ABSTRACT
For finite element analysis, the mechanical properties of each layer in Fig. 2 need to be known parameters. Assuming GPLs as effective rectangular solid fillers uniformly dispersed in a polymer matrix, Young’s modulus of the reinforced nanocomposites can be approximated in terms of the properties of the polymer matrix and the filler by the following Halpin-Tsai micromechanics model (Halpin, 1969; Rafiee et al., 2009)
E V V
E V V
−
−
× + −
−
× 3 8
1 1
5 8
1 1
ξη η
ξη η
(1)
where EC and EM are the effective elastic moduli of the composite and the polymer, respectively, VGPL is the volume fraction of GPL, ξ = (lGPL + wGPL)/hGPL with lGPL, wGPL and hGPL being the length, width and thickness of the GPL, respectively. The other two parameters, ηL and ηW, are
η ξL
=
−
+
( / ) ( / )
E E
1 (2)
and
=
−
+
( / ) ( / )
E E
1 2
(3)
where EGPL is the Young’s modulus of GPL. Given the mass densities of GPL and the polymer matrix, the volume fraction of the GPL in the composite can be approximated as
V f fGPL
= ( )GPL M ( )fGPL (4) where ρGPL and ρM are the mass densities of the GPL and the polymer matrix, respectively, and fGPL is the weight fraction of the GPL in the composite. Using Eq. (4), the mass density for each layer can also be obtained correspondingly.
