DOI QR코드

DOI QR Code

Elastic properties of CNT- and graphene-reinforced nanocomposites using RVE

  • Kumar, Dinesh (Mechanical Engineering Department, Malaviya National Institute of Technology) ;
  • Srivastava, Ashish (Mechanical Engineering Department, Malaviya National Institute of Technology)
  • 투고 : 2015.05.25
  • 심사 : 2016.07.25
  • 발행 : 2016.08.10

초록

The present paper is aimed to evaluate and compare the effective elastic properties of CNT- and graphene-based nanocomposites using 3-D nanoscale representative volume element (RVE) based on continuum mechanics using finite element method (FEM). Different periodic displacement boundary conditions are applied to the FEM model of the RVE to evaluate various elastic constants. The effects of the matrix material, the volume fraction and the length of reinforcements on the elastic properties are also studied. Results predicted are validated with the analytical and/or semiempirical results and the available results in the literature. Although all elastic stiffness properties of CNT- and graphene-based nanocomposites are found to be improved compared to the matrix material, but out-of-plane and in-plane stiffness properties are better improved in CNT- and graphene-based nanocomposites, respectively. It is also concluded that long nanofillers (graphene as well as CNT) are more effective in increasing the normal elastic moduli of the resulting nanocomposites as compared to the short length, but the values of shear moduli, except $G_{23}$ of CNT nanocomposite, of nanocomposites are slightly improved in the case of short length nanofillers (i.e., CNT and graphene).

키워드

과제정보

연구 과제 주관 기관 : Material Research Centre (MRC), Malaviya National Institute of Technology (MNIT)

참고문헌

  1. Al-Ostaz, A., Pal, G., Mantena, P.R. and Cheng, A. (2008), "Molecular dynamics simulation of SWCNT-polymer nanocomposite and its constituents", J. Mater. Sci., 43(1), 164-173. https://doi.org/10.1007/s10853-007-2132-6
  2. Arash, B., Park, H.S. and Rabczuk, T. (2015), "Tensile fracture behavior of short carbon nanotube reinforced polymer composites: A coarse-grained model", Compos. Struct., 134, 981-988. https://doi.org/10.1016/j.compstruct.2015.09.001
  3. Arash, B., Park, H.S. and Rabczuk, T. (2016), "Coarse-grained model of the J-integral of carbon nanotube reinforced polymer composites", Carbon, 96, 1084-1092. https://doi.org/10.1016/j.carbon.2015.10.058
  4. Aydogdu, M. (2014), "On the vibration of aligned carbon nanotube reinforced composite beams", Adv. Nano Res., Int. J., 2(4), 199-210. https://doi.org/10.12989/anr.2014.2.4.199
  5. Besseghier, A., Heireche, H., Bousahla, A.A., Tounsi, A. and Benzair, A. (2015), "Nonlinear vibration properties of a zigzag single-walled carbon nanotube embedded in a polymer matrix", Adv. Nano Res., Int. J., 3(1), 29-37. https://doi.org/10.12989/anr.2015.3.1.029
  6. Bower, C., Rosen, R., Jin, L., Han, J. and Zhou, O. (1999), "Deformation of carbon nanotubes in nanotube-polymer composites", Appl. Phys. Lett., 74(22), 3317-3319. https://doi.org/10.1063/1.123330
  7. Bu, H., Chen, Y., Zou, M., Yi, H., Bi, K. and Ni, Z. (2009), "Atomistic simulations of mechanical properties of graphene nanoribbons", Phys. Lett. A, 373(37), 3359-3362. https://doi.org/10.1016/j.physleta.2009.07.048
  8. 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), 1-11. https://doi.org/10.1016/S0927-0256(03)00090-9
  9. Cho, J. and Sun, C.T. (2007), "A molecular dynamics simulation study of inclusion size effect on polymeric nanocomposites", Comput. Mater. Sci., 41(4), 54-62. https://doi.org/10.1016/j.commatsci.2007.03.001
  10. Coleman, J.N., Khan, U., Blau, W.J. and Gun‟ko, Y.K. (2006), "Small but strong: A review of the mechanical properties of carbon nanotube-polymer composites", Carbon, 44(9), 1624-1652. https://doi.org/10.1016/j.carbon.2006.02.038
  11. Geim, A.K. and Novoselov, K.S. (2007), "The rise of graphene", Nature, 6(3), 183-191. https://doi.org/10.1038/nmat1849
  12. Ghasemi, H., Rafiee, R., Zhuang, X., Muthu, J. and Rabczuk, T. (2014), "Uncertainties propagation in metamodel-based probabilistic optimization of CNT/polymer composite structure using stochastic multiscale modeling", Comput. Mater. Sci., 85, 295-305. https://doi.org/10.1016/j.commatsci.2014.01.020
  13. Ghasemi, H., Brighenti, R., Zhuang, X., Muthu, J. and Rabczuk, T. (2015), "Optimal fiber content and distribution in fiber-reinforced solids using a reliability and NURBS based sequential optimization approach", Struct. Multidiscip. Optim., 51(1), 99-112. https://doi.org/10.1007/s00158-014-1114-y
  14. Halpin, J.C. (1969), "Effects of environmental factors on composite materials", Technical Report; Air Force Mater. Lab Wright-Patterson AFB OH.
  15. Hyer, M.W. (1998), Stress Analysis of Fiber-Reinforced Composite Materials, McGraw-Hill, Boston, MA, USA.
  16. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(6348), 56-58. https://doi.org/10.1038/354056a0
  17. Joshi, P. and Upadhyay, S.H. (2014), "Evaluation of elastic properties of multi walled carbon nanotube reinforced composite", Comput. Mater. Sci., 81, 332-338. https://doi.org/10.1016/j.commatsci.2013.08.034
  18. Joshi, U.A., Sharma, S.C. and Harsha, S.P. (2011), "Analysis of elastic properties of carbon nanotube reinforced nanocomposites with pinhole defects", Comput. Mater. Sci., 50(11), 3245-3256. https://doi.org/10.1016/j.commatsci.2011.06.011
  19. Kim, H. and Macosko, C.W. (2009), "Processing-property relationships of polycarbonate/graphene composites", Polymer, 50(15), 3797-3809. https://doi.org/10.1016/j.polymer.2009.05.038
  20. Kondo, D., Sato, S. and Awano, Y. (2008), "Self-organization of novel carbon composite structure: Graphene multi-layers combined perpendicularly with aligned carbon nanotubes", Appl. Phys. Express., 1(7), 0740031-0740033.
  21. Kuilla, T., Bhadra, S., Yao, D., Kim, N.H., Bose, S. and Lee, J.H. (2010), "Recent advances in graphene based polymer composites", Prog. Polym. Sci., 35(11), 1350-1375. https://doi.org/10.1016/j.progpolymsci.2010.07.005
  22. Laurent, C., Flahaut, E. and Peigney, A. (2010), "The weight and density of carbon nanotubes versus the number of walls and diameter", Carbon, 48(10), 2994-2996. https://doi.org/10.1016/j.carbon.2010.04.010
  23. Li, C. and Chou, T.-W. (2009), "Failure of carbon nanotube/polymer composites and the effect of nanotube waviness", Compos. Part A: Appl. Sci. Manuf., 40(10), 1580-1586. https://doi.org/10.1016/j.compositesa.2009.07.002
  24. Liu, Y.J. and Chen, X.L. (2003a), "Continuum models of carbon nanotube-based composites using the boundary element method", Electron. J. Bound. Elem., 1(2), 316-335.
  25. Liu, Y.J. and Chen, X.L. (2003b), "Evaluations of the effective material properties of carbon nanotube-based composites using a nanoscale representative volume element", Mech. Mater., 35(1-2), 69-81. https://doi.org/10.1016/S0167-6636(02)00200-4
  26. Mousavi, A.A., Arash, B., Zhuang, X. and Rabczuk, T. (2016), "A coarse-grained model for the elastic properties of cross linked short carbon nanotube/polymer composites", Compos. Part B: Eng., 95, 404-411. https://doi.org/10.1016/j.compositesb.2016.03.044
  27. Potts, J.R., Dreyer, D.R., Bielawski, C.W. and Ruoff, R.S. (2011), "Graphene-based polymer nanocomposites", Polymer, 52(1), 5-25. https://doi.org/10.1016/j.polymer.2010.11.042
  28. Qian, D., Dickey, E.C., Andrews, R. and Rantell, T. (2000), "Load transfer and deformation mechanisms in carbon nanotube-polystyrene composites", Appl. Phys. Lett., 76(20), 2868-2870. https://doi.org/10.1063/1.126500
  29. Reith, D., Meyer, H. and Muller-Plathe, F. (2001), "Mapping atomistic to coarse-grained polymer models using automatic simplex optimization to fit structural properties", Macromolecules, 34(7), 2335-2345. https://doi.org/10.1021/ma001499k
  30. Reith, D., Putz, M. and Mller-Plathe, F. (2003), "Deriving effective mesoscale potentials from atomistic simulations", J. Comput. Chem., 24(13), 1624-1636. https://doi.org/10.1002/jcc.10307
  31. Ru, C.Q. (2001), "Axially compressed buckling of a doublewalled carbon nanotube embedded in an elastic medium", J. Mech. Phys. Solids, 49(6), 1265-1279. https://doi.org/10.1016/S0022-5096(00)00079-X
  32. Ruoff, R.S., Qian, D. and Liu, W.K. (2003), "Mechanical properties of carbon nanotubes: theoretical predictions and experimental measurements", Comptes. Rendus. Phys., 4(9), 993-1008. https://doi.org/10.1016/j.crhy.2003.08.001
  33. Rzepiela, A.J., Louhivuori, M., Peter, C. and Marrink, S.J. (2011), "Hybrid simulations: combining atomistic and coarse-grained force fields using virtual sites", Phys. Chem. Chem. Phys., 13(22), 10437-10448. https://doi.org/10.1039/c0cp02981e
  34. Sakhaee-Pour, A. (2009), "Elastic properties of single-layered graphene sheet", Solid State Commun., 149(1-2), 91-95. https://doi.org/10.1016/j.ssc.2008.09.050
  35. Salvetat, J.-P., Briggs, G. and Bonard, J.-M. (1999), "Elastic and shear moduli of single-walled carbon nanotube ropes", Phys. Rev. Lett., 82(5), 944-947. https://doi.org/10.1103/PhysRevLett.82.944
  36. Sears, A. and Batra, R.C. (2004), "Macroscopic properties of carbon nanotubes from molecular-mechanics simulations", Phys. Rev. B, 69(23), 235406. https://doi.org/10.1103/PhysRevB.69.235406
  37. Segurado, J., Gonzalez, C. and LLorca, J. (2003), "A numerical investigation of the effect of particle clustering on the mechanical properties of composites", Acta Mater., 51(8), 2355-2369. https://doi.org/10.1016/S1359-6454(03)00043-0
  38. Semmah, A., Beg, O.A., Mahmoud, S.R., Heireche, H. and Tounsi, A. (2014), "Thermal buckling properties of zigzag single-walled carbon nanotubes using a refined nonlocal model", Adv. Mater. Res., Int. J., 3(2), 77-89.
  39. Shokrieh, M.M. and Rafiee, R. (2010a), "Prediction of Young‟s modulus of graphene sheets and carbon nanotubes using nanoscale continuum mechanics approach", Mater. Des., 31(2), 790-795. https://doi.org/10.1016/j.matdes.2009.07.058
  40. Shokrieh, M.M. and Rafiee, R. (2010b), "On the tensile behavior of an embedded carbon nanotube in polymer matrix with non-bonded interphase region", Compos. Struct., 92(3), 647-652. https://doi.org/10.1016/j.compstruct.2009.09.033
  41. Silani, M., Ziaei-Rad, S., Talebi, H. and Rabczuk, T. (2014), "A semi-concurrent multiscale approach for modeling damage in nanocomposites", Theor. Appl. Fract. Mech., 74, 30-38. https://doi.org/10.1016/j.tafmec.2014.06.009
  42. Sohlberg, K., Sumpter, B.G., Tuzun, R.E. and Noid, D.W. (1998), "Continuum methods of mechanics as a simplified approach to structural engineering of nanostructures", Nanotechnology, 9(1), 30-36. https://doi.org/10.1088/0957-4484/9/1/004
  43. Stankovich, S., Dikin, D.A., Dommett, G.H.B., Kohlhaas, K.M., Zimney, E.J., Stach, E.A., Piner, R.D., Nguyen, S.T. and Ruoff, R.S. (2006), "Graphene-based composite materials", Nature, 442(7100), 282-286. https://doi.org/10.1038/nature04969
  44. Sun, C.T. and Vaidya, R.S. (1996), "Prediction of composite properties from a representative volume element", Compos. Sci. Technol., 56(2), 171-179. https://doi.org/10.1016/0266-3538(95)00141-7
  45. Talebi, H., Silani, M., Bordas, S.P.A., Kerfriden, P. and Rabczuk, T. (2014), "A computational library for multiscale modeling of material failure", Comput. Mech., 53(5), 1047-1071. https://doi.org/10.1007/s00466-013-0948-2
  46. Tsai, J.-L. and Tu, J.-F. (2010), "Characterizing mechanical properties of graphite using molecular dynamics simulation", Mater. Des., 31(1), 194-199. https://doi.org/10.1016/j.matdes.2009.06.032
  47. Vu-Bac, N., Rafiee, R., Zhuang, X., Lahmer, T. and Rabczuk, T. (2015a), "Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters", Compos. Part B: Eng., 68, 446-464. https://doi.org/10.1016/j.compositesb.2014.09.008
  48. Vu-Bac, N., Silani, M., Lahmer, T., Zhuang, X. and Rabczuk, T. (2015b), "A unified framework for stochastic predictions of mechanical properties of polymeric nanocomposites", Comput. Mater. Sci., 96, 520-535. https://doi.org/10.1016/j.commatsci.2014.04.066
  49. Wang, Q., Dai, J., Li, W., Wei, Z. and Jiang, J. (2008), "The effects of CNT alignment on electrical conductivity and mechanical properties of SWNT/epoxy nanocomposites", Compos. Sci. Technol., 68(7-8), 1644-1648. https://doi.org/10.1016/j.compscitech.2008.02.024
  50. Wong, E.W., Sheehan, P.E. and Lieber, C.M. (1997), "Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes", Science, 277(5334), 1971-1975. https://doi.org/10.1126/science.277.5334.1971
  51. Xu, Y., Bai, H., Lu, G., Li, C. and Shi, G. (2008), "Flexible graphene films via the filtration of water-soluble noncovalent functionalized graphene sheets", J. Am. Chem. Soc., 130(18), 5856-5857. https://doi.org/10.1021/ja800745y
  52. Zhang, Y., Zhuang, X., Muthu, J., Mabrouki, T., Fontaine, M., Gong, Y. and Rabczuk, T. (2014), "Load transfer of graphene / carbon nanotube / polyethylene hybrid nanocomposite by molecular dynamics simulation", Compos. Part B, 63, 27-33. https://doi.org/10.1016/j.compositesb.2014.03.009
  53. Zhu, Y., Murali, S., Cai, W., Li, X., Suk, J.W., Potts, J.R. and Ruoff, R.S. (2010), "Graphene and graphene oxide: Synthesis, properties, and applications", Adv. Mater., 22(35), 3906-3924. https://doi.org/10.1002/adma.201001068

피인용 문헌

  1. A continuum model to study interphase effects on elastic properties of CNT/GS-nanocomposite vol.4, pp.2, 2017, https://doi.org/10.1088/2053-1591/aa5dd2
  2. The computation of bending eigenfrequencies of single-walled carbon nanotubes based on the nonlocal theory vol.9, pp.2, 2018, https://doi.org/10.5194/ms-9-349-2018
  3. Crack growth analysis of carbon nanotube reinforced polymer nanocomposite using extended finite element method pp.2041-2983, 2018, https://doi.org/10.1177/0954406218776034
  4. Proper-Orthogonal-Decomposition-Based Buckling Analysis and Optimization of Hybrid Fiber Composite Shells vol.56, pp.5, 2018, https://doi.org/10.2514/1.J056920
  5. Comparison of different cylindrical shell theories for stability of nanocomposite piezoelectric separators containing rotating fluid considering structural damping vol.23, pp.6, 2016, https://doi.org/10.12989/scs.2017.23.6.691
  6. Elastodynamic and wave propagation analysis in a FG graphene platelets-reinforced nanocomposite cylinder using a modified nonlinear micromechanical model vol.27, pp.3, 2016, https://doi.org/10.12989/scs.2018.27.3.255
  7. Postbuckling behavior of functionally graded CNT-reinforced nanocomposite plate with interphase effect vol.8, pp.1, 2016, https://doi.org/10.1515/nleng-2017-0133
  8. Small-scale effect on the forced vibration of a nano beam embedded an elastic medium using nonlocal elasticity theory vol.6, pp.1, 2019, https://doi.org/10.12989/aas.2019.6.1.001
  9. Thermoelastic static and vibrational behaviors of nanocomposite thick cylinders reinforced with graphene vol.31, pp.5, 2019, https://doi.org/10.12989/scs.2019.31.5.529
  10. On axial buckling and post-buckling of geometrically imperfect single-layer graphene sheets vol.33, pp.2, 2016, https://doi.org/10.12989/scs.2019.33.2.261
  11. Concurrent Patch Optimization of Hybrid Composite Plates Based on Proper Orthogonal Decomposition vol.57, pp.11, 2019, https://doi.org/10.2514/1.j058064
  12. Using IGA and trimming approaches for vibrational analysis of L-shape graphene sheets via nonlocal elasticity theory vol.33, pp.5, 2019, https://doi.org/10.12989/scs.2019.33.5.717
  13. Influence of vacancy defects on vibration analysis of graphene sheets applying isogeometric method: Molecular and continuum approaches vol.34, pp.2, 2020, https://doi.org/10.12989/scs.2020.34.2.261
  14. Representative Volume Element for Mechanical Properties of Carbon Nanotube Nanocomposites Using Stochastic Finite Element Analysis vol.142, pp.3, 2016, https://doi.org/10.1115/1.4045708
  15. A multiscale homogenization procedure to predict the elasto-viscoplastic behavior of polymer-based nanocomposites vol.29, pp.9, 2016, https://doi.org/10.1177/09673911211023305