Abstract
The present study uses a nonlinear representative volume element (RVE) to investigate the effective mechanical properties of a nano-reinforced polymer system. Here, the RVE represents the reinforcing carbon nanotube (CNT), the surrounding polymer matrix, and the CNT–polymer interface. Due to the inherent nanoscale involved in simulating CNT structures, an atomistic description is incorporated via the atomistic-based continuum multiscale modeling technique. In this way, the continuum constitutive relations are derived solely from atomistic formulations. The nonlinear response of armchair and zigzag nanotubes and their nano-reinforced polymer equivalents are considered and presented. The results reveal that reinforcing polymeric matrices with 1 to 10 vol% CNTs can result in upward of approximately 23- and 8-fold increases in the tensile and shear stiffness, respectively. These results have a direct bearing on the design and development of nano-reinforced composites.
Similar content being viewed by others
References
Iijima S.: Helical microtubules of graphitic carbon. Nature 354, 56–58 (1991)
Endo M., Hayashi T., Kim Y.A., Terrones M., Dresselhaus M.S.: Applications of carbon nanotubes in the twenty-first century. Phil. Trans. R. Soc. Lond. A 362, 2223–2238 (2004)
Kim B.C., Park S.W., Lee D.G.: Fracture toughness of the nano-particle reinforced epoxy composite. Compos. Struct. 86, 69–77 (2008)
Zhai L.L., Ling G.P., Wang Y.W.: Effect of nano-Al2O3 on adhesion strength of epoxy adhesive and steel. Int. J. Adhes. Adhes. 28, 23–28 (2008)
Salehi-Khojin A., Jana S., Wei-Hong Z.: Thermal-mechanical properties of a graphitic-nanofibers reinforced epoxy. J. Nanosci. Nanotechnol. 7, 898–906 (2007)
Huang, C.K.: Prediction model of thermal conductivity for composite materials with nano particles. Technical Proceedings of the NSTI Nanotechnology Conference and Trade Show, NSTI, pp. 320–323 (2007)
Qinghua L., Jianhua Z.: Effects of nano fillers on the conductivity, adhesion strength, and reliability of isotropic conductive adhesives (ICAs). Key Eng. Mater. 353, 2879–2882 (2007)
Qian D., Dickey E.C., Andrews R., Rantell T.: Load transfer and deformation mechanisms in carbon nanotube-polystyrene composites. Appl. Phys. Lett. 76, 2868–2870 (2000)
Schadler L.S., Giannaris S.C., Ajayan P.M.: Load transfer in carbon nanotube epoxy composites. Appl. Phys. Lett. 73, 3842–3844 (1998)
Meguid S.A., Sun Y.: On the tensile and shear strength of nano-reinforced composite interfaces. Mater. Des. 25, 289–296 (2004)
Chang T., Geng J., Guo X.: Prediction of chirality- and size-dependent elastic properties of single-walled carbon nanotubes via a molecular mechanics model. Proc. R. Soc. A 462, 2523–2540 (2006)
Rudd R.E.: The atomic limit of finite element modeling in MEMS: Coupling of length scales. Analog. Integr. Circ. Signal Process. 29, 17–26 (2001)
Abraham F.F., Walkup R., Gao H., Duchaineau M., DeLa Rubia T.D., Seager M.: Simulating materials failure by using up to one billion atoms and the world’s fastest computer: brittle fracture. Proc. Natl. Acad. Sci. USA 99, 5777–5782 (2002)
Wernik J.M., Meguid S.A.: Coupling atomistics and continuum in solids: status, prospects, and challenges. Int. J. Mech. Mater. Des. 5, 79–110 (2009)
Hyer, M.W.: Stress analysis of fiber-reinforced composite materials. McGraw-Hill, Boston
Nemat-Nasser S., Hori M., Denda M.: Micromechanics: overall properties of heterogeneous materials. Appl. Mech. Rev. 47, B24 (1998)
Shan Z., Gokhale A.M.: Representative volume element for non-uniform micro-structure, Comput. Mater. Sci. 24, 361–379 (2002)
Sun C.T., Vaidya R.S.: Prediction of composite properties from a representative volume element. Compos. Sci. Technol. 56, 171–179 (1996)
Bogetti T.A., Wang T., VanLandingham M.R., Gillespie J.W. Jr: Characterization of nanoscale property variations in polymer composite systems: 2. numerical modeling. Compos.: Part A 30, 85–94 (1999)
Liu Y.J., Chen X.L.: Evaluations of the effective material properties of carbon nanotube-based composites using a nanoscale representative volume element. Mech. Mater. 35, 69–81 (2003)
Hu N., Fukunaga H., Lu C., Kameyama M., Yan B.: Prediction of elastic properties of carbon nanotube reinforced composites. Proc. R. Soc. A 461, 1685–1710 (2005)
Tserpes K.I., Papanikos P., Labeas G., Pantelakis S.G.: Multi-scale modeling of tensile behavior of carbon nanotube-reinforced composites. Theor. Appl. Fract. Mech. 49, 51–60 (2008)
Li C., Chou T.: A structural mechanics approach for the analysis of carbon nanotubes. Int. J. Solids Struct. 40, 2487–2499 (2003)
Li C., Chou T.: Multiscale modeling of compressive behavior of carbon nanotube/polymer composites. Compos. Sci. Technol. 66, 2409–2414 (2006)
Shokrieh M.M., Rafiee R.: On the tensile behavior of an embedded carbon nanotube in polymer matrix with non-bonded interphase region. Compos. Struct. 92, 647–652 (2010)
Belytschko T., Xiao S.P., Schatz G.C., Ruoff R.S.: Atomistic simulations of nanotube fracture. Phys. Rev. B 65, 1–8 (2002)
Esfarjani K., Gorjizadeh N., Nasrollahi Z.: Molecular dynamics of single wall carbon nanotube growth on nickel surface. Comput. Mater. Sci. 3, 117–120 (2006)
Liew K.M., Chen B.J., Xiao Z.M.: Analysis of fracture nucleation in carbon nanotubes through atomistic-based continuum theory. Phys. Rev. B 71, 235424-1–235424-7 (2005)
Sun X., Zhao W.: Prediction of stiffness and strength of single-walled carbon nanotubes by molecular mechanics based finite element approach. Mater. Sci. Eng. A 390, 366–371 (2005)
Xiao J.R., Staniszewski J., Gillespie J.W. Jr: Fracture and progressive failure of defective graphene sheets and carbon nanotubes. Compos. Struct. 88, 602–609 (2009)
Natsuki T., Endo M.: Structural dependence of nonlinear elastic properties for carbon nanotubes using continuum analysis. Appl. Phys. A 80, 1463–1468 (2005)
Wernik J.M., Meguid S.A.: Atomistic-based continuum modeling of the nonlinear behavior of carbon nanotubes. Acta Mech. 212, 167–179 (2010)
Lu J.P.: Elastic properties of carbon nanotubes and nanoropes. Phys. Rev. Lett. 79, 1297–1300 (1997)
Hernandez E., Goze C., Bernier P., Rubio A.: Elastic properties of C and B x C y N z composite nanotubes. Phys. Rev. Lett. 80, 4502–4505 (1998)
Jin Y., Yuan F.G.: Simulation of elastic properties of single-walled carbon nanotubes. Compos. Sci. Technol. 63, 1507–1515 (2003)
Odegard G.M., Gates T.S., Nicholson L.M., Wise K.E.: Equivalent-continuum modeling of nano-structured materials . Compos. Sci. Technol. 62, 1869–1880 (2002)
Natsuki T., Tantrakan K., Endo M.: Effects of carbon nanotubes structures on mechanical properties. Appl. Phys. A 79, 117–124 (2004)
Keller T., De Castro J., Schollmayer M.: Adhesively bonded and translucent glass fiber reinforced polymer sandwich girders. J. Compos. Constr. 8, 461–470 (2004)
Lordi V., Yao N.: Molecular mechanics of binding in carbon-nanotube-polymer composites. J. Mater. Res. 15, 2770–2779 (2000)
Fiedler B., Gojny F.H., Wichmann M.H.G., Nolte M.C.M., Schulte K.: Fundamental aspects of nano-reinforced composites. Compos. Sci. Technol. 66, 3115–3125 (2006)
Hu Y., Shenderova O.A., Zushou H., Padgett C.W., Brenner D.W.: Carbon nanostructures for advanced composites. Rep. Prog. Phys. 69, 1847–1895 (2006)
Battezzati L., Pisani C., Ricca F.J.: Equilibrium conformation and surface motion of hydrocarbon molecules physisorbed on graphite. Chem. Soc., Faraday Trans. 71, 1629–1639 (1975)
Montazeri, A., Naghdabadi, R.: Investigation the stability of SWCNT-polymer composites in the presence of CNT geometrical defects using multiscale modeling. Proc. Fourth Int. Conf. Multiscale Mater. Model., pp. 163–166 (2008)
Yu M.F., Files B.S., Arepalli S., Ruoff R.S.: Tensile loading of ropes of single wall carbon nanotubes and their mechanical properties. Phys. Rev. Lett. 84, 5552–5555 (2000)
Meo M., Rossi M.: Tensile failure prediction of single wall carbon nanotube. Eng. Fract. Mech. 73, 2589–2599 (2006)
Giannopoulos G.I., Kakavas P.A., Anifantis N.K.: Evaluation of the effective mechanical properties of single walled carbon nanotubes using a spring based finite element approach. Comput. Mater. Sci. 41, 561–569 (2008)
Srivastava D., Wei C.: Nanomechanics of carbon nanotubes and composites. Appl. Mech. Rev. 56, 215–230 (2003)
Gupta S., Dharamvir K., Jindal V.K.: Elastic moduli of single-walled carbon nanotubes and their ropes. Phys. Rev. B 72, 165428-1–165428-16 (2005)
Xiao J.R., Gama B.A., Gillespie J.W. Jr: An analytical molecular structural mechanics model for the mechanical properties of carbon nanotubes. Int. J. Solids Struct. 42, 3075–3092 (2005)
Yeh M., Hsieh T., Tai N.: Fabrication and mechanical properties of multi-walled carbon nanotubes/epoxy nanocomposites. Mater. Sci. Eng. A 483, 289–292 (2008)
To C.W.S.: Bending and shear moduli of single-walled carbon nanotubes. Finite Elements Anal. Des. 42, 404–413 (2006)
Krishnan A., Dujardin E., Ebbesen T.W., Yianilos P.N., Treacy M.M.J.: Young’s modulus of single-walled nanotubes. Phys. Rev. B 58, 14013–14019 (1998)
Tombler T.W., Zhou C., Kong J., Dai H., Liu L., Jayanthi C.S., Tang M., Wu S.Y.: Reversible electromechanical characteristics of carbon nanotubes under local-probe manipulation. Nature 405, 769–772 (2000)
Hall A.R., An L., Liu J., Vicci L., Falvo M.R., Superfine R., Washburn S.: Experimental measurement of single-wall carbon nanotubes torsional properties. Phys. Rev. Lett. 96, 256102-1–256102-4 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wernik, J., Meguid, S. Multiscale modeling of the nonlinear response of nano-reinforced polymers. Acta Mech 217, 1–16 (2011). https://doi.org/10.1007/s00707-010-0377-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-010-0377-7