GTBL042-07 GTBL042-Callister-v2 August 6, 2007 12:43
220 • Chapter 7 / Mechanical PropertiesTemperature (°C)Relaxation modulus,Er(10) (MPa)Relaxation modulus (psi)60(^1010) –1
–3
10 –4
80 100
Tg Tm
120 140
Glassy
Leathery
Rubbery
Rubbery flow
Viscous flow (liquid)
160 180 200
10 –2
10 –1
1
10
102
103
104
105
160 200 240
Temperature (°F)
280 320 360
1
10
102
103
104
105
106
107
Figure 7.28 Logarithm
of the relaxation modulus
versus temperature for
amorphous polystyrene,
showing the five different
regions of viscoelastic
behavior. (From A. V.
Tobolsky,Properties and
Structures of Polymers.
Copyright©c1960 by
John Wiley & Sons, New
York. Reprinted by
permission of John Wiley
& Sons, Inc.)
the load application. Several distinct regions may be noted on this curve. At the
lowest temperatures, in the glassy region, the material is rigid and brittle, and the
value ofEr(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 7.26b. On a molecular level, the long molecular chains are
essentially frozen in position at these temperatures.
As the temperature is increased,Er(10) drops abruptly by about a factor of
103 within a 20◦C (35◦F) temperature span; this is sometimes called the leathery,
or glass transition region, and the glass transition temperature (Tg, Section 11.16)
lies near the upper temperature extremity; for polystyrene (Figure 7.28),Tg= 100 ◦C
(212◦F). 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 7.26c.
Within the rubbery plateau temperature region (Figure 7.28), the material de-
forms 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.
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 com-
ponents. Within the viscous flow region, the modulus decreases dramatically with
increasing temperature; again, the strain–time behavior is as represented in Fig-
ure 7.26d. From a molecular standpoint, chain motion intensifies so greatly that for
viscous flow, the chain segments experience vibration and rotational motion largely