Page 526 - Carrahers_Polymer_Chemistry,_Eighth_Edition

Rheology and Physical Tests 489

14.1.2 RESPONSE TIME

We can get a first approximation of the physical nature of a material from its response time. For a

Maxwell element, the relaxation time is the time required for the stress in a stress–strain experi-
ment to decay to 1/e or 0.37 of its initial value. A material with a low relaxation time fl ows easily
so it shows relatively rapid stress decay. Thus, whether a viscoelastic material behaves as a solid

or fluid is indicated by its response time and the experimental time scale or observation time. This

observation was first made by Marcus Reiner who defined the ratio of the material response time
to the experimental time scale as the Deborah Number, D . Presumably, the name was derived by
n
Reiner from the Biblical quote in Judges 5, Song of Deborah where it says “The mountains fl owed
before the Lord.”
Response time (14.15)
D =
n
Experimental time scale
A high Deborah Number designates the solid behavior of a viscoelastic material while a low

Deborah Number corresponds to a viscoelastic material behaving as a fluid. Thus, window glass
has a high relaxation time at room temperature. Application of a stress to produce a little strain and
looking for it to return to its approximate prestressed state will take a long time as we count our
observation time in hours, days, and weeks. Thus, it would have a relatively high Deborah Number
under this observation time scale and be acting as a solid. Yet, if we were to have as our observation
scale millions of years, the return to the prestressed state would be rapid with the glass acting as a
viscous liquid and having a low Deborah Number. Again, this represents only a fi rst approximation
measure of the behavior of a material.

14.2 TYPICAL STRESS–STRAIN BEHAVIOR

For perspective, Figure 14.6 contains general ranges for the three major polymer groupings with
respect to simple stress–strain behavior.
Most physical tests involve nondestructive evaluations. For our purposes, three types of mechan-
ical stress measures (described in Figure 14.7) will be considered. The ratio of stress to strain is
called Young’s modulus. This ratio is also called the modulus of elasticity and tensile modulus. It is
calculated by dividing the stress by the strain.

Stress (Pa)
Young's modulus = (14.16)
Strain (mm/mm)

Large values of Young’s modulus indicate that the material is rigid and resistant to elongation
and stretching. Many synthetic organic polymers have Young’s modulus values in the general
10
5
range of about 10 –10 Pa for stiff fi bers. Polystyrene has a Young’s modulus of about 10 Pa and
9
soft rubber a value of about 10 Pa. For comparison, fused quartz has a Young’s modulus of about
6
11
10
10 ; cast iron, tungsten, and copper have values of about 10 ; and diamond has a value of about
10 Pa. Thus, PS represents a glassy polymer at room temperature and is about 100 times as soft
12
as copper, but soft rubber, such as present in rubber bands, is about 1,000 times softer than PS.

Carswell and Nason assigned fi ve classifications to polymers (Figure 14.8). It must be remem-
bered that the ultimate strength of each of these is the total area under the curve before breaking.
The soft and weak class, such as polyisobutylene, is characterized by a low modulus of elasticity,
low yield (stress) point, and moderate time-dependent elongation. The Poisson ratio, that is, ratio
of contraction to elongation, for soft and weak polymers is about 0.5, which is similar to that found
for many liquids.

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