Page 330 - Mechanics Analysis Composite Materials

Chapter 7. Environmental, special loading. and manufacturing ~@c.cts 315

M:, =Jif'- d;:)= 1840 x 10-'AT GPa mm'/"C,
M?;__ = 5100 x AT GPa mm'/"C .

Thus, the thermal terms entering costitutive equations of thermoplasticity, Eqs.
(7.23), are specified. Apply the obtained results to determine the apparent
coefficients of thermal expansion for the space telescope section under study (see
Fig. 7.3). We can assume that under uniform heating the curvatures do not change
in the middle part of the cylinder so that K,T = 0 and K,T = 0. Because there are no
external loads, free body diagram allows us to conclude that N, = 0 and N, = 0. As
a result, the first two equations of Eqs. (7.23) for the structure under study become:

N:,
=
BIIe:., +BI~E~~
B', E!., + ~22.~:~= N&-- .
Solving these equations for thermal strains and taking into account Eqs. (7.20) we
get

1
.
Fo,IT - -(BIIN,T,-B12N;I;)= CI~.AT
-
B
where B = BIIB~~B!?. For the laminate under study, calculation yields
-
CI, = -0.94 x 10.' 1/"C, CI,. = 14.7 x l/"C .

Return to Eqs. (7.13) and (7.20) based on the assumption that coefficients
of thermal expansion do not depend on temperature. For moderate temperatures,
this is a reasonable approximation. This conclusion follows from Fig. 7.6 in
which experimental results of Sukhanov et al. (1990) (shown with solid lines) are
compared with Eqs. (7.20), where AT = T - 20°C (broken lines) for carbon-poxy
angle-ply laminates. However, for relatively high temperatures, some deviation from
the linear behavior can be seen. In this case, Eqs. (7.13) and (7.20) for thermal
strains can be generalized as

cT = 1a(T)dT .

77,
Temperature action can result also in the change of material mechanical properties.
As follows from Fig. 7.7 in which circles correspond to experimental data of Ha and
Springer (1 987), elevated temperature causes higher or lower reduction of material
strength and stiffness characteristics depending on whether the corresponding
material characteristic is controlled mainly by the fibers or by the matrix. The curves