Page 319 - Mechanics Analysis Composite Materials

304 Mechanics and analysh qf composite materials

Fig. 3.34 showing the structure of the first-order ply model, we can write the
following equations specifying thermal conductivity of a unidirectional ply along
and across the fibers:

Here Klr and AZf are thermal conductivities of the fiber in longitudinal and transverse
directions (for some fibers they are different), A,,, is the corresponding charac-
teristic of the matrix, and uf, urn = 1 - uf are fibers and matrix volume fractions.
Conductivity coefficients in Eqs. (7.8) are analogous to elastic constants specified by
Eqs. (3.76) and (3.78), and the discussion presented in Section 3.3 is valid for
Eqs. (7.8) as well. Particularly, it should be noted that application of higher-order
microstructural models practically does not change 21 but substantially improves 12
determined by Eqs. (7.8). Typical properties of unidirectional and fabric composites
are listed in Table 7. I.
Consider heat transfer in an orthotropic ply or layer in coordinate frame x, y
whose axes x and y make angle 4 with the principal material coordinates XI and x2
as in Fig. 7.2. Heat flows in coordinates x, y and XI, x2 are linked by the following
equations:

q.x= q1 cos 4 - q2 sin 4, qJ,= q1 sin 4 + qz cos 4 . (7.9)

Here, in accordance with Eq. (7.1)

Table 7.1
Typical thermal conductivity and expansion coefficients of composite materials.
Property Glass- Carbon- Aramid- Boron- Glass Aramid
epoxy epoxy epoxy epoxy fabric-epoxy fabric-epoxy
~
Longitudinal 0.6 1 0.17 0.5 0.35 0.13
conductivity
4W/m K)
Transverse 0.4 0.6 0.1 0.3 0.35 0.13
conductivity
(W/m K)
Longitudinal 7.4 -0.3 -3.6 4.1 8 0.8
CTE 10'
XI (]/"a
Transverse 22.4 34 60 19.2 8 0.8
CTE IO"
(1PC)