Callister - An introduction - 8th edition

15.4 Viscoelastic Deformation • 575
a ball and dropped onto a horizontal surface, it bounces elastically—the rate of deformation
during the bounce is very rapid. On the other hand, if pulled in tension
with a gradually increasing applied stress, the material elongates or flows like a
highly viscous liquid. For this and other viscoelastic materials, the rate of strain determines
whether the deformation is elastic or viscous.
relaxation modulus
Relaxation
modulus—ratio of
time-dependent
stress and constant
strain value
Viscoelastic Relaxation Modulus
The viscoelastic behavior of polymeric materials is dependent on both time and
temperature; several experimental techniques may be used to measure and quantify
this behavior. Stress relaxation measurements represent one possibility. With
these tests, a specimen is initially strained rapidly in tension to a predetermined and
relatively low strain level. The stress necessary to maintain this strain is measured
as a function of time, while temperature is held constant. Stress is found to decrease
with time because of molecular relaxation processes that take place within the polymer.
We may define a relaxation modulus E r (t), a time-dependent elastic modulus
for viscoelastic polymers, as
E r 1t2 s1t2
0
(15.1)
where (t) is the measured time-dependent stress and 0 is the strain level, which
is maintained constant.
Furthermore, the magnitude of the relaxation modulus is a function of temperature;
to more fully characterize the viscoelastic behavior of a polymer, isothermal
stress relaxation measurements must be conducted over a range of temperatures.
Figure 15.6 is a schematic log E r (t)-versus-log time plot for a polymer that exhibits
Log relaxation modulus, E r (t)
Figure 15.6 Schematic plot of logarithm of
relaxation modulus versus logarithm of time
for a viscoelastic polymer; isothermal curves
T 1
are generated at temperatures T 1 through
T 7 . The temperature dependence of the
relaxation modulus is represented as log
E r (t 1 ) versus temperature.
T T3 2
T 7 > T 6 > . . . > T 1
T 4
T 5
T 6
T 7
t 1
Log time, t