Callister - An introduction - 8th edition

576 • Chapter 15 / Characteristics, Applications, and Processing of Polymers
Relaxation modulus, E r (10) (MPa)
Temperature (°F)
10 5 160 200 240 280 320 360
10 4
10 3
Glassy
10 2
10
Leathery
1
10 –1 Rubbery
Rubbery flow
Figure 15.7 Logarithm
of the relaxation modulus
10 7 versus temperature for
amorphous polystyrene,
10 6 showing the five different
regions of viscoelastic
behavior. (From A. V.
10 5 Tobolsky, Properties and
Structures of Polymers.
Copyright © 1960 by
10 4
John Wiley & Sons, New
York. Reprinted by
10 3 permission of John
Wiley & Sons, Inc.)
10 2
10
Relaxation modulus (psi)
10 –2
1
10 –3
Viscous flow (liquid)
10 –1
10 –4 60 80 100
T g
120 140
Temperature (°C)
160 180 200
T m
viscoelastic behavior. Curves generated at a variety of temperatures are included.
Key features of this plot are that (1) the magnitude of E r (t) decreases with time
(corresponding to the decay of stress, Equation 15.1), and (2) the curves are displaced
to lower E r (t) levels with increasing temperature.
To represent the influence of temperature, data points are taken at a specific
time from the log E r (t)-versus-log time plot—for example, t 1 in Figure 15.6—and
then cross-plotted as log E r (t 1 ) versus temperature. Figure 15.7 is such a plot for an
amorphous (atactic) polystyrene; in this case, t 1 was arbitrarily taken 10 s after the
load application. Several distinct regions may be noted on the curve shown in this
figure. At the lowest temperatures, in the glassy region, the material is rigid and
brittle, and the value of E r (10) is that of the elastic modulus, which initially is virtually
independent of temperature. Over this temperature range, the strain–time
characteristics are as represented in Figure 15.5b. On a molecular level, the long
molecular chains are essentially frozen in position at these temperatures.
As the temperature is increased, E r (10) drops abruptly by about a factor of 10 3
within a 20C (35F) temperature span; this is sometimes called the leathery, or glass
transition region, and the glass transition temperature (T g , Section 15.13) lies near
the upper temperature extremity; for polystyrene (Figure 15.7), T g 100C (212F).
Within this temperature region, a polymer specimen will be leathery; that is, deformation
will be time dependent and not totally recoverable on release of an applied
load, characteristics that are depicted in Figure 15.5c.
Within the rubbery plateau temperature region (Figure 15.7), the material deforms
in a rubbery manner; here, both elastic and viscous components are present,
and deformation is easy to produce because the relaxation modulus is relatively low.