Page 69 - Plastics Engineering

52 Mechanical Behaviour of Plastics

Occasionally in creep analysis it is convenient to use a Creep Compliance
instead of the creep modulus. This is simply given by

N)
1
Creep compliance, c(t) = - - (2.10)
=
at) 0
An alternative to the isometric graph may be obtained by taking a constant
time section through the creep curves and plotting stress versus strain as shown
in Fig. 2.10(c). This Isochronous Graph can also be obtained experimentally
by performing a series of mini-creep and recovery tests on a plastic. In this
experiment a stress is applied to a plastic test-piece and the strain is recorded
after a time, t (typically 100 seconds). The stress is then removed and the
plastic allowed to recover, normally for a period of 4t. A larger stress is then
applied to the same specimen and after recording the strain at time t, this stress
is removed and the material allowed to recover. This procedure is repeated until
sufficient points have been obtained for the isochronous graph to be plotted.
These latter curves are particularly important when they are obtained exper-
imentally because they are less time consuming and require less specimen
preparation than creep curves. Isochronous graphs at several time intervals can
also be used to build up creep curves and indicate areas where the main exper-
imental creep programme could be most profitably concentrated. They are also
popular as evaluations of deformational behaviour because the data presenta-
tion is similar to the conventional tensile test data referred to in Section 2.3. It
is interesting to note that the isochronous test method only differs from that of
a conventional incremental loading tensile test in that (a) the presence of creep
is recognised, and (b) the memory which the material has for its stress history
is accounted for by the recovery periods.
Quite often isochronous data is presented on log-log scales. One of the
reasons for this is that on linear scales any slight, but possibly important,
non-linearity between stress and strain may go unnoticed whereas the use of
log-log scales will usually give a straight-line graph, the slope of which is an
indication of the linearity of the material. If it is perfectly linear the slope will
be 45". If the material is non-linear the slope will be less than this.
As indicated above, the stress-strain presentation of the data in isochronous
curves is a format which is very familiar to engineers. Hence in design situ-
ations it is quite common to use these curves and obtain a secant modulus
(see Section 1.4.1, Fig. 1.6) at an appropriate strain. Strictly speaking this will
be different to the creep modulus or the relaxation modulus referred to above
since the secant modulus relates to a situation where both stress and strain are
changing. In practice the values are quite similar and as will be shown in the
following sections, the values will coincide at equivalent values of strain and
time. That is, a 2% secant modulus taken from a 1 year isochronous curve will
be the same as a 1 year relaxation modulus taken from a 2% isometric curve.