To verify the transverse isotropy of the square and hexagonal unit cells, the shear
modulus G23 calculated from the transverse Young's modulus and Poisson's ratio is
compared with the G23 calculated using the results from the FE analysis. If the composite
is truly transversely isotropic, then it should satisfy the relationG3 E2 As shown in
2(1 + v23 )
Table 2-6, the difference in the shear moduli calculated from the two methods is small for
the hexagonal unit-cell. Therefore, the hexagonal unit cell is a better model for the
micromechanics model to satisfy the transverse isotropy and can be considered as more
realistic for fiber-reinforced composites [28]. Also, the results the micromechanics
method provides better approximate results of laminate properties than empirical
solutions.
Table 2-6. Comparisons of G23 for square and hexagonal unit-cells in order to test
transverse isotropy.
Square Cell (MPa) Hexagonal Cell (MPa)
E23 E23
G23 23 % Error G23 % Error
2(1+v, V) 2(1+v, V)
Glass/Epoxy 4.62 7.74 67.5 5.83 5.91 1.41
Graphite/Epoxy 3.40 4.06 19.3 3.72 3.74 0.56
Effects of Fiber Volume Fraction
The effect of fiber volume fraction on the thermal coefficients of graphite/epoxy
composite was analyzed using the micromechanics method. Figures 2-6 and 2-7 show the
variation of longitudinal and transverse thermal coefficients as a function of fiber volume
fraction for glass/epoxy and graphite/epoxy composites. The CTE's estimated using both
square and hexagonal unit-cells are very close. It should be noted that the graphite fiber
has a negative thermal coefficient, and also the product of thermal coefficient a and
Young's modulus (cLE) is almost equal for the fiber and matrix. Hence the longitudinal