Composite Materials Research Progress

12
Macroscopic stiffness
component [GPa]
CME component
1,4
1,2
0,8
0,6
0,4
0,2
0, 25
0,2
0, 15
0,1
0, 05
250
200
150
100
1
50
0
Jacquemin Frédéric and Fréour Sylvain
0 0,25 0,5 0,75 1
matrix volume fraction
0
0 0,25 0,5 0,75 1
0
I
Y22
I
Y11
I
β11
I
β22
epoxy volume fraction
Macroscopic stiffness component
[GPa]
CTE component [10 -6 K -1 ]
80
60
40
20
-20
16
14
12
10
8
6
4
2
0
0 0,25 0,5 0,75 1
epoxy volume fraction
0
0 0,25 0,5 0,75 1
epoxy volume fraction
Longitudinal (KESC) Transverse (KESC)
Longitudinal (Mori-Tanaka) Transverse (Mori-Tanaka)
0 0,25 0,5 0,75 1
matrix volume fraction
Figure 1. Macroscopic effective hygro-thermo-mechanical properties of T300/N5208 plies, estimated as
a function of the epoxy volume fraction, through scale transition homogenisation procedures.
Comparison between Mori-Tanaka approximate and Kröner-Eshelby self-consistent model.
Figure 1 shows the following interesting results:
1) In pure elasticity, both the investigated scale transition methods manage to reproduce
the expected mechanical behaviour of the composite ply: the material is stiffer in the
longitudinal direction than in the transverse direction. Moreover, the bounds are satisfying:
the properties of the single constituents are correctly obtained for those of the composite ply
in the cases where the epoxy volume fraction is either taken equal to v m =0 (transversely
isotropic elastic properties of T300 fibers) or v m =1 (isotropic elastic properties of N5208
resin).
2) The curves drawn for each checked elastic constant are almost superposed, except for
I
Coulomb’s modulus G 12 . Thus Mori-Tanaka model constitutes a rather reliable alternate
homogenization procedure to Eshelby-Kröner rigorous solution for estimating the
macroscopic elastic properties of typical carbon-epoxies.
I
G 23
I
M11
I
G12
I
M22