Page 133 - Plastics Engineering

116 Mechanical Behaviour of Plastics

2.14 Time-Temperature Superposition
It has been shown throughout this chapter that the properties of plastics are
dependent on time. In Chapter 1 the dependence of properties on temperature
was also highlighted. The latter is more important for plastics than it would be
for metals because even modest temperature changes below 100°C can have
a significant effect on properties. Clearly it is not reasonable to expect creep
curves and other physical property data to be available at all temperatures. If
information is available over an appropriate range of temperatures then it may
be possible to attempt some type of interpolation. For example, if creep curves
are available at 20°C and 60°C whereas the service temperature is 40°C then a
linear interpolation would provide acceptable design data.
If creep curves are available at only one temperature then the situation
is a little more difficult. It is known that properties such as modulus will
decrease with temperature, but by how much? Fortunately it is possible to use
a time-temperature superposition approach as follows:
It was shown earlier that the variation of creep or relaxation moduli with
time are as illustrated in Fig. 2.9. If we now introduce temperature as a variable
then a series of such curves will be obtained as shown in Fig. 2.58. In general
the relaxed and unrelaxed modulus terms are independent of temperature. The
remainder of the moduli curves are essentially parallel and so this led to the
thought that a shift factor, UT, could be applied to move from one curve to
another.
Modulus ’
L

log (time)
Fig. 2.58 Modulus-time curves for a range of temperatures

It may be seen from Fig. 2.59 that the two modulus curves for temperatures
TI and TZ are separated by a uniform distance (1oguT). Thus, if the material
behaviour is known at TI, in order to get the modulus at time, f, and temperature