation Threshold in Carbon-Nanotube-Epoxy Composites," Polymer, 44(19), pp. 5893-5899.
10. Sandler, J. K., W., 2004, "A Comparative Study of Melt Spun Polyamide-12 Fibres Reinforced With Carbon Nanotubes and Nanofibres," Polymer, 45(6), pp. 2001-2015.
11. Coleman, J. N., Cadek, M., Blake, R., Nicolosi, V., Ryan, K. P., Belton, C., Fonseca, A., Nagy, I. B., Gun'ko, Y. K., and Blau, W. J., 2004, "High-Performance Nanotube-Reinforced Plastics: Understanding the Mechanism of Strength Increase," Adv. Funct. Mater., 14(8), pp. 791-798.
12. Dalton, A. B., Collins, S., Munoz, E., Razal, J. M., Ebron, V. H., Ferraris, J. P., Coleman, J. N., Kim, B. G., and Boughman, R. H., 2003, "Super-Tough Carbon-Nanotube Fibres: These Extraordinary Composite Fibres Can Be Woven Inlo Electronic Textiles," Nature (London), 423(6941), p. 703.
13. Cadek, M., Coleman, J. N., Barron, V., Hedicke, K., and Blau, W. J., 2002, "Morphological and Mechanical Properties of Carbon-Nanotube- Reinforced Semicrystalline and Amorphous Polymer Composites," Appl. Phys. Lett., 81(27), pp. 5123-5125.
14. Kilbride, B. E., Coleman, J. N., Fraysse, J., Fournet, P., Cadek, M., Drury, A., Hutzler, S., Roth, S., and Blau, W. J., 2002, "Experimental Observation of Scaling Laws for Alternating Current and Direct Current Conductivity in Polymer-Carbon Nanotube Composite Thin Films," J. Appl. Phys., 92(7), pp. 4024-4030.
15. Biercuk, M. J., Llaguno, M. C., Radosavljevic, M., Hyun, J. K., Johnson, A. T., and Fischer, J. E., 2002, "Carbon Nanotube Composites for Thermal Management," Appl. Phys. Lett., 80(15), pp. 2767-2769.
16. Wei, C. Y., Shrivastava, D., and Choi, K., 2002, "Thermal Expansion and Diffusion Coefficients of Carbon Nanotube-Polymer Composites," Nano Lett., 2(6), pp. 647-650.
17. Lim, S. K., 2002, "Preparation and Interaction Characteristics of Organically Modified Montmorillonite Nanocomposite With Miscible Polymer Blend of Poly(Ethylene Oxide) and Poly(methyl Methacrylate)," Chem. Mater., 14(5), pp. 1989-1994.
18. Hyun, Y. H., Lim, S. T., Choi, H. J., and Jhon, M. S., 2001, "Rheology of Polyfethylene Oxide)/Organoclay Nanocomposites," Macromolecules, 34(23), pp. 8084-8093.
19. Messersmith, P. B., and Glannelis, E. P., 1995, "Synthesis and Barrier Properties of Poly(epsilon-Caprolactone)-Layered Silicate Nanocomposites," J. Polym. Sci., Part A: Polym. Chem., 33(7), pp. 1047-1057.
20. Messersmith, P. B., and Giannelis, E. P., 1994, "Synthesis and Characterization of Layered Silicate-Epoxy Nanocomposites," Chem. Mater., 6(10), pp. 1719-1725.
21. Coleman, J. N., Curran, S., Dalton, A. B., Davey, A. P., McCarthy, B., Blau, W., and Barklie, R. C., 1998, "Percolation-Dominated Conductivity in a Conjugated-Polymer-Carbon-Nanotube Composite," Phys. Rev. B, 58(12), pp. R7492-R7495.
22. Putz, K. W., Mitchell, C. A., Krishnamoorti, R., and Green, P. F., 2004, "Bias tic Modulus of Single-Walled Carbon Nanotube/Poly(Melhyl Methacrylate) Nanocomposites." J. Polym. Sci., Part A: Polym. Chem., 42(12), pp. 2286-2293.
23. Fisher, F. T., Eitan, A., Andrews, R., Sehadler, L. S., and Brinson, L. C., 2004, "Spectral Response and Effective Viscoelastic Properties of MWNT-Reinforced Polycarbonate." Adv. Compos. Lett., 13(2), pp. 105-111.
24. Cox, H. L., 1952, "The Elasticity and Strength of Paper and Other Fibrous Materials," Br. J. Appl. Phys., 3, pp. 72-78.
25. Wagner, H. D. Lourie, O. Feldman, Y., and Tenne, R., 1998, "Stress-Induced Fragmentation of Multiwall Carbon Nanotubes in a Polymer Matrix," Appl. Phys. Lett., 72(2), pp. 188-190.
26. Cooper, C. A., Cohen, S. R., Barber, A. H., and Wagner, H. D., 2002, "Detachment of Nanotubes From a Polymer Matrix," Appl. Phys. Lett., 81(20), pp. 3873-3875.
27. Frankland, S. J. V., Caglar, A., Brenner, D. W., and 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( 12), pp. 3046-3048.
28. Frankland, S. J. V., and Harik, V. M., 2003, "Analysis of Carbon Nanotube Pull-Out From a Polymer Matrix," Surf. Sci., 525(1-3), pp. L103-L108.
29. Liao, K., and Li, S., 2001, "Interfacial Characteristics of a Carbon Nanotube-Polystyrene Composite System," Appl. Phys. Lett., 79(25), pp. 4225-4227.
30. Wong, M., Paramsothy, M., Xu, X. J., Ren, Y., Li, S., and Liao, K., 2003, "Physical Interactions at Carbon Nanotube-Polymer Interface." Polymer. 44(25), pp. 7757-7764.
31. Wagner, H. D., 2002, "Nanotube-Polymer Adhesion: A Mechanics Approach," Chem. Phys. Lett. 361(1-2), pp. 57-61.
32. Schadler, L. S., Giannaris, S. C., and Ajayan, P. M., 1998, "Load Transfer in Carbon Nanotube Epoxy Composites," Appl. Phys. Lett. 73(26), pp. 3842-3844.
33. Ajayan, P. M., Schadler, L. S., Giannaris, C., and Rubio, A., 2000, "Single-Walled Carbon Nanotube-Polymer Composites: Strength and Weakness," Adv. Mater. (Weinheim, Ger.), 12(10), pp. 750-753.
34. Thomason, J. L., 1995, "The Interface Region in Glass Fibre-Reinforced Epoxy Resin Composites: 3. Characterization of Fibre Surface Coatings and the Interphase," Composites, 26, pp. 487-498.
35. Mai, K., Mader, E., and NMuhle, M., 1998, "Interphase Characterization in Composites With New Non-Destructive Methods," Composites, Part A. 29A, pp. 1111-1119.
36. Starr, F. W., Schroder, T. B., and Glotzer, S. C., 2002, "Molecular Dynamics Simulation of a Polymer Melt With a Nanoscopic Particle," Macromolecules, 35(11), 4481-4492.
37. Starr, F. W., Schroder, T. B., and Glotzer, S. C., 2001, "Effects of a Nanoscopic Filler on the Structure and Dynamics of a Simulated Polymer Melt and the Relationship to Ultrathin Films," Phys. Rev. E, 64(2), p. 021802.
38. Smith, G. D., Bedrov, D., Li, L. W., and Byutner, O., 2002, "A Molecular Dynamics Simulation Study of the Viscoelastic Properties of Polymer Nanocomposites," J. Chem. Phys., 117(20), pp. 9478-9489.
39. Brune, D. A., and Bicerano, J., 2002, "Micromechanics of Nanocomposites: Comparison of Tensile and Compressive Elastic Moduli, and Prediction of Effects of Incomplete Exfoliation and Imperfect Alignment on Modulus," Polymer, 43(2), pp. 369-387.
40. Sheng, N., Boyce, M. C., Parks, D. M., Rutledge, G. C., Abes, J. I., and Cohen, R. E., 2004, "Multiscale Micromechanical Modeling of Polymer/Clay Nanocomposites and the Effective Clay Particle," Polymer. 45(2), pp. 487-506.
41. Frogley, M. D., Ravich, D., and Wagner, H. D., 2003. "Mechanical Properties of Carbon Nanoparticle-Reinforced Elastomers," Compos. Sci. Technol., 63(11), pp. 1647-1654.
42. Shia, D., Hui, C. Y., Burnside, S. D., and Giannelis, E. P., 1998, "An Interface Model for the Prediction of Young's Modulus of Layered Silicate-Elastomer Nanocomposites," Polym. Compos., 19(5), pp. 608-617.
43. Fisher, F. T., Bradshaw, R. D., and Brinson, L. C., 2003, "Fiber Waviness in Nanotube-Reinforced Polymer Composites-1: Modulus Predictions Using Effective Nanotube Properties," Compos. Sci. Technol., 63(11), pp. 1689-1703.
44. Luo, J. J., and Daniel, I. M., 2003, "Characterization and Modeling of Mechanical Behavior of Polymer/Clay Nanocomposites," Compos. Sci. Technol. 63(11), pp. 1607-1616.
45. Liu, Y.J., and Chen, X. L., 2003, "Evaluations of the Effective Material Properties of Carbon Nanolube-Based Composites Using a Nanoscale Representative Volume Element," Mech. Mater., 35(1-2), pp. 69-81.
46. Chen, X. L., and Liu, Y. J., 2004, "Square Representative Volume Elements for Evaluating the Effective Material Properties of Carbon Nanotube-Based Composites," Comput. Mater. Sci., 29(1), pp. 1-11.
47. Li, C. Y., and Chou, T. W., 2003, "Multiscale Modeling of Carbon Nanotube Reinforced Polymer Composites," J. Nanosci. Nanotechnol. 3(5), pp. 423-430.
48. Li, C. Y. and Chou, T. W., 2004, "Modeling of Elastic Buckling of Carbon Nanotubes by Molecular Structural Mechanics Approach," Mech. Mater. 36(11), pp. 1047-1055.
49. Miller, R. E., and Tadmor, E. B., 2002, "The Quasicontinuum Method: Overview, Applications and Current Directions," J. Comput.-Aided Mater. Des., 9(3), pp. 203-239.
50. Mon, T., and Tanaka, K., 1973, "Average Stress in Matrix and Average Elastic Energy of Materials With Misfitting Inclusions," Acta Metall., 21, pp. 571-574.
51. Eshelby, J. D., 1957, "The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems," Proc. Phys. Soc. London, Sect. A. 241(1226), pp. 376-396.
52. Eshelby, J. D., 1961, "Elastic Inclusions and Inhomogeneities," Progress in Solid Mechanics, Vol. 2, I. N. Sneddon and R. Hills, eds. North-Holland, Amsterdam, pp. 89-140.
53. Benveniste, Y., 1987, "A New Approach to the Application of Mori-Tanaka Theory in Composite-Materials," Mech. Mater., 6(2), pp. 147-157.
54. Tandon, G. P., and Weng, G. J., 1986, "Average Stress in the Matrix and Effective Moduli of Randomly Orientated Composites." Compos. Sci. Technol., 27, pp. 111-132.
55. Hill, R., 1963, "Elastic Properties of Reinforced Solid: Some Theoretical Principles," J. Mech. Phys. Solids, 11(5), pp. 357-372.
56. Hashin, Z., 1965, "Viscoelastic Behavior of Heterogeneous Media," ASME J. Appl. Mech., 32(3), pp. 630-636.
57. Wang, Y. M., and Weng, G. J., 1992, "The Influence of Inclusion Shape on the Overall Viscoelastic Behavior of Composites," ASME J. Appl. Mech. 59(3), pp. 510-518.
58. Mura, T., 1982. Micromechanics of Defects in Solids, Kluwer, Dordrecht.
59. Yasmin, A., Abot, J. L., and Daniel, I. M., 2003, "Processing of Clay/Epoxy Nanocomposites by Shear Mixing," Ser. Mater. 49(1), pp. 81-86.
60. Bradshaw, R. D., Fisher, F. T., and Brinson, L. C., 2003, "Fiber Waviness in Nanotube-Reinforced Polymer Composites-11: Modeling via Numerical Approximation of the Dilute Strain Concentration Tensor." Compos. Sci. Technol. 63(11), pp. 1705-1722.
61. Park, C. H., Kim, J. H., Ree, M., Sohn, B. H., Jung, J. C., and Zin, W. C., 2004, "Thickness and Composition Dependence of the Glass Transition Temperature in Thin Random Copolymer Films," Polymer, 45(13), pp. 4507-4513.
62. Ellison, C. J., and Torkelson, J. M., 2003, "The Distribution of Glass-Transition Temperatures in Nanoscopically Confined Glass Formers," Nat. Mater., 2(10), pp. 695-700.
63. Ding, W., Eitan, A., Fisher, F. T., Chen, X., Dikin, D. A., Andrews, R., Brinson, L. C., Schadler, L. S., and Ruoff, R. S., 2003, "Direct Observation of Polymer Sheathing in Carbon Nanotube-Polycarbonate Composites," Nano Lett., 3(11), pp. 1593-1597.
64. Shodja, H. M., and Sarvestani, A. S., 2001, "Elastic Fields in Double Inhomogeneity by the Equivalent Inclusion Method," ASME J. Appl. Mech., 68(1), pp. 3-10.
65. Sarvestani, A. S., 2003, "On the Overall Elastic Moduli of Composites With Spherical Coated Fillers," Int. J. Solids Struct., 40(26), pp. 7553-7566.
66. Bradshaw, R. D., and Brinson, L. C., 1997, "A Sign Control Method for Fitting and Interconverting Material Functions for Linearly Viscoelastic Materials," Mech. Time-Depend, Mater., 1, pp. 85-108.