Geology Reference
In-Depth Information
processes become more strongly temperature dependent, possibly with a transition
in mechanism, such as from cross-slip control to climb control, and the recovery is
now envisaged as being primarily a function of time. A steady state condition is
then more readily achieved, often after quite small strains (*0.01-0.1). We
therefore begin by discussing in a general and largely phenomenological way the
deformation kinetics when time-dependent recovery is important, taking the case
of creep, for simplicity, and generalizing the treatment of
Sect. 6.6.4
.
As in
Sect. 6.6.4
, we assume that the applied stress is supported primarily by the
mutual dislocation interactions, as represented by the flow stress component s
d
;
and that s
d
tends to increase due to strain hardening during creep. We now assume,
in addition, that s
d
tends to decrease due to recovery as time progresses, and that
the resultant effect can be written as
Ds
d
¼
hc
rt
and hence (
6.34
) becomes
DE
¼
bDA
ð
hc
rt
Þ
U
ð
6
:
39
Þ
where c is the plastic strain, t the elapsed time, and the parameters h, r, respec-
tively, the strain-hardening rate and the recovery rate. Both h and r can, in prin-
ciple, be determined empirically, h by carrying out a stress-strain test at a
relatively high strain rate at the conclusion of the creep test and r as set out in
Sect.
6.5.3
(Poirier
1985
, p. 105). Using the above expression for Ds
d
in (
6.34
) and
following the same procedure as in deriving (
6.35a
) the following relation for the
strain is obtained:
h
i
e
t
r
1
c
tot
¼
c
inst
þ
c
0
ln 1
þ
ms
r
ð
6
:
40a
Þ
where c
tot
and c
inst
are the total and instantaneous (elastic plus plastic) strains,
respectively, and c
0
;
s and m are given by
kT
hbDA
c
0
¼
ð
6
:
40b
Þ
kT
rbDA
s
r
¼
ð
6
:
40c
Þ
exp
U
bDA
m
¼
q
2
bDAm
0
c
0
ð
s
hc
inst
Þ
1
exp
sbDA
kT
ð
6
:
40d
Þ
kT
For the case sbDA
kT
;
(
6.40d
) reduces to (
6.35c
) and for the case sbDA
kT (and therefore also sbDA
kT), (
6.40d
) becomes
m
¼
q
2
sb
2
D
ð
2
m
0
c
0
exp
U
þ
hc
inst
bDA
kT
ð
6
:
40e
Þ
