Chemistry Reference
In-Depth Information
and determined from the plots similar to the ones from Figs. 2.5 and 2.6, that
is,
G
(n
cl
), e
o
is the IP proper strain, n
2
is Poisson's ratio for clusters.
Since the Eq. (4.10) characterizes inelastic deformation of clusters, the
following can be accepted: n
2
= 0.5. Further on, under the assumption that t
Y
= t
IP
, the expression for the minimal (with regard to inequality in the left part
of the Eq. (4.10)) proper strain
min
0
e
is obtained [24]:
t
e =
min
Y
(4.11)
0
24
G
cl
The condition for IP (clusters) stability looks as follows [37]:
'
“
3
e
e
3
t
”
”
,
(4.12)
q
=⋅ +-
0
1
0
Y
•
-
(
)
2
t
e
8
G
e n
1
+
”
”
—
˜
Y
0
cl
0
2
where
q
is the parameter, characterizing plastic deformation,
e
is the proper
0
strain of the loosely packed matrix.
The cluster stability violation condition is fulfillment of the following
inequality [37]:
q
<
0.
(4.13)
Comparison of the Eqs. (4.12) and (4.13) gives the following criterion of
stability loss for IP (clusters) [24]:
T
e
3
t
0
Y
1
+=
,
(4.14)
(
)
e
8
G
e n
1
+
0
cl
0
2
T
t
) can be determined, after reaching of
which the criterion (4.13) is fulfilled.
To perform quantitative estimations, one should make two simplifying
assumptions [24]. Firstly, for IP the following condition is fulfilled [37]:
from which theoretical stress τ
Y
(
(
)
2
0
≤
sin
IP
qee
≤
1
,
(4.15)
00
where q
IP
is the angle between the normal to IP and the main axis of proper
strain.
Since for arbitrarily oriented IP (clusters) sin
2
q
IP
= 0.5, then for fulfill-
ment of the condition (4.15) the assumption is enough. Secondly, the Eq.
(4.11) gives the minimal value of e
o
, and for the sake of convenience of
