Thermo-mechanical properties of polymer nanocomposites reinforced with randomly distributed silica nanoparticles- Micromechanical analysis

Document Type : Original Research Paper


Department of Mechanical Engineering, University of Guilan, Rasht, I. R. Iran


A three-dimensional micromechanics-based analytical model is developed to study thermo-mechanical properties of polymer composites reinforced with randomly distributed silica nanoparticles. Two important factors in nanocomposites modeling using micromechanical models are nanoparticle arrangement in matrix and interphase effects. In order to study these cases, representative volume element (RVE) of nanocomposites is extended to c×r×h nano-cells in three dimensions and consists of three phases including nanoparticles, polymer matrix and interphase between the nanoparticles and matrix. Nanoparticles are surrounded by the interphase in all composites. Effects of volume fraction, aspect ratio and size of nanoparticle on the effective thermo-mechanical response of the nanocomposite are studied. Also, the effects of polymer matrix properties and interphase including its elastic modulus and thickness are theoretically investigated in detail. It is revealed that when nanoparticles are randomly distributed in the matrix and interphase effects are considered, the results of present micromechanical model are in very good agreement with experimental data.


[1] B.M. Novak: Hybrid nanocomposite materialsbetween inorganic glasses and organic polymers, Adv Mater 5 (1993) 422-433.

[2] H.L. Frisch, J.E. Mark: Nano composites prepared by threading polymer chains through zeolites, mesoporous silica, or Silica nanotubes, Chem Mater 8 (1996) 1735-1738.
[3] B. Wetzel, F. Haupert, M.Q. Zhang: Epoxy nanocomposites with high mechanical and tribological performance, Compos Sci Technol 63 (2003) 2055–2067.

[4] H. Wang, Y. Bai, S. Liu, J. Wu, C.P. Wong: combinedeffects of silica filler and its interface in epoxy resin,
Acta Mater 50 (2002) 4369–4377.

[5] J.N. Coleman, M. Cadek, R. Blake, V. Nicolosi,K.P. Ryan, C. Belton, A. Fonseca, J.B. Nagy, Y.K. Gun'ko, W. J. Blau: High-performance nanotubereinforcedplastics: understanding the mechanism of strength increase, Adv Func Mater 14 (2004) 791–798.

[6] M. Izadi, M.M. Shahmardan, A. Behzadmehr, A.M.Rashidi, A. Amrollahi: Modeling of effective
thermal conductivity and viscosity of carbonstructured nanofluid, Trans Phenom in Nano Micro scale 3 (2015) 1-13.

[7] G.D. Seidel, D.C. Lagoudas: A micromechanics model for the electrical conductivity of nanotubepolymer nanocomposites, J Compos Mater 43(2009) 917–941.

[8] H. Liu, L.C. Brinson: Reinforcing efficiency of nanoparticles: A simple comparison for polymer nanocomposites, Compos Sci Technol 68 (2008) 1502-1512.

[9] L.S. Schadler, L.C. Brinson, W.G. Sawyer: Polymer Nanocomposites: A Small Part of the Story, J Miner Metal Mater Soc 59 (2007) 53-60.

[10] M. Avella, F. Bondioli, V. Cannillo, M.E. Errico, A.M. Ferrari, B. Focher, M. Malinconico, T. Manfredini, M. Montorsi: Preparation, characterisation and computational study of poly (ecaprolactone) based nanocomposites, Mater Sci Technol 20 (2004a) 1340–1344.

[11] M. Avella, F. Bondioli, V. Cannillo, S. Cosco, M.E. Errico, A.M. Ferrari, B. Focher, M. Malinconico: Properties/structure relationships in innovativePCL–SiO2 nanocomposites, Macromol Symp 218 (2004b) 201–210.

[12] L.S. Schadler: Designed Interfaces in Polymer Nanocomposites: A Fundamental Viewpoint, MRS Bulletin 32 (2007) 335-340.

[13] R.A. Vaia, H.D. Wagner: Framework for Nanocomposites, Mater Today 7 (2004) 32-37.

[14] J.S. Snipes, C.T. Robinson, S.C. Baxter: Effects of scale and interface on the three-dimensional micromechanics of polymer nanocomposites, J Compos Mater 45 (2011) 2537-2546.

[15] S.C. Baxter, C.T. Robinson: Pseudo-percolation: Critical volume fractions and mechanical percolation in polymer nanocomposites, Compos Sci Technol 71 (2011) 1273–1279.

[16] M.J. Mahmoodi, M.M. Aghdam: Damage analysis of fiber reinforced Ti-alloy subjected to multi-axial loading—A micromechanical approach, Mater Sci Eng A 528 (2011) 7983-7990.

[17] S.R . Falahatgar, M. Salehi, M.M. Aghdam: Nonlinear viscoelastic response of unidirectional fiber reinforced composites in off-axis loading, J Reinf Plast Compos 28 (2009)1793–1812.

[18] R.P. Nimmer, R.J. Bankert, E.S. Russell, G.A. Smith, P.K. Wright: Micromechanical modeling offiber/matrix interface effects in transversely loaded SiC/Ti-6-4 metal matrix composite, J Compos Technol Res 13 (1991) 3-13.

[19] R. Haj-Ali, J. Aboudi: Nonlinear micromechanical formulation of the high fidelity generalized method of cells, Int J Solids Struct 46 (2009) 2577-2592.

[20] T.W. Chou, S. Nomura, M. Taya: A self-consistent approach to the elastic stiffness of short-fiber composites, J Compos Mater 14 (1980) 178-188.

[21] J.C. Halpin, S.W. Tsai: Stiffness and expansion estimates for oriented short fiber composites, J Compos Mater 3 (1969) 732–734.

[22] T. Mori, K. Tanaka: Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metal 21 (1973) 571-574.

[23] J.I. Weon, H.J. Sue: Effects of clay orientation and aspect ratio on mechanical behavior of nylon-6 nanocomposite, Polymer 46 (2005) 6325–6334.

[24] H.W. Wang, H.W. Zhou, R.D. Peng, J. Leon Mishnaevsky: Nanoreinforced polymer composites: 3D FEM modeling with effective interface concept, Compos Sci Technol 71 (2011) 980–988.

[25] S. Dhala, M.C. Ray:Micromechanics of piezoelectric fuzzy fiber-reinforced composite, Mech Mater 81 (2015) 1–17.

[26] R.D. Peng, H.W. Zhou, H.W. Wang, J. Leon Mishnaevsky: Modeling of nano-reinforced polymer composites: Microstructure effect on Young’s modulus, Comput Mater Sci 60 (2012) 19–31.

[27] B. Mortazavi, J. Bardon, S. Ahzi: Interphase effect on the elastic and thermal conductivity response of polymer nanocomposite materials: 3D finite element study, Comput Mater Sci 69 (2013) 100–106.

[28] S. Ajori, R. Ansari, M. Mirnezhad: Mechanical properties of defective γ-graphyne using molecular dynamics simulations, Mater Sci Eng: A 561 (2013) 34–39.

[29] R. Ansari, S. Rouhi, S. Ajori: Elastic properties and large deformation of two-dimensional silicene nanosheets using molecular dynamics, Super Microstruct 65 (2014) 64–70.

[30] M.M. Shokrieh, R. Rafiee: Development of a full range multi-scale model to obtain elastic properties of CNT/polymer composites, Iran Polymer J 21 (2012) 397-402.

[31] M.J. Mahmoodi, M.M. Aghdam, M. Shakeri: The effects of interfacial debonding on the elastoplastic response of unidirectional silicon carbide–titanium composites, J Mech Eng Sci 223 (2010) 259-269.

[32] Z. Wanga, J. Lua, Y. Li, S.Y. Fu, S. Jiang, X. Zhao: Studies on thermal and mechanical properties of
PI/SiO2 nanocomposite films at low temperature, Composites A 37 (2006) 74–79.

[33] G.M. Odegard, T.C. Clancy, T.S. Gates: Modeling of the mechanical properties of nanoparticle/polymer composites, Polymer 46 (2005) 553–562.

[34] E. Kontou, G. Anthoulis:The effect of silica nanoparticles on the thermomechanical properties of polystyrene, J. Appl. Polym. Sci 105 (2007) 1723–1731.