Page 135 - Plastics Engineering

118 Mechanical Behaviour of Plastics

determine ET^ without knowing how the modulus varies with time. This is
illustrated in Fig. 2.60 where it is readily seen that a knowledge of ET, and UT
do not lead to a single value of ET* unless the E(t) relationship is known.

Fig. 2.60 Various modulus-time curves

Example 2.18 A particular grade of polypropylene can have its relaxation
modulus described by the equation

E(t) = 1.8t-O”

where E(t) is in GN/m2 when ’t’ is in seconds. The temperature of the material
is 20°C. Use the WLF equation to determine the 1 year modulus of the material
at 60°C. The glass transition temperature for the polypropylene is -10°C.
Solution To use equation (2.76) it would be necessary to know the properties
at - 10°C. In this example, the properties are known at 20°C which becomes the
reference temperature (TI). The approach taken will be to get the shift factor
at T2(= 60°C) and the shift factor at TI(= 20°C) and then subtract these to
get the shift factor from T1 to T2.

- 17.4(20 + 10) 17.4(60 + 10)
- -
51.6 + (20 + 10) 51.6 + (60 + 10)
= -3.62

UT = 2.4 x 10-~