Page 70 - Plastics Engineering

Mechanical Behaviour of Plastics 53

Pseudo-Elastic Design Method for Plastics
Throughout this chapter the viscoelastic behaviour of plastics has been
described and it has been shown that deformations are dependent on such
factors as the time under load and the temperature. Therefore, when structural
components are to be designed using plastics, it must be remembered that the
classical equations which are available for the design of springs, beams, plates,
cylinders, etc., have all been derived under the assumptions that
(i) the strains are small
(ii) the modulus is constant
(iii) the strains are independent of loading rate or history and are immedi-
ately reversible
(iv) the material is isotropic
(v) the material behaves in the same way in tension and compression
Since these assumptions are not always justified for plastics, the classical
equations cannot be used indiscriminately. Each case must be considered' on
its merits and account taken of such factors as mode of deformation, service
temperature, fabrication method, environment and so on. In particular it should
be noted that the classical equations are derived using the relation.

stress = modulus x strain
where the modulus is a constant. From the foregoing sections it should be clear
that the modulus of a plastic is not a constant. Several approaches have been
used to allow for this and some give very accurate results. The drawback is
that the methods can be quite complex, involving Laplace transforms or numer-
ical methods and they are certainly not attractive to designers. However, one
method that has been widely accepted is the so called Pseudo Elastic Design
Method. In this method, appropriate values of time dependent properties, such
as modulus, are selected and substituted into the classical equations. It has
been found that this approach gives sufficient accuracy in most cases provided
that the value chosen for the modulus takes into account the service life of the
component and the limiting strain of the plastic. This of course assumes that
the limiting strain for the material is known. Unfortunately this is not just a
straightforward value which applies for all plastics or even for one plastic in
all applications. It is often arbitrarily chosen although several methods have
been suggested for arriving at a suitable value. One method is to plot a secant
modulus which is 0.85 of the initial tangent modulus (see Fig. 1.6) and note
the strain at which this intersects the stress-strain characteristic. However, for
many plastics (particularly crystalline ones) this is too restrictive and so in
most practical situations the limiting strain is decided in consultations between
the designer and the material manufacturers.
Once the limiting strain is known, design methods based on the creep
curves are quite straightforward and the approach is illustrated in the following