Chemistry Reference
In-Depth Information
Another aspect of the indicated relationships is prevalent usage in them
of the fracture surface fractal dimension, but not the structure, although it
is quite obvious, that
d
fr
is defined by the structure fractal dimension
d
f
[21]
and the fracture mechanism, which in its turn depends on
d
f
[6]. This is more
so important that
d
fr
can have an extremely indirect relation to the value
U
(or
A
p
) from the point of view of physical significance. So, in polymers
impact tests at quasibrittle fracture the value
U
is defined by the dynamical
competition of two parameters - critical defect stiffness and local plastic
deformation zone ability to dissipation of impact energy [38]. At a definite
strain reaching a sample breaks down in such tests, as a rule, by an instable
crack, the propagation of which does not required energetic expenditures
and which gives almost no contribution in
U
(or
A
p
) for this reason [39].
Hence, if the connection between
U
and
d
fr
exists, then it is defined by more
general correlation
d
fr
(
d
f
) or
U
(
d
f
). Williford [40] shows within the frame-
works of fracture process multifractal analysis, that the material structure
is supporting fractal (having the greatest dimension from possible fractal
dimensions) in the indicated process and sample surface or fracture surface
is the first subfractal. The authors of Ref. [42] obtained the direct analytical
intercommunication of the values
U
and fractal dimension and elucidated,
which from the latter (
d
fr
or
d
f
) defined fracture energy on the example of
HDPE samples with varied length of sharp notch.
As Williford has shown [42], the fractal dimension
D
(not obligatory
equal to
d
fr
), connected with fracture energy
U
, can be determined from the
relationship:
(
)
ln
UC
,
(10.17)
D
=
ln
L
where
C
is the material constant,
L
is observation characteristic scale.
The value
L
is coupled with damage volume
V
f
by the following relation-
ship [42]:
V
f
=
L
D
.
(10.18)
It is obvious, that in impact tests the volume
V
f
represents itself that sam-
ple part, where local plastic deformation and microcracks formation are oc-
curred [43]. In HDPE impact tests such zone is formed at a notch tip, has in
estimated as follows [41]:
