Chemistry Reference
In-Depth Information
FIGURE 14.5
The comparison of experimental s
Y
and calculated according to the Eq.
(14.15)
s
yield stress values for UHMPE (1), UHMPE-Al (2) and UHMPE-bauxite (3) [31].
From the Eq. (14.15) it follows, that polymers structure fractality (
d
f
<
d
)
results to yield stress essential reduction. From the point of view of thermo-
dynamics is
Y
indicated reduction is due to accumulation in sample of internal
(latent) energy, the relative fraction of which is equal to about n
fr
[41]. For
Euclidean solids (
d
f
=
d
) the Eq. (14.15) gives Hooke law. At the same time
for the indicated materials extrudates s
Y
strong increase in comparison with
initial samples is due to
E
and
d
f
simultaneous growth. It is follows to note
also, that the Eq. (14.15) can be used for description of polymers deforma-
tion on the elasticity part (at
d
f
=
d
) and on cold flow plateau (at
d
f
=
d
and
elasticity modulus replacement on strain hardening modulus) [32].
And in conclusion we will dwell upon the units measurement agreement
in both parts of the Eq. (14.15). Since for the convenience of considerations
s
Y
value is determined in MPa, then the constant coefficient
=
according to the generally accepted technique should be introduced into the
right-hand part of the Eq. (14.15) [42]. Units measurement change results to
C
change. So, at using GPa
(
)
3
d
C
1
MPa
f
(
)
-
-
=
and so on.
Hence, the stated above results shown the conformity of fractional de-
rivatives method and traditional fractal analysis, using Hausdorff dimension
d
f
notion. The physical significance of fractional exponent and its determi-
nation method were elucidated. The theoretical analysis is given the good
quantitative correspondence to experiment [31].
3
d
3
C
10
f
