Page 160 - Plastics Engineering

Mechanical Behaviour of Plastics 143

drop in stress amplitude. There is therefore a drop in energy dissipation and
hence temperature. In this case it is found that this self stabilising mechanism
prevents the Occurrence of thermal softening failures. The nett result is that
under this mode of control the temperature rise always stabilises and only
fatigue type failures are observed.

2.21.4 Effect of Mean Stress
For convenience, in the previous sections it has been arranged so that the mean
stress is zero. However, in many cases of practical interest the fluctuating
stresses may be always in tension (or at least biased towards tension) so that
the mean stress is not zero. The result is that the stress system is effectively
a constant mean stress, a,,, superimposed on a fluctuating stress a,. Since the
plastic will creep under the action of the steady mean stress, this adds to the
complexity because if the mean stress is large then a creep rupture failure
may occur before any fatigue failure. The interaction of mean stress and stress
amplitude is usually presented as a graph of (a,Va,) as shown in Fig. 2.76.
This represents the locus of all the combinations of a, and a,,, which cause
fatigue failure in a particular number of cycles, N. For plastics the picture
is slightly different from that observed in metals. Over the region WX the
behaviour is similar in that as the mean stress increases, the stress amplitude
must be decreased to cause failure in the same number of cycles. Over the
region YZ, however, the mean stress is so large that creep rupture failures are
dominant. Point Z may be obtained from creep rupture data at a time equal to
that necessary to give N cycles at the test frequency. It should be realised that,
depending on the level of mean stress, different phenomena may be the cause
of failure.
The level of mean stress also has an effect on the occurrence of thermal
failures. Typically, for any particular stress amplitude the stable temperature
rise will increase as the mean stress increases. This may be to the extent that a
stress amplitude which causes a stable temperature rise when the mean stress is
zero, can result in a thermal runaway failure if a mean stress is superimposed.
For design purposes it is useful to have a relationship between a, and a,,
similar to those used for metals (e.g. the Soderberg and Goodman relationships).
It is suggested that the equation of a straight line joining points W and Z in
Fig. 2.76 would be best because it is simple and will give suitably conservative
estimates for the permissible combinations of a, and a,,, to produce failure in
a pre-selected number of cycles. Such an equation would have the form
aa=af (I -%) (2.116)

where af is the fatigue endurance at N cycles
a, is the creep rupture strength at a time equivalent to N cycles