Geology Reference
In-Depth Information
dependences of dislocation nucleation rate and velocity. However, the interesting
point is that a stress exponent greater than unity can be rationalized, since observed
values are often around 1.5-2.5. The stress exponent might also vary with strain
rate or temperature if the nature of the factors limiting the dislocation velocity
were to vary.
The above formulae (
7.12
)-(
7.18
) should be regarded as being of a generic
nature, illustrating the general character of possible granular flow mechanisms
rather than displaying all the properties of deformation in specific situations.
However, some semi-quantitative conclusions can be arrived at through consid-
eration of possible values of the constants C
1
to C
3
and tan w
;
as follows:
C
1
The volumetric strain e
v
required for accommodation is most simply
achieved by the displacement of a layer of relative thickness e
a
from one
side of the grain to the other, in which case, from
7.8
, C
1
¼
1
C
2
This can be expected to be less than typical elastic stress concentration
factors because of the non-elastic deformation involved: We make the
subjective choice of C
1
2
C
3
In the cases 1, 2 and 3, it may suffice to postulate the diffusive transfer of
interface, that is, for a typical 12-faced grain, of the order of
1
6
p
d
;
or
C
3
1
6
p
and C
3
15
tan w
The dilatancy that would occur in the granular flow of a low-porosity
polycrystalline body in the absence of accommodation processes could be
expected to be similar to that in dense sand, for which a typical value of
tan w is around 0.7 (see Fig. 6.20c in Wood
1990
). An alternative estimate
is obtained by supposing that a transition from close packing of equal
spheres (porosity &0.26) to loose random packing {porosity &0.38;
Cargill 1984} requires a strain of about half that for complete neighbour
exchange (
Sect. 7.1.2
), that is, about 0.2, leading to a value of tan w of
(0.38-0.26)/0.2 = 0.6. We therefore choose tan w
¼
2
=
3 as a typical value
Using the above estimates, we therefore obtain values for the first terms in
(
7.12
), (
7.14
) and (
7.16
) of:
C
1
C
2
C
3
tan w
¼
45 and
C
1
C
2
C
3
tan w
¼
7
The strain rate predicted for the grain-boundary-diffusion-accommodated
granular flow model (
7.12
) is thus around 45 times that for the classical Coble
creep model (5-11), a large factor in favour of the granular flow model, as was first
noted by Ashby and Verrall (
1973
). A granular flow view is similarly favoured in
the case of diffusion-controlled solution transfer accommodation (
7.14
), and, to a
lesser extent, in the case of the reaction-controlled accommodation (
7.16
).
