Chemistry Reference
In-Depth Information
The authors of Ref. [36] offered to use for polymers stress-strain (s-e)
curves description the following general model of viscoelastic body, based
on the fractional order derivatives, which has the appearance:
m
m
∑
∑
a
b
s se
+
bD
=
E
ED
e
j
j
,
(14.13)
j
l
0
j
l
i
i
j
=
1
j
=
1
where s = s (
t
), e = e (t) are stress and strain in time t moment,
b
j
,
E
j
, a
i
,
b
i
are assigned values and
is an operator of fractional differentiation of
D
order n
fr
[36].
After a number of assumptions the authors of Ref. [36] have come to the
conclusion, that the yield part of the curve s - e can be described with the
help of fractional differentiation calculus. For this purpose the following
equation was used [36]:
D
n
s
=
e
.
(14.14)
fr
However, in Ref. [36] although the good conformity of theory and ex-
periment was obtained, but parameters
D
and n
fr
were not identified within
the frameworks of polymers structure or properties. Therefore, the goals
propounded above were solved on the example of yield process description
of polymerization-filled compositions (componors) on the basis UHMPE,
prepared by solid-phase extrusion method [2].
At solid body deformation the heat flow is formed, which is due to de-
formation. The thermodynamics first law establishes that the internal energy
change in sample
dU
is equal to the sum of work
dW
, carried out on a sam-
ple, and the heat flow
dQ
into sample (see the Eq. (4.31)). This relation is
valid for any deformation, reversible or irreversible. There are two thermo-
dynamically irreversible cases, for which
dQ
= -
dW
; uniaxial deformation
of Newtonian liquid and ideal elastoplastic deformation. For solid-phase
polymers deformation has an essentially different character: the ratio
Q
/
W
is not equal to one and varies within the limits of 0.35 ÷ 0.75, depending
on testing conditions [37]. In other words, for these materials thermody-
namically ideal plasticity is not realized. The cause of such effect is ther-
modynamically nonequilibrium nature or fractality of solid-phase polymers
structure. Within the frameworks of fractal analysis it has been shown that
this results to polymers yielding process realization not in the entire sample
volume, but in its part only.
