Page 85 - Engineering Plastics Handbook

Processing 59

single most important consideration when one is designing polymer sys-
tems for ease of injection molding.

Time-Temperature Superposition
Shift Principle
A cursory description of the time-temperature superposition shift princi-
ple is provided with a cartesian graph for a given viscoelastic polymer, with
the y axis equal to Young’s modulus (as tensile or compression modulus),
MPa, and the x axis equal to time, s. Data are plotted at increasing times,
for different temperatures. Atemperature is selected as the reference tem-
perature, and isotherms for other temperatures are shifted along the x axis
(time) to provide a master curve. The master curve shows the dynamic
characteristics of the viscoelastic polymer beyond the time and frequency
ranges of conventional test measurements.
To calculate the time-temperature superposition shift factor [2], use
ητ / ητ
a = 0 test 0 ref
T
T ρ / T ρ
ref ref test test
where a = time-temperature superposition shift factor
T
η = zero shear rate viscosity (steady-state viscosity at zero
0
shear rate)
τ test = relaxation time for tested specimen
τ ref = relaxation time for reference specimen
T ref = reference temperature, K
ρ ref = reference density
T test = test temperature, K
ρ test = test density
τ T
a = test test
T
τ ref T ref
To calculate the time-temperature superposition shift factor by using
the WLF (Williams-Landel-Ferry) equation for polymers at tempera-
o
o
tures less than 100 C (232 F) above their T [2], use
g
− CT − T )
(
lna = 1 ref
T
C + (T − T )
2 ref
where a = time-temperature superposition shift factor
T
C = WLF constant for an individual polymer
1
T = specified temperature
T ref = reference temperature
C = WLF constant for an individual polymer
2
Ferry published a list of WLF C and C constants when T ref = T in
g
1
2
Viscoelastic Properties of Polymers (2d ed., Wiley, New York, 1970).