melting temperature Tm, the epoxy resin becomes a rubbery solid and then becomes

viscous liquid. When the laminate is cooled down to the glass transition temperature Tg,

the epoxy resin becomes an amorphous solid. The difference in the coefficients of

thermal expansion (CTE) for the constituents under temperature changes causes residual

stresses in the composite laminate. Thermal stresses in composites are largely influenced

by matrix thermo-mechanical properties. Also, the chemical reaction of epoxy causes

shrinkage which rises residual stress in matrix phase. In this study, the residual stress due

to chemical reaction of epoxy is assumed to be negligible.

 In this study, the 977-3 epoxy system is used as the matrix material. The

coefficient of thermal expansion and the Young's modulus of this material system [25] as

a function of temperature are shown in Figures 2-4 and 2-5, respectively. The actual and

average CTE of the epoxy resin are nonlinear with respect to temperature as shown in

Figure 2-4. The average CTE from a reference temperature is used as input in the

ABAQUS finite element program. The average CTE is calculated by using the relation

 Tcryogenic
 fa(T)dT
 a = (2.1)
 T TCurg

In the above equation, the curing temperature Tcuring is 455K where the epoxy resin

becomes solid during curing process of composite laminates. The cryogenic temperature

Tcryogenic is 50K where the liquid hydrogen boils.

 When the temperature decreases from curing to cryogenic temperature, the actual

CTE decreases from 73.0 10 6/K to 18.1 x 106/K and the Young's moduli increases

from 1.2 MPa to 5.2 MPa. The tensile strength for heat-cured epoxy is in the range of 70

MPa to 90 MPa at room temperature [26]. In general, the strength of epoxy increases