Composite Materials Research Progress

Multi-scale Analysis of Fiber-Reinforced Composite Parts… 19
obviously directly related to the discrepancies previously underlined in subsection 2.5 where
the question of comparing the homogenization relations of the two scale transition methods
presented in this paper, was investigated.
Table 3. Pseudomacroscopic elastic moduli and stiffness tensor components assumed for
the epoxy matrix of the composite plies at ΔC 0
I = % and T I = 300 K, according to
(Herakovich, 1998).
Elastic moduli
Stiffness tensor
components
m
1
m
Y 2 [GPa]
m
ν 12 [1]
m
G 12 [GPa]
m
23
5.35 5.35 0.350 1.98 1.98
Y [GPa]
G [GPa]
m
11
m
L 22 [GPa]
m
L 12 [GPa]
m
L 44 [GPa]
m
L 55 [GPa]
8.62 8.62 4.66 1.98 1.98
L [GPa]
Table 4. Pseudomacroscopic elastic moduli and stiffness tensor components identified
for the carbon fiber reinforcing the composite plies at ΔC 0
I = % and T I = 300 K,
according to either Mori-Tanaka estimates, or Eshelby-Kröner self-consistent model.
Comparison with the corresponding properties exhibited in practice by typical highstrength
carbon fibers, according to (Herakovich, 1998).
Elastic moduli
r
Y 1 [GPa]
r
Y 2 [GPa]
r
ν 12 [1]
r
G 23 [GPa]
r
G 12 [GPa]
Mori-Tanaka estimate 213.1 13.7 0.27 4.1 22.7
Eshelby-Kröner model 213.2 13.3 0.27 4.0 12.1
Typical expected
properties
Stiffness tensor
components
232 15 0.279 5.0 15
r
L 11[GPa]
r
L 22 [GPa]
r
L 12 [GPa]
r
L 44 [GPa]
r
L 55 [GPa]
Mori-Tanaka estimate 219.2 24.9 11.2 4.1 22.7
Eshelby-Kröner model 219.2 23.9 10.8 4.0 12.1
Typical expected
properties
236.7 20.1 8.4 5.02 15
3.3.2. Determination of AS4/3501-6 Matrix Coefficients of Moisture Expansion
Macroscopic values of the Coefficients of Moisture Expansion are sometimes available,
contrary to the corresponding pure epoxy resin CME. Simulations were performed in the cas
e of an AS4/3501-6 composite, with a reinforcing fiber volume fraction v r =0.60. The
calculations were achieved using the elastic properties given in Table 5, and the macroscopic
coefficients of moisture expansion listed in Table 6. The same table summarizes the results
obtained with both inverse Eshelby-Kröner self-consistent model (21) and Mori-Tanaka