Geology Reference
In-Depth Information
Empirically, the determination of an apparent activation energy Q directly by
temperature stepping procedures should indicate a continual increase in Q during
the progress of logarithmic creep. However, because of the limited range over
which creep rates can be measured, the observed values of Q at a given stress will
fall in a limited range at any given temperature, even though a wide range of
activation energies may exist; also the values typical of the observable range may
be expected to increase with temperature, as can be seen by writing (
6.33
)as
DE
sbDA
¼
kT ln
ð
q
2
bDAm
0
=
c
Þ
and noting that the In term will be effectively
nearly constant(Weertman and Weertman
1983a
).
Before concluding this section it is appropriate to emphasize the distinction
between logarithmic creep and anelastic creep. Whereas logarithmic creep is
observed in situations where the yield stress has been exceeded and some athermal
plastic deformation brought about, anelastic creep is observed under small stresses,
below the macroscopic yield stress, and is not limited to the athermal regime.
Anelastic deformation is defined as reversible, time-dependent strain that is line-
arly related to the stress in the sense that the Boltzmann superposition principle is
obeyed in summing the contributions to the current strain rate due to all the past
stress history (Jackson
1986
; Nowick and Berry
1972
; Zener
1948
). Models for
anelastic dislocation creep involve the movement of dislocation segments within
finite limits set by insurmountable barriers (see discussion of amplitude-inde-
pendent internal friction from dislocation motion in Sect. 2 of Fantozzi et al.
1982
).
6.6.5 Thermal Models Based on Viscous Drag
This first category of models for temperature-sensitive dislocation flow is con-
cerned with situations in which the flow rate is determined primarily by the rate at
which dislocations move against viscous drag forces that act more or less uni-
formly on them. Thermal recovery processes (
Sect. 6.5.3
) play a relatively minor
role and so the term glide-controlled creep is sometimes applied (Poirier
1985
,
p. 101). It is a category that is especially relevant in the low-temperature thermal
regime (
Sect. 6.6.1
), in cases in which the dislocation velocity is strongly influ-
enced by Peierls or similar atom-scale barriers that are thermally surmountable in
this temperature range and which tend to be largely of an intrinsic nature. A cross-
slip controlled deformation might be included in here. However, the category also
has application in the high-temperature thermal regime where effects such as
solute drag are important; these tend to be extrinsic effects. Thus, it is a category
that is potentially of importance in minerals in either thermal regime.
The two prototype models of the category are the microdynamical models of
(Weertman
1957
) and of (Haasen
1964
). Both models are based on the Orowan
equation for the strain rate,
c
¼
qbv
ð
6
:
36
Þ
