Chemistry Reference
In-Depth Information
show that polymers fracture surfaces are characterized by roughnesses of
the very various scale availability (see Fig. 8.2). Therefore, a real crack in
mesoscale is not much resembling ideal cracks with the flat edges, consid-
ered usually in the linear fracture mechanics. There was established statisti-
cal self-similarity of fracture surface microrelief was established and this
means, that cracks surface structure can be simulated by fractal surfaces. In
this case a crack true length
l
cr
is coupled with its current mean size
R
cr
ac-
cording to the fractal law [20]:
d
l
=
R
,
(10.23)
fr
cr
cr
where
d
fr
is crack surface fractal dimension, presented by a stochastic fractal.
In the case of sample complete breakdown
l
cr
= (
D
-
a
) and the effective
area of rough fracture
S
ef
is determined as follows [45]:
(
)
fr
=-
.
fr
(10.24)
e
S
Da B
Further the dependences of effective fracture energy
U
ef
on sample frac-
ture surface effective area
S
ef
can be plotted and determined the values
G
Ic
and
J
Ic
can be determining, characterizing a polymer plasticity. It is clear,
that in the Eq. (10.21) U
ef
= U, S
ef
= BDØ and in the Eq. (10.22)
U
ef
= 2
U
,
(
)
fr
=-
. Let us note, that the parameters
G
Ic
and
J
Ic
are polymer
property and in virtue of this they should not depended neither on testing
geometry nor on their determination mode [23, 44].
The value
d
fr
can be determined according to the Eq. (4.51). As it was
noted in chapter seven, the value
d
fr
was determined for fracture surface and
to find the corresponding value
d
I
,
for a curve (fracture surface section), that
the Eq. (10.23) assumes, is necessary to divide the value
d
fr
by 2 [46] (see
the Eq. (7.20)).
three testing temperatures. Despite a definite data scattering (typical for
impact tests), it is obvious, that the Eqs. (10.21) and (10.22) in its fractal
treatment are approximated by one straight line that allows to determine the
only parameter
G
Ic
(
J
Ic
) for HDPE, characterizing its plasticity. Such corre-
spondence was to be expected, since the values
G
Ic
and
J
Ic
characterize the
same polymer property. The obtained at
T
= 293 K
G
Ic
values are typical for
polyethylenes [22, 44].
e
S
Da B
fr
