Callister - An introduction - 8th edition

15.4 Viscoelastic Deformation • 577
The final two high-temperature regions are rubbery flow and viscous flow. Upon
heating through these temperatures, the material experiences a gradual transition
to a soft rubbery state, and finally to a viscous liquid. In the rubbery flow region,
the polymer is a very viscous liquid that exhibits both elastic and viscous flow components.
Within the viscous flow region, the modulus decreases dramatically with
increasing temperature; again, the strain–time behavior is as represented in Figure
15.5d. From a molecular standpoint, chain motion intensifies so greatly that for viscous
flow, the chain segments experience vibration and rotational motion largely
independent of one another. At these temperatures, any deformation is entirely viscous
and essentially no elastic behavior occurs.
Normally, the deformation behavior of a viscous polymer is specified in terms
of viscosity, a measure of a material’s resistance to flow by shear forces. Viscosity
is discussed for the inorganic glasses in Section 12.10.
The rate of stress application also influences the viscoelastic characteristics. Increasing
the loading rate has the same influence as lowering temperature.
The log E r (10)-versus-temperature behavior for polystyrene materials having
several molecular configurations is plotted in Figure 15.8. The curve for the amorphous
material (curve C) is the same as in Figure 15.7. For a lightly crosslinked atactic
polystyrene (curve B), the rubbery region forms a plateau that extends to the
temperature at which the polymer decomposes; this material will not experience
melting. For increased crosslinking, the magnitude of the plateau E r (10) value will
also increase. Rubber or elastomeric materials display this type of behavior and are
ordinarily used at temperatures within this plateau range.
Also shown in Figure 15.8 is the temperature dependence for an almost totally
crystalline isotactic polystyrene (curve A). The decrease in E r (10) at T g is much less
pronounced than the other polystyrene materials because only a small volume
fraction of this material is amorphous and experiences the glass transition. Furthermore,
the relaxation modulus is maintained at a relatively high value with increasing
temperature until its melting temperature T m is approached. From Figure 15.8,
the melting temperature of this isotactic polystyrene is about 240C (460F).
Relaxation modulus, E r (10) (MPa)
Temperature (°F)
10 4 150 200 250 300 350 400 450
10 6
10 3
10 5
10 2
A
10 4
10 –3 T g
50 100 150 200 250
10
10 3
1
B
10 2
10 –1
10
C
10 –2
1
Temperature (°C)
Relaxation modulus (psi)
Figure 15.8
Logarithm of the
relaxation modulus
versus temperature for
crystalline isotactic
(curve A), lightly
crosslinked atactic
(curve B), and
amorphous (curve C)
polystyrene. (From
A. V. Tobolsky,
Properties and
Structures of Polymers.
Copyright © 1960 by
John Wiley & Sons,
New York. Reprinted
by permission of John
Wiley & Sons, Inc.)