Page 129 - Mechanics Analysis Composite Materials

114 Mechanics and analysis of composite materials
hybrid composites, the plies can include fibers of two, or may be more types, e.g.,
carbon and glass, glass and aramid and so on. Hybrid composites provide wider
possibilities to control material stiffness, strength and cost. A promising application
of these materials is associated with the so-called thermostable structures that do
not change their dimensions under heating or cooling. For some composites, e.g.,
with glass of boron fibers, longitudinal coefficient of thermal expansion is positive,
while for other materials, e.g., with carbon or aramid fibers, it is negative (see
Table 7.1 and Section 7.1.2 of Chapter 7). So, the proper combination of fibers with
positive and negative coefficients can result in material with zero thermal expansion.
Consider the problem of micromechanics for a unidirectional ply reinforced with
two types of fibers. Naturally, the stiffness of these fibers should be different, and we
assume that E:') > E?). The first-order model of the ply that generalizes the model
in Fig. 3.34 is presented in Fig. 3.66. For tension in the fiber direction, the apparent
stress and strain, 01 and E', are linked by Hooke's law

in which the effective modulus is specified by the following equation generalizing
Eq. (3.76)

El = E~l)u~')+E,(2) (2) +Emu, . (3.125)

Here, v!') and up) are volume fractions of the fibers of the first and of the second
type and om is the matrix volume fraction, so that

We also introduce the total volume fraction of the fibers

and normalized volume fractions of fibers as

Fig. 3.66. A first-order microstructural model of a hybrid unidirectional ply.