Page 41 - Plastics Engineering

24 General Properties of Plastics

6=a1 (G)
will be given by

where a1 is a constant and W represents the loading.
The stiffness may then be expressed as
W

where a2 is a constant and again it is assumed that the beam width and length
are the same in all cases.
Once again the beam weight will be given by equation (1.3) so substituting
for d from equation (1.7)
1/3
w = (~3p/E (1.8)
Hence, the desirability factor, Df , expressed as maximum stiffness for
minimum weight will be given by

where E is the elastic modulus of the material in question and p is the density.
As before a range of similar factors can be derived for other structural elements
and these are illustrated in Section 1.4.6. (Tables 1.11 and 1.12) where the
effect of material cost is also taken into account. Note also that since for
plastics the modulus, E, is not a constant it is often necessary to use a long-
term (creep) modulus value in equation (1.9) rather than the short-term quality
control value usually quoted in trade literature.
Ductility. A load-bearing device or component must not distort so much
under the action of the service stresses that its function is impaired, nor must it
fail by rupture, though local yielding may be tolerable. Therefore, high modulus
and high strength, with ductility, is the desired combination of attributes.
However, the inherent nature of plastics is such that high modulus tends to
be associated with low ductility and steps that are taken to improve the one
cause the other to deteriorate. The major effects are summarised in Table 1.6.
Thus it may be seen that there is an almost inescapable rule by which increased
modulus is accompanied by decreased ductility and vice versa.
Creep and Recovery Behaviour. Plastics exhibit a time-dependent strain
response to a constant applied stress. This behaviour is called creep. In a
similar fashion if the stress on a plastic is removed it exhibits a time dependent
recovery of strain back towards its original dimensions. This is illustrated in