Geology Reference
In-Depth Information
dimensions per unit pressure change) is anisotropic in the grains, then pressur-
ization may give rise to intergranular stresses large enough to cause yielding in the
grains, and thus increase the dislocation density before the specimen is subjected
to the macroscopic stress in the stress-strain test. A similar effect can arise in the
presence of a second phase of different elastic properties (for example, Bullen
et al.
1964
). If there is a change in pore volume during the deformation, there will
be an associated increment in the flow stress of
ð
p
=
V
Þ
dV
=
de
ð
Þ
and in the strain-
d
e
2
, where V is the specimen volume and e the axial
strain in an axisymmetric triaxial test (Edmond and Paterson
1972
).
Þ
d
2
V
hardening rate of
ð
p
=
V
6.9.3 Pressure Effects in the Thermal Regime
We consider first the case of viscous drag control in single crystals (
Sect. 6.6.5
),
expressed in c
¼
qbv
;
assuming the dislocation density to be sufficiently low that
the effective stress acting on the dislocations can still be taken as being equal to the
applied stress s. In order to gain some idea of the magnitude of the pressure effect
and of what are the important factors likely to affect it, we consider a specific
model based on the expression (
6.14
) for v for the case of relatively low stress,
which gives the approximation
v
¼
m
0
bDA
2
s
lkT
exp
DE
G
kT
ð
6
:
65
Þ
and leads, through c
¼
qbv
;
to
clkT
v
0
qb
2
DA
2
exp
DE
G
kT
s
¼
s
eff
¼
ð
6
:
66
Þ
where the symbols are as in
Sect. 6.4.1
and DE
G
is the activation energy for
dislocation glide. If we assume that v
0
/
G
ð
2
and l
=
DA
2
/
b
3
, noting that qb
2
is dimensionless and therefore independent of pressure for a given dislocation
content, and we write DE
G
¼
DE
G
ð Þ
0
þ
pDV
G
where DE
ð Þ
0
is the activation
energy at zero pressure and DV
G
is the activation volume for dislocation glide,
then we obtain for a given dislocation configuration and strain rate,
1
s
ds
dp
¼
1
dG
dp
7
db
dp
þ
DV
G
ð
6
:
67
Þ
2G
2b
kT
Integrating, and putting
ð
1
=
b
Þð
db
=
dp
Þ¼
1
=
3 K
;
where K is the bulk modulus,
we obtain finally, in analogy to (
6.63
)
p
G
s
¼
s
0
exp a
1
ð
6
:
68a
Þ
