Chemistry Reference
In-Depth Information
peal for this to the percolation cluster fractal model, offered in Ref. [32]
for particulate-filled composites. In this model the structure of infinite clus-
ter, consisting of disperse particles, represents itself a rare spatial distorted
network, composed from a filler particles set. For simplification a particles
chains can be replaced by lines, assuming, that along the line particles den-
sity remains constant and the greatest one and sharply decreases on the side
of the line [32]. The completely similar network macromolecular entangle-
ments cluster network forms in HDPE amorphous phase [18]. This allows
to consider the indicated phase as quasi-two-phase system and apply for
its description a composite models [33]. In this treatment the critical in-
dex b, which is equal to ~0.40, characterizes macromolecular entanglements
cluster network (the first subset [32]). Since impact energy dissipation and,
hence, local shear zones formation is associated with loosely packed matrix
[2] (the second subset [32]), then in the Eq. (10.16) exponent equality to
index n
p
, is expected which characterizes this subset, that confirms the plot
of
Fig. 10.10
.
Let us note, that within the frameworks of treatment [32] the
value n
p
is defined by polymer structure and connected with fractal dimen-
sion
d
f
of the latter by the Eq. (5.5). The estimation
d
f
according to the indi-
cated equation at n
p
≈ 0.77 gives the value ~2.60. The calculation df
f
by the
mechanical tests results [3] for HDPE samples with notch lengths
a
= 0.5 ÷
1.5 mm was gives
d
f
range of 2,688 and 2,546 with mean value
d
f
≈ 2,617,
that corresponds excellently to the estimation according to the Eq. (5.5).
Now the value
U
can be calculated theoretically, proceeding from the
known
r
p
values, estimating the constant coefficient in the Eq. (10.16) from
the best conformity of theory and experiment. The comparison of experi-
mental
U
and calculated by the indicated mode
U
T
HDPE samples with dif-
ferent notch length and at different testing temperatures fracture energy is
adduced i
n
Fig. 10.11
.
The data of this figure has shown the good correspon-
dence of theory and experiment, that the percolation relationship (the Eq.
(10.16)) correctness confirms.
Let us consider now the reason for percolation linear model choice. As
it has been shown in Ref. [34], for samples of HDPE, modified by high-
disperse mixture Fe/FeO(Z) at Z content 0.05 mas.% the extreme
U
increase
up to ~0.78 J is observed, accompanied by shear transvers band at notch tip
appearance. Thus, two side and one transverse bands of shear are formed
closed arch-like construction, forming actually the linear percolation in the
indicated above sense by sample width. Despite small
r
p
increase for side
bands of shear and small value
r
p
for transverse band of shear (~0.5 mm),
the sharp increase
U
in the indicated compositions HDPE+Z is observed.
