Geology Reference
In-Depth Information
clearly defined cell structure in the dislocation population is also a feature of stage
III and at least two structural parameters will therefore still be required, but they
may have to be treated as being independent rather than as a single parameter
through their ratio, as has been done for stage II (see, for example, Mecking
1981a
).
At very large strains (
1), the strain-hardening rate becomes small. In some
cases, it appears to approach zero, corresponding to a ''saturation'' state, but, in
other cases, no saturation limit is apparent up to strains of at least 10 (Hecker and
Stout
1984
). It has been suggested that the presence of solutes is important in this
connection since they may retard dynamical recovery and so prevent the attain-
ment of the balance between hardening and dynamical recovery that is implied in a
saturation limit (Hecker and Stout
1984
; Kocks
1984
). See further discussion on
large strains in
Sect. 6.8.5
.
6.6.4 Creep in the Athermal Regime
Under this somewhat self-contradictory heading we consider the time-dependent
or thermally activated contributions to the deformation which have been ignored in
the previous two sections as being of secondary importance relative to the more or
less instantaneous, athermal deformation that occurs under an applied stress
greater than the yield stress. We now consider the occurrence of further straining at
a finite but decaying rate that may be observed if the stress is maintained at the
same level and measurements are made with sufficient sensitivity. This transient
creep in the athermal regime usually obeys a logarithmic law (
Sect. 4.3.2
)
.
The athermal part of the deformation can be imagined to have terminated with
the dislocations being forced against barriers (internal stress and/or other obsta-
cles) that are too high to be overcome by the applied stress. However, some of
these barriers will be only slightly too high and, with the passage of time, may
subsequently be surmounted with the aid of thermal fluctuations, leading to a
contribution to deformation that will appear as transient creep. The decrease in the
creep rate with time can be attributed either to a progressive elimination of the
situations where a dislocation is resting against a relatively low barrier (exhaustion
effect) or to a progressive raising of the barriers as a result of the strain hardening
accompanying the additional strain (hardening effect). The exhaustion hypothesis
was early explored by (Mott and Nabarro
1948
) but the hardening hypothesis has
become more favored (Friedel
1964
, p. 305; Mott
1953
; Weertman and Weertman
1983a
).
Theories of logarithmic creep are commonly based on an expression for the strain
rate c such as may be obtained from Orowan's equation c
¼
qbv
;
using (
6.13b
),
for
l
¼
q
2
:
relatively
high
stress
and
low
temperature,
and
finally
putting
This approach leads to
