Geology Reference
In-Depth Information
density of network links, that is, to q
3
=
2
(see Ardell and Przystupa
1984
) so that
dq
/
q
3
=
2
dc
;
then the exponential relationship would be replaced by
q
¼
q
0
=
1
ð
e
p
1
Þð
c
=
c
e
Þ=
e
p
2
ð
6
:
23d
Þ
which increases catastrophically as c
!
p
1
Þ:
In either case, the ten-
dency for exponential or catastrophic growth in dislocation density with strain will
be moderated by two factors: (1) the circumstance that the dislocations may not be
all equally mobile and (2) the occurrence of a certain rate of elimination of
dislocations by escape at or incorporation into boundaries or by recovery or
recrystallization. As a consequence the dislocation density will tend to level off
eventually but a quantitative description of its behavior is very difficult to obtain.
p
c
e
=ð
6.5.3 Recovery and Recrystallization
(see also
Sects. 3.3.2
and
3.3.3
)
When the temperature is high enough for dynamic recovery processes to be
thermally activated, the build-up in dislocation density due to multiplication
during straining is counteracted by the mutual annihilation of dislocations, pos-
sibly at a rate that is proportional to q
2
(Ardell and Przystupa
1984
; Johnson and
Gilman
1959
). There is then a tendency for a steady dislocation density to be
approached. The occurrence of recovery also involves the reorganization of the
remaining dislocations into lower energy configurations, especially into well-
organized subgrain boundaries (it may be noted, in passing, that the analogous
process in static recovery, observed as polygonization at the microscopic scale by
Cahn (
1949
,
1951
), is sometimes regarded as the first experimental evidence for
the existence of dislocations). The presence of well-organized walls of disloca-
tions, such as shown in Fig.
6.13
, is therefore widely taken as evidence that
recovery has occurred.
As in the case of static recovery, the quantitative treatment of dynamic recovery
requires a measure for the recovery. Since the changes in structure are difficult to
document fully even if relevant parameters such as mean dislocation density,
subgrain size, and subboundary mesh size can be identified, the integrated effect of
the structural changes as expressed in change in the flow stress is commonly used
in specifying the recovery. However, it should be recognized that the use of such a
measure is an empirical expedient which does little to elucidate the processes at
the dislocation scale. Following Mitra and McLean (
1966
, see Poirier
1985
,
p. 105), the rate of dynamic recovery r can then be determined from stress drop
tests, at least in situations where the flow stress is governed primarily by mutual
dislocation interaction (athermal regime;
Sect. 6.6.1
), as
Ds
Dt
r
¼
lim
t
!
0
ð
6
:
24
Þ
