Page 123 - Plastics Engineering

106 Mechanical Behaviour of Plastics

equation (2.63) permits the problem of intermittent loading to be analysed in
a relatively straightforward manner thus avoiding uneconomical overdesign
which would result if the recovery during the rest periods was ignored.
From equation (2.63) and the definition of Fractional Recovery, F,, the
residual strain is given by
&r(t) = &c(T) - Fr * &c(T)

If there have been N cycles of creep and recovery the accumulated residual
strain would be
x=N
&,(t) = EC(T) [ (F) ?I - ( y - 1) '1
x=l
where tp is the period of each cycle and thus the time for which the total
accumulated strain is being calculated is t = t,N.
Note also that the total accumulated strain after the load application for the
(N + 1)th time will be the creep strain for the load-on period ie cC(T) plus the
residual strain s,(t).

-
ie (&N+l)max = &c(T) { 1 + x=N [(F)" (y - l)n]} (2.65)
x= I
Tests have shown that when total strain is plotted against the logarithm of
the total creep time (ie NT or total experimental time minus the recovery time)
there is a linear relationship. This straight line includes the strain at the end of
the first creep period and thus one calculation, for say the 10th cycle allows
the line to be drawn. The total creep strain under intermittent loading can then
be estimated for any combinations of loading/unloading times.
In many design calculations it is necessary to have the creep modulus in
order to estimate deflections etc from standard formulae. In the steady loading
situation this is straightforward and the method is illustrated in the Exam-
ples (2.1)-(2.5). For the intermittent loading case the modulus of the material
is effectively increased due to the apparent stiffening of the material caused
by the recovery during the rest periods. For example, if a constant stress of
17.5 MN/m2 was applied to acetal (see Fig. 2.51) for 9600 hours then the total
creep strain after this time would be 2%. This would give a 2% secant modulus
of 17.5/0.02 = 875 MN/m2. If, however, this stress was applied intermittently
for 6 hours on and 18 hours off, then the total creep strain after 400 cycles
(equivalent to a total time of 9600 hours) would only be 1.4%. This would be
equivalent to a stress of 13 MN/m2 being applied continuously for 9600 hours
and so the effective creep modulus would be 13/0.014 = 929 MN/m2.