Chemistry Reference
In-Depth Information
DATA
MASTER CURVE
GLASSY
T
1
T
2
T
3
T
4
T
5
T
6
T
7
T
8
RUBBERY
VISCOUS
T
9
−
10 1
−
6
−
4
−
2
0
2
LOG TIME
(min)
LOG TIME (min)
FIGURE 4.19
Left panel: Stress decay at various temperatures T
1
, T
2
, ..., T
9
. right panel: Master
curve for stress decay at temperatureT
8
.
temperature scale in dynamic mechanical experiments can be replaced by an
inverse log frequency scale.
Master curves permit the evaluation of mechanical responses at very long
times by increasing the test temperature instead of prolonging the experiment. A
complete picture of the behavior of the material is obtained in principle by operat-
ing in experimentally accessible time scales and varying temperatures.
Time
temperature superposition can be expressed mathematically as
G
ð
T
1
;
t
Þ 5
G
ð
T
2
;
t
=
a
T
Þ
(4-69)
for a shear stress relaxation experiment. The effect of changing the temperature is
the same as multiplying the time scale by shift factor
a
T
. A minor correction is
required to the formulation of
Eq. (4-69)
to make the procedure complete. The
elastic modulus of a rubber is proportional to the absolute temperature
T
and to
the density
of the material, as summarized in
Eq. (4-31)
. It is therefore proper
to divide through by
T
and
ρ
to compensate for these effects of changing the test
temperature. The final expression is then
G
ρ
ð
T
1
;
t
Þ
G
ð
T
2
;
t
=
a
T
Þ
T
1
5
(4-70)
ρð
T
1
Þ
ρð
T
2
Þ
T
2
