Chemistry Reference
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does not pass through coordinates origin [21]. This discrepancy reasons are
obvious.
G
Ic
value is controlled by plastic strain in “shear lips” or crazes in
the case of instable crack. Therefore, the value
G
Ic
should depend not on
fracture surface, but on local deformation zone, which was designated as
d
r
.
If to present such zone as triangle with height of r
p
and basis of d
p
(where d
p
is the indicated zone opening, Fig. 10.7), as it was often made [22], then by
analogy with crack (Fig. 8.2) the value
d
r
can be determined as follows [10]:
2 ln
ln
d
p
d
=
.
(10.15)
r
r
p
The obvious physical significance of local plasticity zone fractal dimen-
sion
d
r
follows from the adduced analysis: the greater d
p
at fixed
r
p
the larger
strain in the indicated zone (see the Eq. (5.6)) and the larger its fractal di-
mension [21].
FIGURE 10.7
The schematic picture of crack and local plasticity zone (which is shaded)
within the frameworks of the Dugdale-Barenblatt model [22].
d
a
is presented, corresponding
to the Eq. (10.14), for HDPE and PS. Let us note, that within the frameworks
of linear fracture mechanics the value
G
Ic
is assumed as material property,
that is, at fixed testing temperature and strain rate it should be constant and
independent on a value [23]. However, in impact tests HDPE and PC sam-
ples the value
G
Ic
changes in 2 ÷ 3 times. This is usually explained by the
circumstance, that the condition
G
Ic
= const is valid only for plane-deformed
state, which is not carried out in usual impact tests, since the samples of
large sizes, particularly for such ductile polymer as HDPE, are required for
its fulfillment, that happens technically difficult or even impossible [24].
r
-
1
