Page 235 - Plastics Engineering

218 Mechanical Behaviour of Composites
For the [& 451, laminate this would give
18.1
G - = 5 GN/m2
xy - 2(1 + 0.814)
However, Fig. 3.25 shows that G,, = 45.2 GN/m2 for the [f 45Is laminate.
Some laminates do exhibit quasi-isotropic behaviour. The simplest one is
[0, f 601,. For this laminate
E, = E, = 66.4 GN/m 2 and uxy = uyx = 0.321, Gxy = 25.1 GN/m2

(using the individual ply data in the above Example).
If we check Gxy from the isotropic equation we get

-
Gxy = Ex - 66.4 = 25.1 GN/m2
2(1+ uxy) 2(1 + 0.321)
This agrees with the value calculated from the laminate theory.
In general any laminate with the lay-up

or

is quasi-isotropic where N is an integer equal to 3 or greater. The angles for
the plies are expressed in radians.

3.12 Analysis of Multi-layer Isotropic Materials

The Plate Constitutive equations can be used for curved plates provided the
radius of curvature is large relative to the thickness (typically r/h > 50). They
can also be used to analyse laminates made up of materials other than unidi-
rectional fibres, eg layers which are isotropic or made from woven fabrics can
be analysed by inserting the relevant properties for the local 1-2 directions.
Sandwich panels can also be analysed by using a thickness and appropriate
properties for the core material. These types of situation are considered in the
following Examples.
Example 3.14 A blow moulded plastic bottle has its wall thickness made of
three layers. The layers are:
Outside and inside skin - Material A
thickness = 0.4 mm, El = E2 = 3 GN/m2, Gl2 = 1.1 GN/m2, u12 = 0.364
Core - Material B
thickness = 0.4 mm, E1 = E2 = 0.8 GN/m2, Glz = 0.285 GN/m2,
1112 = 0.404.