Abstract :
We present a stochastic multi-scale approach to evaluate the effective mechanical properties of carbon nanotube
CNT/polymer composites. This paper deals with the effects of different parameters of CNTs such as length,
diameter, curvature, orientation, volume fraction ratio and dispersion on mechanical behaviour of composites. The
basic idea consists in introducing a random 2D-periodic REV (Representative Elementary Volume) where CNTs
are small inclusions randomly spread out in polymer so that a pseudo-homogenization technique can be used.
In order to consider different scales (micro-scale, meso-scale and macro-scale) a hierarchical homogenization is
performed without using a micromechanical model as in [2].
Calculations are based on CNT.s properties read in the literature (see [1] and [3]). First we spread out nanoparticles
in REV according to Gaussian or Log-normal distribution. In our own model, bonds at the interface between
nanoparticles and matrix are supposed perfect, nevertheless we introduce a likewise boundary layer to take into
account this interaction and the fact that the CNTs are multi-walled [3] and not single-walled [1]. The second
step consists in introducing aggregates that are modelled by isotropic circular areas, once again, we use the homogenization
method to predict mechanical properties. Finally, as we have built a database resulting from our
calculations we use statistical tools to explain the effects of relevant parameters to describe the macro-scale.
Bibiography :
[1] G.M. Odegard and T. C. Clancy and T.S. Gates - Modeling of the mechanical properties of nanoparticle/
polymer composites - Polymer 46 (2) 533-562 DOI:10.1016/j.polymer.2004.11.022, 2005.
[2] M.M. Shokrieh and R. Rafiee - Stochastic multi scale modeling of CNT/polymer composites - Computational
Materials Science 50 (2) 437-446 DOI:10.1016/ j.commastsci.2010.08.036, 2010.
[3] A.L. Kalamkarov and all - Analytical and numerical techniques to predict carbon nanotubes properties -
International Journal of Solids and Structures 43 (22-23) 6832-6854 DOI: 10.1016/j.ijsolstr.2006.02.009,
2006.