Geology Reference
In-Depth Information
(a) The barriers are spaced on a scale of the order of the Burgers vector b and arise
from the Peierls potential, possibly with modifications due to the presence of
point defects such as solute atoms. Insofar as it can be separately distin-
guished, the contribution of these barriers to the flow stress will be designated
s
p
(it should be made clear that s
p
here is not being used in strictly the same
sense as in
Sect. 6.2.3
where the definition of the Peierls stress applied pri-
marily at absolute zero temperature).
(b) The barriers consist of obstacles such as dispersed phases and the misfit elastic
fields around solute atoms, the dimensions and spacings of these barriers being
large compared with b. Their distinguishable contribution to the flow stress
will be designated s
f
;
signifying a frictional or viscous drag.
(c) The barriers are the interactions with other dislocations, which are often
represented by an internal stress field s
i
made up of the long-range stress fields
of the dislocations but which, as will be discussed in
Sect. 6.6.3
, can be
interpreted in other ways also. The contribution of these barriers to the flow
stress will be here designated as s
d
.
The magnitudes of the activation energies DE
*
and activation areas DA
*
for
particular cases can thus vary widely, leading to corresponding variations in the
characteristics of the mean dislocation velocity (
Sect. 6.4
) and eventually, through
the Orowan relation (
6.4a
), being reflected in the macroscopic flow behavior.
However, it must be borne in mind that the stress dependence of the flow rate may
reflect a role of stress in the mean dislocation density as well as one in the
dislocation velocity.
Insofar as separate components of the flow stress can be related to the particular
classes of barriers to dislocation motion listed above, the macroscopic flow stress s
can be viewed as a summation of these components,
s
¼
s
p
þ
s
f
þ
s
d
However, such linear additivity may not always apply, as in the case of solid
solutions for which the strain-hardening effects that would normally be treated as
increases in the component s
d
are observed to depend on the presence of the
solute, the effect of which would otherwise be treated as a contribution to the
component s
f
(Kocks
1984
,
1985b
).
We first consider athermal models. Since the flow stress component s
p
is
normally rather sensitive to temperature, it is not of primary concern in the
athermal regime, where attention focusses on the components s
f
and s
d
;
treated in
the next two subsections.
6.6.2 Athermal Models Based on Discrete Obstacles
If the moving dislocations have to cut through or circumvent fixed structural
obstacles without much aid from thermal fluctuations, the applied stress itself must
supply the force that is required locally for overcoming or circumventing the
