Chemistry Reference
In-Depth Information
Let us consider further the free path length of dislocations, l
d
. As it is
known for metals [3], in which the main role in plastic deformation belongs
to the mobile dislocations, l
d
assesses as ~ 10
4
Å. For polymers, this param-
eter can be estimated as follows [28]:
e
l
=
Y
,
(4.6)
Y
b
r
d
where e
Y
is the yield strain,
b
is Burgers vector, r
d
is the density if linear
defects, determined according to the Eq. (4.1).
The value e
Y
assesses as ~0.10 [29] and the value of Burgers vector
b
can
be estimated according to the equation [30]:
1/ 2
60, 7
b
=
, Å.
(4.7)
C
∞
The values for different polymers, l
d
assessed by the Eq. (4.6) is about
2.5 Å. The same distance, which a segment passes at shearing, when it oc-
cupies the position, shown i
n
Fig. 4.1 b
,
that can be simply calculated from
purely geometrical considerations. Hence, this assessment also indicates no
reasons for assuming any sufficient free path length of dislocations in poly-
mers rather than transition of a segment (or several segments) of macromol-
ecule from one quasiequilibrium state to another [31].
It is commonly known [3, 25] that for crystalline materials Baily Hirsh
relationship between shear stress, t
Y
, and dislocation density, r
d
, is fulfilled:
,
(4.8)
1/ 2
ttar
=+
Gb
Y
in
d
where t
in
is the initial internal stress, a is the efficiency constant.
The Eq. (4.8) is also true for amorphous metals [21]. In Ref. [20] it was
used for describing mechanical behavior of polymers on the example of these
materials main classes representatives. For this purpose, the data for amor-
phous glassy PAr [32], semicrystalline HDPE [33] and cross-linked epoxy
polymers of amine and anhydride curing types (EP) were used [34]. Differ-
ent loading schemes were used: uniaxial tension of film samples [32], high-
between calculated and experimental values t
Y
for the indicated polymers
are adduced, which correspond to the Eq. (4.8). As one can see, they are
linear and pass through the coordinates origin (i.e., t
in
= 0), but a values for
linear and cross-linked polymers are different. Thus in the frameworks of the
