Page 189 - Plastics Engineering

172 Mechanical Behaviour of Composites

to the volume fraction as follows.

(3.1)

where p is the density and the subscripts f and c refer to fibres and composite
respectively .
Table 3.3 indicates the extent to which the properties of plastics are influ-
enced by the level of fibre content. Full details of the forms in which reinforcing
fibres are available for inclusion in plastics are given in Chapter 4.

Table 3.3
Effect of fibre content on properties of glass reinforced nylon 66

Weight fraction, Wf
property 0 0.10 0.20 0.30 0.40 0.50 0.60
Density 1140 1210 1280 1370 1460 1570 1700
Tensile strength (GN/m2) 0.07 0.09 0.13 0.18 0.21 0.23 0.24
96 elongation at break 60 3.5 3.5 3.0 2.5 2.5 1.5
Flexural modulus (GN/m2) 2.8 4.2 6.3 9.1 11.2 15.4 19.6
Thermal expansion pddC 90 37 32 30 29 25 22
Water absorption (24 tu) 1.6 1.1 0.9 0.9 0.6 0.5 0.4

3.5 Analysis of Continuous Fibre Composites
The greatest improvement in the strength and stiffness of a plastic is achieved
when it is reinforced with uni-directional continuous fibres. The analysis of
such systems is relatively straightforward.

(i) Longitudinal Properties
Consider a composite with continuous aligned fibres as shown in Fig. 3.3.
If the moduli of the matrix and fibres are E, and Ef respectively then the
modulus of the composite may be determined as follows.

Equilibrium Equation
The applied force on the composite will be shared by the fibres and the
matrix. Hence
F1 = Ff + F, (3.2)

Geometry of Deformation Equation
The strain, E, is the same in the fibres and matrix and is equal to the strain
in the composite.
E1 = Ef = Em (3.3)