Page 350 - Mechanics Analysis Composite Materials

Chapter 7. Environmental, special loading, and manufacturing e#kcts 335

Fig. 7.22. Stress-strain diagrams for viscoelastic (a) and elastic (b)materials.

*=-(l-$).271t,.O
1 +t,?w?

As follows from this equation, $ depends on the number of oscillations
accomplished during the period of time equal to the material relaxation time, t,.,
and reaches the maximum value for trw = 1.
As shown by Zinoviev and Ermakov (1994), for anisotropic materials, thc
dissipation factor depends also on the direction of loading. Particularly, for a
unidirectional composite ply, referred to axes x and y making angle 4 with the
principal material axes 1 and 2 as in Fig. 4.18, the dissipation factors are
1
cos 24 + *45p12sin24 cos' 4 ,
t,bv = E, [(2cos' 4 -

where

E,, E,, and Gx,,. are specified by Eqs. (4.76) and $,*, and $45 are the
ply dissipation factors corresponding to loading along the fibers, across the fibers,
under in-plane shear and at 45" with respect to principal material axes 1 and 2. As
follows from Fig. 7.23, calculation based on the foregoing equations provides fair
agreement with experimental results of Ni and Adams (1984).
Energy dissipation in conjunction with relatively low heat conductivity of
composite materials induces self-heating of them during the cyclic loading.