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Mechanical Behaviour of Composites 189
Example 3.6 A unidirectional composite consisting of carbon fibres in a
PEEK matrix has the fibres aligned at 25" to the loading axis. If the fibres and
matrix have the properties indicated below, calculate E,, E,, G,,, v,,, and up.
Ef = 240 GN/m2 E, = 3 GN/m2
vf = 0.23 urn = 0.35
Vf = 0.6
pf = 1700 kg/m3 pm = 1300 kg/m3
Gf= 80 GN/m2 G,= 1.1 GN/m2

Solution The lamina properties in the local (1-2) directions are calculated
as follows:

El = EfVf + Em.(l - Vj), E1 = 145.2 GN/m2

Halpin-Tsai Equation

Gl2 = 4.185 GN/m2 Halpin-Tsai Equation
~12 = ~f * Vf + U, . (1 - Vf) ~12 = 0.278
v21 = v12. (2) ~21 = 0.029

The behaviour of the lamina when subjected to loading at 8 degrees off the
fibre axis is determined using matrix manipulation as follows:

Loading On-Axis Compliance Matrix Stifiess Matrix

S=
1
0 0 -
Gl2
Stress Transformation Matrix Overall Compliance Matrix

c2 s2 2.s.c
To = [ s2 c2 -2.s.c
-s.c s.c (c2 - 2)