Chemistry Reference
In-Depth Information
FIGURE 15.11
The dependences of reinforcement degree
E
p
/
E
l.m
on nanoclusters relative
fraction j
cl
for PC. 1 - calculation according to the Eq. (15.7); 2 - calculation according to
the Eq. (15.10); 3 - the experimental data [34].
Takayanagi model belongs to a micromechanical composite models
group, allowing empirical description of composite response upon mechani-
cal influence on the basis of constituent it elements properties. One of the
possible expressions within the frameworks of this model has the following
look [38]:
(
)
φ aφ
aφ
G
++
G
G
G
mm
f
f
,
(15.11)
c
=
(
)
1
+
G
+
aφ
G
m
f
m
mf
where
G
c
,
G
m
and
G
f
are shear moduli of composite, polymer matrix and
filler, accordingly, jf
m
and j
f
are polymer matrix and filler relative fractions,
respectively, a is a fitted parameter.
Kerner equation is identical to the Eq. (15.11), but for it the parameter a
does not fit and has the following analytical expression [38]:
(
)
24 5
75
-
n
,
(15.12)
m
a
=
(
)
m
-
n
m
where a
m
and n
m
are parameter a and Poisson's ratio for polymer matrix.
Let us consider determination methods of the Eqs. (15.11) and (15.12)
parameters, which are necessary for the indicated equations application in
