Page 232 - Plastics Engineering

Mechanical Behaviour of Composites 215

the matrix manipulation - although this is not difficult, it is quite time-
consuming if it has to be done manually.
The following Example compares the behaviour of a single ply and a
laminate.
Example 3.13 A single ply of carbon fibre/epoxy composite has the
following properties:
El = 175 GN/m2, E2 = 12 GN/m2, G12 = 5 GN/m2, u12 = 0.3

Plot the variations of E,, E,, G,, and uxy for values of 8 in the range 0 to 90"
for (i) a single ply 0.4 mm thick and (ii) a laminate with the stacking sequence
[4=8],. This laminate has four plies, each 0.1 mm thick. Discuss the meaning
of the results.

Solution
(i) Single ply The method of solution simply involves the determination of
[SI, [el, [el, [SI and [a] as illustrated previously, ie

PI =

1
0 0 -
GI2
Then
= T, . Q . T, and

IAl = le1 . h and
Then for 8 = 25" (for example)
1
= 28.3 GN/m2
E, = -
allh
E 1 - 11.7 GN/m2
Y-
a22h
1
G,, = - 7.3 GN/m2
=
Q66h
--a12
--a12
-
-
=
uxy = - 0.495 and u,, = - 0.205
-a1 I a22
Fig. 3.24 shows the variation of these elastic constants for all values of 8
between 0 and 90".