Geology Reference
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into account. Such effects are therefore properly measured in instantaneous pres-
sure step tests, from which a
1
is obtained as
;
D ln s
Dp
a
1
¼
G
or DV
G
as
D ln s
Dp
DV
G
kT
q
where bulk elastic effects are neglected. When stress-strain curves, each measured
entirely at a given constant pressure, are to be compared, additional pressure
effects may enter through the evolution of the qb
2
term. Then, using (
6.70
) with
Eqs. (
6.63
) and (
6.67
) it can be shown that a term
3s
i
2s
2s
G
q
dq
dp
2
G
K
ð
6
:
72
Þ
3
has to be added to (
6.71
), where q is now the dislocation density developed during
straining at a given pressure p up to the strain at which the flow stresses are
compared. Taking (
6.72
) into account in the respective extreme cases of s
i
¼
0 and
s
i
¼
aGbq
2
ab initio) shows that if the rate of growth of dislocation density up to a
given strain is reduced at higher pressure (dq
=
dp\0in(
6.72
)), then the effect of
increasing the pressure will be to raise the stress-strain curve in the viscous drag
case and to lower it in the athermal case and to introduce corresponding transients
in a step test. In the case of polycrystals, the additional pressure effects mentioned
in the previous subsection may also come into play.
We now turn to the case of thermal models based on mutual dislocation
interaction (
Sect. 6.6.6
). We also here restrict consideration to steady-state flow
and,
specifically,
to
the
particular
simple
recovery-controlled
creep
model
expressed in the flow law in (
6.45
), which leads to
c
s
/
G
2
b
2
s
3
exp
pDV
D
kT
ð
6
:
73
Þ
when it is assumed that D
/
G
ð
2
b
2
exp
pDV
D
=
kT
ð
putting v
0
/
G
ð
2
ð Þ
0
þ
pDV
D
for the
activation energy, where DE
ð Þ
0
is the zero pressure activation energy and DV
D
the activation volume for the diffusion that is required for the dislocation climb. In
a creep test, the pressure effect can then be expressed through
d c
s
dp
1
c
s
¼
3
2G
dG
dp
þ
7
db
dp
DV
D
ð
6
:
74
Þ
2b
kT
s
