Geology Reference
In-Depth Information
The local accommodation strain rate e
a
will be determined by the local stresses
brought into play and by the accommodation mechanism.
The local stress r
1
r
ð Þ
a
driving the accommodation strain rate e
a
will derive
from the macroscopic applied stress r
1
r
3
;
subject to a degree of stress con-
centration, so that
ð
r
1
r
3
Þ
a
¼
C
2
r
1
r
3
ð
Þ
ð
7
:
10
Þ
where C
2
is the stress concentration factor, C
2
[ 1
:
The relationship between
r
1
r
3
ð
Þ
a
and e
a
will then be determined by the nature of the accommodation
mechanism.
Of
the
various
possible
cases,
we
select
the
following
for
consideration:
1. Accommodation by diffusion along grain boundaries, diffusion controlled. This
accommodation mechanism corresponds to Coble creep (
Sect. 5.4
), the local
accommodation strain rate e
a
being governed by
e
a
¼
C
CO
V
m
D
gb
d
RT
ð
r
1
r
3
Þ
a
ð
d
0
Þ
3
ð
7
:
11
Þ
and sink, related to the grain size d by d
0
¼
C
3
d; the constant C
3
will be sub-
stantially less than unity because the accommodation adjustments do not involve
the whole extent of the grain (cf. Ashby and Verrall
1973
). From (
7.9
), (
7.10
) and
(
7.11
) we then obtain the macroscopic flow law
C
3
tan w
C
CO
V
m
D
gb
d
C
1
C
2
ð
r
1
r
3
Þ
d
3
e
¼
ð
7
:
12
Þ
RT
This result is similar to that of (Raj and Chyung
1981
); Wakai (
1994
) has
developed an alternative theory based on the notion of migrating steps on the grain
boundary from which higher stress dependence is possible.
2. Accommodation by solution transfer along grain boundaries, solute diffusion
controlled. In the notation of § 5.5 the accommodation strain rate is now
controlled by
e
a
¼
C
FT
V
m
cD
f
d
RT
ð
r
1
r
3
Þ
a
ð
d
0
Þ
3
ð
7
:
13
Þ
where d
0
¼
C
3
d
;
C
3
\1 as for (
7.11
). From (
7.9
), (
7.10
) and (
7.13
) we obtain
C
3
tan w
C
FT
V
m
cD
f
d
C
1
C
2
r
1
r
3
d
3
e
¼
ð
7
:
14
Þ
RT
