Chemistry Reference
In-Depth Information
As it is known [1], the main characteristics of local plasticity zone (“shear
lips” or crazes) are its length h
p
and critical opening d
c
. Both indicated pa-
rameters are connected with polymer structure fractal dimension
d
f
. The au-
thors of Ref. [2] obtained the following relationship between df:
c
and
d
f
:
2
p
Gd
d
=
Ic
f
1/ 2
,
(5.1)
c
(
)
Eb
r
d
where
G
Ic
is deformation energy release critical rate,
b
is Burgers vector, de-
termined according to the Eq. (4.7), r
d
is density of structure linear defects.
The value r
d
is determined as linear defects length per polymer volume
unit (see the Eq. (4.1)). Since in the cluster model a segment included in
densely packed regions (crystallites or clusters) is assumed as linear defect
(dislocation analog) then value r
d
is determined as follows [3]:
K
+
φ
r
=
cl
,
(5.2)
d
S
where
K
is crystallinity degree, j
cl
is clusters relative fraction,
S
is macro-
molecule cross-sectional area.
The authors of Ref. [1, 2] obtained a good correspondence of experimen-
tal and calculated according to the Eq. (5.1) d
c
values for HDPE at different
testing temperatures.
The local plasticity zone is the most important element of the deformed
polymer at quasibrittle (quasiductile) fracture. A local plasticity zone type
defines fracture type: if the craze is formed at critical defect tip, then polymer
is destroyed by quasibrittle mode, and if local shearing yielding zone (“shear
lips”), then by quasiductile mode [4]. An inelastic deformation mechanism
change is considered usually as brittle-ductile transition [5]. Length increase
of both craze [6, 7] and shear yielding zone [8] results to polymer fracture
toughness increase. As a matter of fact the sole theoretical method of local
plasticity zone length
r
p
estimation is the Dugdale-Barenblatt equation [4]:
2
Ic
2
Y
p
K
r
=
,
(5.3)
p
8
s
where
K
Ic
is stress intensity critical factor, is
Y
is yield stress.
Although the Eq. (5.3) gives for polymers good correspondence to ex-
periment in the case of both crazes [6] and local shear zones [9], but it does
not connect the parameter h
p
with any structural characteristics of polymers.
