identically equal to zero and a uniform ATis applied to the unit-cell. From the macro-
stresses the CTE's can be calculated as
{a}= C 1-'1 } (2.4)
AT
In this study the properties and residual stresses were calculated at 50 K which
corresponds to AT=-405 K. The elastic constants such as Young's moduli, shear moduli
and Poisson's ratios can be obtained from the compliance matrix S=C 1.
Table 2-4. Results of elastic constants for laminated composites calculated by empirical
formulas.
Elastic constants Empirical Formulas (EMP)
El (GPa) 45.4
E2, E3 (GPa) 19.4
G12, G13 (GPa) 6.00
G23 (GPa) 7.71
Glass/Epoxy V12, V13 0.260
V23 0.255
aO (10 6/C) 5.41
(2, 3(10 6/C0) 9.92
El (GPa) 160
E2, E3 (GPa) 11.1
G12, G13 (GPa) 5.90
G23 (GPa) 4.05
Graphite/Epoxy v12, v13 0.260
V23 0.367
S(10( 6/Co) -0.712
a2, 3 (106/Co) 12.1
The empirical formulas are used to estimate the elastic constant based on
constituent properties as shown in Table 2-4. The rule of mixture is used to calculate the
approximate elastic constant El, v12 and v13. Halpin-Tsai [26] equations are used to
calculate the approximate elastic constants E2, E3, G12, G13, G23 and V23. Schaprey's
formulas [26] are used for the coefficient of thermal expansion aO, a2 and a3. The