COMPOSITES - Materials for Civil and Construction Engineers - page 459

Sample Problem 11.1

Calculate the modulus of elasticity of fiberglass under isostrain condition if the fiber-
glass consists of 70% E-glass fibers and 30% epoxy by volume. Also, calculate the
percentage of load carried by the glass fibers. The modulus of elasticity of the glass
fibers and the epoxy are 70.5 GPa and 6.9 GPa, respectively.

Solution
From Equation 11.6,

E c = 1 0.3 21 6.9 2 + 1 0.7 21 70.5 2 = 51.4 GPa

From Equation 11.7,

F f
F c

70.5
51.4

= 0.7 = 0.96 = 96 %

1 2

This example shows that, under the given conditions, 96% of the load is carried by the
fibers.

Equation 11.6 can be generalized to cover other composite properties as
a function of the properties of the components as

X c = n m X m + n f X f (11.8)

where X is a property such as Poisson's ratio, thermal conductivity, elec-
trical conductivity, or diffusivity.

■ 11.3.2 Loading Perpendicular to Fibers

When load is applied to an aligned fiber-reinforced composite perpendicu-
lar to the fibers [Figure 11.13(b)], both matrix and fiber phases will be sub-
jected to the same stress (isostress condition). In other words,

s c = s m = s f = s (11.9)

The elongation of the composite in the direction of the applied stress is the
sum of the elongations of the matrix and fibers:

¢L c =¢L m +¢L f (11.10)

Dividing Equation 11.10 by the composite length L c in the stress direction

gives

¢L f
L c

¢ L c
L c

¢ L m
L c

= + (11.11)