Geology Reference
In-Depth Information
importance for reaction control at finer grain sizes and lower stresses. However, in
geological systems with fluid phases present, multiple phases and potentially more
complicated reactions, reaction control may be relatively more important.
5.7 Dislocation Climb Creep
Dislocations (
Chap. 6
) can also, in principle, serve as sources and sinks for atomic
transfer creep. The addition or removal of material at the dislocation cores cor-
responds to climb of the dislocations, which can be viewed as the removal of
material from, or addition to, the ''extra half plane'' associated with the edge
component of the dislocation. However, dislocations acting as sources must have
different Burgers vectors from those acting as sinks in order that the material
transfer be effective as a strain mechanism, so there must be a multiplicity of
Burgers vectors present. Also the dislocation lines must be of such orientations
that they have at least some edge character. Dislocation arrays meeting these
requirements will, in general, be three dimensional networks, with the dislocations
either more or less randomly distributed or organized into subgrain boundaries.
Theories of dislocation climb creep have, in general, assumed diffusion control.
In applying (
5.7
), the transfer path length l can be taken as being of the order of the
average mesh dimension of the dislocation network, that is, q
2
where q is
the dislocation density, the domain volume V can be taken as of the order of
the average mesh volume q
2
, and the transfer path cross-sectional area A
t
as of the
order of q
1
if volume diffusion is involved. Then, with c
¼
1
=
V
m
,(
5.7
) becomes
e
¼
C
DC
V
m
D
V
q
RT
ð
r
1
r
3
Þ
ð
5
:
15
Þ
where D
V
is the volume diffusion coefficient. The numerical coefficient C
DC
will
depend on mean values of the angle between the dislocation lines and the stress
direction as well as on other geometric factors similar to those arising for Nabarro-
Herring creep. However, the compatibility requirements are somewhat different in
character from where grain boundaries are involved as sources and sinks, and grain
boundary sliding will no longer contribute to the strain. To achieve an arbitrary
strain within a crystal by dislocation climb at least six Burgers vectors must be
independently involved (Groves and Kelly
1969
,
Sect. 6.8.2
)
and this requirement
therefore must probably also be met in polycrystalline deformation, although there
will tend to be some heterogeneity in behaviour from grain to grain and within
grains. However, the independence of the activity of the climb systems of different
Burgers vectors may be put in question, firstly, by any tendency for long range
stress fields to build up and lead to interaction between the different groups of
dislocations and, secondly and more seriously, by the pinning of dislocations at the
nodes of the network.
