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