Chemistry Reference
In-Depth Information
Three types of experiments are used in the study of viscoelasticity. These
involve creep, stress relaxation, and dynamic techniques. In creep studies a body
is subjected to a constant stress and the sample dimensions are monitored as a
function of time. When the polymer is first loaded an immediate deformation
occurs, followed by progressively slower dimensional changes as the sample
creeps toward a limiting shape. Figure 1.3 shows examples of the different beha-
viors observed in such experiments.
Stress relaxation is an alternative procedure. Here an instantaneous, fixed
deformation is imposed on a sample, and the stress decay is followed with time.
A very useful modification of these two basic techniques involves the use of a
periodically varying stress or deformation instead of a constant load or strain. The
dynamic responses of the body are measured under such conditions.
4.7.1
Phenomenological Viscoelasticity
Consider the tensile experiment of
Fig. 4.14a
as a creep study in which a steady
stress
τ
0
is suddenly applied to the polymer specimen. In general, the resulting
strain
(
t
) will be a function of time starting from the imposition of the load. The
results of creep experiments are often expressed in terms of compliances rather
than moduli. The tensile creep compliance
D
(
t
)is
ε
DðtÞ 5εðtÞ=σ
0
(4-40)
The shear creep compliance
J
(
t
) (see
Fig. 4.14b
) is similarly defined as
JðtÞ 5γðtÞ=τ
0
(4-41)
where
ε
0
is the constant shear stress and
γ
(
t
) is the resulting time-dependent
strain.
Stress relaxation experiments correspond to the situations in which the defor-
mations sketched in
Fig. 4.14
are imposed suddenly and held fixed while the
resulting stresses are followed with time. The tensile relaxation modulus
Y
(
t
)is
then obtained as
Y
ð
t
Þ 5σð
t
Þ=ε
0
(4-42)
with
ε
0
being the constant strain. Similarly, a shear relaxation experiment mea-
sures the shear relaxation modulus
G
(
t
):
G
ð
t
Þ 5τð
t
Þ=γ
0
(4-43)
where
γ
0
is the constant strain.
Although a compliance is the inverse of a modulus for an ideal elastic body,
this is not true for viscoelastic materials. That is,
Y
ð
t
Þ 5σð
t
Þ=ε
0
6¼ εð
t
Þ=σ
0
5
D
ð
t
Þ
(4-44)
