Composite Materials Research Progress

18
Jacquemin Frédéric and Fréour Sylvain
r 1 r 1 r
−1
⎡ i i
I m m
M = T : L : ⎢ L : T : M − v L : M
r
v
⎢⎣
i=
r, m
− m
r 1 r −1 r
−1
⎡ i i
I I m m m m ⎤
β = T : L : ⎢ L : T : β ΔC − v L : β ΔC ⎥ (31)
r r
v ΔC
⎢⎣
i=
r, m
⎥⎦
3.3. Examples of Properties Identification in Composite Structures Using
Inverse Scale Transition Methods
3.3.1. Determination of Reinforcing Fibers Elastic Properties
The literature often provides elastic properties of carbon-fiber reinforced epoxies (see for
instance Sai Ram and Sinha, 1991), that can be used in order to apply inverse scale transition
model and thus identify the properties of the reinforcing fibers, as an example. Table 2 of the
present work summarizes the previously published data for an unidirectional composite
designed for aeronautic applications, containing a volume fraction v r =0.60 of reinforcing
fibers. In order to achieve the calculations, according to relations (18) or (26) depending on
whether Eshelby-Kröner model or Mori-Tanaka approximation, input values are required for
the pseudo-macroscopic properties of the epoxy matrix constituting the composite ply. The
elastic constants considered for this purpose are listed in Table 3 (from Herakovich, 1998).
Both the above-cited inverse scale transition methods have been applied. The obtained results
are provided in Table 4, where they are compared to typical values, reported in the literature,
for high-strength reinforcing fibers (Herakovich, 1998). It is shown that a very good
agreement between the two inverse models is obtained. Moreover, the calculated values are
similar to those expected for typical reinforcements according to the literature. Nevertheless,
some discrepancies between the identified moduli do exist, especially for
r G 12 (that
r
corresponds to L 55 stiffness component). Actually, the value deduced for this component
through Mori-Tanaka inverse model deviates from both the expected properties and the
estimations of Eshelby-Kröner model. This deviation, occurring for this very component, is
Table 2. Macroscopic elastic moduli (from the literature) and stiffness tensor
components (calculated) considered for the composite ply at ΔC 0
I = % and T I = 300
K, according to (Sai Ram and Sinha, 1991).
Elastic moduli
Stiffness tensor
components
I
1
I
Y 2 [GPa]
I
ν 12 [1]
I
G 12 [GPa]
I
23
130 9.5 0.3 6.0 3.0
Y [GPa]
⎤
⎥
⎥⎦
G [GPa]
I
11
I
L 22 [GPa]
I
L 12 [GPa]
I
L 44 [GPa]
I
L 55 [GPa]
134.2 14.8 7.1 6.0 3.0
L [GPa]
(30)