Composite Materials Research Progress

10
Jacquemin Frédéric and Fréour Sylvain
the macroscopic stiffness. Nevertheless, according to the already cited same subsection, the
reaction tensor involved in Eshelby-Kröner model was also implicitely depending on the
macroscopic stiffness through the calculation procedure entailed for estimating Hill’s tensor.
Within Mori-Tanaka procedure (Benveniste, 1987; Baptiste 1996; Fréour et al., 2006a),
Hill’s tensor E i expresses the dependence of the strain localization tensor on the morphology
assumed for the embedding phase and the particulates it surrounds (Hill, 1965). It can be
i
expressed as a function of Eshelby’s tensor S esh , through:
i i e
−1
E = Sesh
: L
(15)
In practice, the calculation of Hill’s tensor for the embedded inclusions phase only would
be necessary, since obvious simplifications of (14), leading to T I
e = , occur in the case that
the embedding constituent localisation tensor is considered. According to relations (14-15),
the strain localization tensor T i does not involve the macroscopic stiffness tensor (or any other
macroscopic property). As a consequence, contrary to Eshelby-Kröner self-consistent
procedure, Mori-Tanaka approximation provides explicit relations (actually, the
homogenization equations (11-13)) for estimating the researched macroscopic effective
properties of a composite ply.
2.5. Example of Homogenization: The Case of T300-N5208 Composites
The present subsection is focused on the application of the theoretical frameworks described
in the above 2.3 and 2.4 sections to the numerical simulation of the effective properties of a
typical, high-strength, fiber-reinforced composite made up of T300 carbon fibers and N5208
epoxy resin. The choice of such a material is justified because of the strong heterogeneities of
the hygro-thermo-elastic properties of its constituents (actually, the numerical deviation
occurring among the macroscopic properties of composites determined through various scale
transition relations rises with this factor, see Jacquemin et al, 2005; Herakovich, 1998). Table
1 accounts for the pseudo-macroscopic properties reported in the literature for these
constituents. The comparison between the results obtained through the two, considered in the
present work alternate scale transition framework of Mori-Tanaka model are displayed on
figure 1, for:
- the longitudinal and transverse Young’s moduli
- Coulomb’s moduli
I
G 12 ,
I
G 23 ,
I I
- the coefficients of thermal expansion M 11,
M 22
I I
- the coefficients of moisture expansion β 11,
β 22 .
I
Y 11 ,
I
Y 22 ,