A(T)EO = IQ(T)Ef~5 _N(T) (4-2)
where so~is the non-mechanical strain induced by thermal load. The right hand side of
Equation 4-2 is defined as the thermal load N". From Equation 4-2, the non-mechanical
strain induced by thermal load can be expressed by
soN(T)= A-'(T)N"(T) (4-3)
The residual thermal stress is given by the constitutive equation
aR Q()( ON F (T)) (4-4)
The mechanical strain is expressed by
EM(T) = A '(T)NM(T) (4-5)
Therefore, the mechanical stress is given by
a" (T) = Q(T)Eh" (T) (4-6)
By the principle of superposition, the residual strain and total stress in the laminate are
expressed by
eResidual(T Mh~ ()ON (T_ EF (T) (4-7)
ca"" (T) = aR () M (T) (4-8)
Properties of IM600/133 Composite Materials
The composite material used in the present study is the IM600/133 graphite-epoxy
material system, which has a glass-transition temperature of 3560F. Aoki et al. (2000)
tested IM600/133 (material Aa in their paper) composite material system at various
temperatures, ranging from 3560F to -452.20F (1800C to -2690C), with mechanical
tensile loads. The material properties of IM600/133 were taken from Aoki et al. (2000)