Page 83 - Plastics Engineering

66 Mechanical Behaviour of Plastics
As a practical point, it should be noted that the separation force will change
with time. This is because the modulus, E, will decrease with time. Suppose
that in this Example, the assembly is to be maintained in position for 1 year
and that during this time the modulus decreases to half its initial value (the 1
year modulus would be obtained from the creep curves in the normal way).
The above analysis shows that the interface pressure would then be half its
initial value (because 6r is fixed) and this in turn means that the separation
force would become 500 N instead of 1 kN.

2.7 Multi-layer Mouldings
It is becoming common practice to have the cross-section of a plastic moulding
made up of several different materials. This may be done to provide a perme-
ation barrier whilst retaining attractive economics by having a less expensive
material making up the bulk of the cross-section. To perform stress analysis in
such cases, it is often convenient to convert the cross-section into an equivalent
section consisting of only one material. This new section will behave in exactly
the same way as the multi-layer material when the loads are applied. A very
common example of this type of situation is where a solid skin and a foamed
core are moulded to provide a very efficient stiffnesdweight ratio. This type
of situation may be analysed as follows:
Example 2.8 A polypropylene sandwich moulding is 12 mm thick and
consists of a foamed core sandwiched between solid skin layers 2 mm thick. A
beam 12 mm wide is cut from the moulding and is subjected to a point load, W,
at mid-span when it is simply supported over a length of 200 mm. Estimate the
depth of a solid beam of the same width which would have the same stiffness
when loaded in the same way. Calculate also the weight saving by using the
foam moulding. The density of the solid polypropylene is 909 kg/m3 and the
density of the foamed core is 600 kg/m3.
Solution The first step in analysing the foamed sandwich type structure is
to calculate the second moment of area of the cross-section. This is done by
converting the cross section to an equivalent section of solid plastic. This is
shown in Fig. 2.18.
The equivalent width of the flange in the I section is given by

(2.18)

where E, and E, refer to the modulus values for the core (c) and solid (s)
material. In most cases there is very little information available on the modulus
of foamed plastics but fortunately an empirical relationship has been found to