Page 24 - Handbook of Plastics Technologies

INTRODUCTION TO POLYMERS AND PLASTICS

1.10 CHAPTER 1

FIGURE 1.9 Spring and dashpot models.

where τ is the characteristic relaxation time (η/k). Under a fixed load, the specimen will
continue to elongate with time, a phenomenon termed creep, which can be modeling using
a spring and dashpot in parallel as seen in Fig. 1.9. This model predicts the time-dependent
strain as

t – ⁄ τ
ε t() = ε e (1.6)
o
For more accurate prediction of the time-dependent behavior, other models with more
elements are often employed. In the design of polymeric products for long-term applica-
tions, the designer must consider the time-dependent behavior of the material.
If a series of stress relaxation curves is obtained at varying temperatures, it is found
that these curves can be superimposed by horizontal shifts to produce a master curve. 3
This demonstrates an important feature in polymer behavior: the concept of time-tempera-
ture equivalence. In essence, a polymer at temperatures below room temperature will be-
have as if it were tested at a higher rate at room temperature. This principle can be applied
to predict material behavior under testing rates or times that are not experimentally acces-
sible through the use of shift factors (aT) and the equation below:

⎛⎞ 17.44 T –( T )
t
g
ln a = ln ---- = – ---------------------------------- (1.7)
T t ⎝⎠ 51.6 + T – T
o g
where T is the glass transition temperature of the polymer.
g
1.4.2 Failure Behavior
The design of plastic parts requires the avoidance of failure without overdesign of the part,
leading to increased part weight. The type of failure can depend on temperatures, rates,
and materials. Some information on material strength can be obtained from simple tensile
stress-strain behavior. Materials that fail at rather low elongations (1 percent strain or less)
4
can be considered to have undergone brittle failure. Polymers that produce this type of

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)
Copyright © 2006 The McGraw-Hill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.