Geology Reference
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in the complex configuration of dislocations that presumably exists in the neigh-
borhood of the particles. On the other hard, a more direct and mechanistic
approach in terms of the dislocation dynamics can be taken, the creep rate being
related directly to the climb rate of the mobile dislocations as they circumvent the
particles. However, again the concept of an internal stress tends to enter in
determining the local driving stress for the dislocation motion. In either case, the
concept of there being an internal stress can be used to rationalize the high values
of the observed stress exponent n and activation energy Q. Thus, if, instead of
writing the observed strain rate as
c
¼
As
n
exp
Q
RT
ð
6
:
48
Þ
in terms of the applied stress s, where A is a constant and
;
n
¼
o
ln c
o ln s
o ln c
o 1
=
T
;
Q
R
ð
6
:
49
Þ
ð
Þ
s
T
we relate the observed strain rate to the local processes by writing
c
¼
A
0
s
n
e
exp
Q
e
ð
6
:
50
Þ
RT
where s
e
¼
s
s
i
(s
i
is the internal stress), A
0
is a constant and
n
e
¼
o
ln c
o ln s
e
o ln c
o 1
=
T
;
Q
e
¼
R
;
ð
6
:
51
Þ
ð
Þ
T
s
e
then it can be shown, following Saxl and Kroupa (
1972
), that
os
T
s
s
i
n
¼
n
e
s
1
o
s
i
ð
6
:
52
Þ
oT
s
s
s
i
o
s
i
Q
¼
Q
e
n
e
RT
2
ð
6
:
53
Þ
It follows that the experimental quantities n and Q can be substantially larger than
the quantities n
e
and Q
e
that are effective locally.
The two approaches outlined in the previous paragraph for the case of hard
particles correspond more or less, on the scale of the crystal, to the recovery and
viscous drag models of creep discussed in
Sects. 6.6.5
and
6.6.6
, respectively.
However, the distinction may ultimately prove to be an artificial one because of the
common dependence on dislocation climb, generally agreed to be the rate-con-
trolling process (Strudel
1983
). It seems that climb can be especially rapid in
the neighborhood of hard particles, presumably due to short-circuit diffusion at
the particle interface or some sort of coordinated pipe diffusion on the scale of the
particles. It has even been suggested (Strudel
1983
) that the climb activity may be
