Page 82 - Mechanics Analysis Composite Materials

Chapter 3. Mechanics of a unidirectional ptv 61

Table 3.4
Variation coefficient for fibers and unidirectional composites.

Fibers Variation coefficient r2 (YO)
Fibers Composite
Glass 29 2.0
Carbon 30 4.7
Aramid 24 5.0
Boron 23 3.0

Let the central fiber have a crack induced by the fiber damage or by the shortage of
this fiber strength. At a distance from the crack, the fibers are uniformly loaded with
stress 0 (see Fig. 3.15).
First, derive the set of equations describing the ply under study. Because the
stiffness of the matrix is much less than that of fibers, we neglect the stress in the
matrix acting in the x-direction and assume that the matrix works only in shear. We
also assume that there are no displacements in the y-direction.
Considering equilibrium of the last (n = k)fiber, an arbitrary fiber, and the central
(n = 0) fiber shown in Fig. 3.16 we arrive at the following equilibrium equations

(3.18)

k

(n + 1)
n

(n -1)

1
0

I'
sym. sym.

Fig. 3.15. Model of a unidirectional ply with a broken fiber.