Geology Reference
In-Depth Information
As in the athermal case ( Sect. 6.6.2 ) we need first to make a broad distinction
between situations in which the precipitates or particles can be sheared through by
the passage of dislocations at stresses below the Orowan bypass stress and situ-
ations in which the particles remain undeformed. For this purpose, we shall des-
ignate the particles as shearable particles and hard particles, respectively, using the
term particle now to refer both to the precipitates and to particles introduced in
other ways, as in fabrication by sintering.
Creep deformation in the presence of shearable particles involves a viscous
drag on the motion of the dislocations when the deformation is viewed at a scale
larger than the particle spacing; that is, the deformation is of the type discussed in
Sect. 6.6.5 . At stresses below the level for athermal cutting of the particles
( Sect. 6.6.3 ), there can still be a certain rate of cutting as a result of thermal
activation and hence a certain dislocation velocity and strain rate. Kocks et al.
( 1975 , pp. 147-163, 196-225) have discussed in considerable detail the kinetics of
such a cutting process and have proposed that, if the strain rate is represented in the
form
c ¼ c 0 v 0 exp E ðÞ
kT
ð 6 : 47a Þ
where c 0 is a term containing the mobile dislocation density and the area swept out
following each successful activation event (cf. ( 6.33 )) and v 0 is the attempt fre-
quency (Kocks et al. 1975 , p.124 estimate v 0 to be of the order of 10 10 -10 11 s -1 in
this situation). Then, the activation energy E can be represented in the form
p
q
s
s 0
E ¼ E 0 1
ð 6 : 47b Þ
where s is the applied stress, s 0 the threshold stress for athermal flow, E 0 the
(Gibbs) energy needed to cut through the particle in the absence of thermal acti-
vation, and p, q numerical factors (0 p 1 ; 1 q 2; typically
p ¼ 2 = 3 ; q ¼ 3 = 2). Such a particle-shearing model is probably most relevant at
stresses not markedly below the threshold for athermal flow.
In practice, experimental studies in metal-based systems involving particles that
are shearable at certain stress levels show that significant creep rates can also be
observed at substantially lower stresses than those envisaged in the previous
paragraph. In these cases, the particles are probably not being sheared and pro-
cesses of particle circumvention involving diffusion are thought to be rate con-
trolling, as in crystals with hard particles.
The creep of crystals containing hard particles can be approached in two ways.
On the one hand, if the resistance to deformation is viewed as arising from the
presence of an internal stress—a rather phenomenological approach—then the
creep can be discussed in terms of recovery in which this internal stress is reduced
by thermally activated processes, allowing further deformation in the course of
time, as in Sect. 6.6.6 . The theoretical development of this approach requires the
identification and treatment of the rate-controlling recovery processes taking place
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