Geology Reference
In-Depth Information
with b
2
;
indicating that there is some factor other than a viscous drag involving a
simple core interaction controlling the motion (for data, see Sprackling
1976
,
Chap. 9). Values of m substantially greater than unity suggest that the population
of sites of effective thermal activation is also stress dependent and perhaps
evolving with dislocation motion, an understanding of which depends on detailed
microstructural study.
Transmission electron microscope observations in situ in metals (for example,
Caillard and Martin
1983
) reveal, in fact, behavior that is in marked contrast to the
picture of a steady viscous drag. The observed motion tends to be unsteady on a
relatively large scale in that periods of no motion alternate with periods during
which relatively large areas are swept out in rapid motion; that is, the dislocation
advances
in
spurts.
This
behavior
can
be
explicitly
taken
into
account
by
expressing the mean velocity v as:
Ds
t
0
þ
t
g
DA
l
ð
t
0
þ
t
g
Þ
v
¼
v
¼
ð
6
:
17
Þ
or
(Kocks et al.
1975
, p. 93; Philibert
1979
; Poirier
1985
, p. 94),, where Ds is the
distance or DA the area swept out by a dislocation segment of length l in a typical
interval of time consisting of t
0
spent waiting at an obstacle and t
g
spent in actual
motion. In view of the possible variety of obstacles and drag processes and, hence,
variation in the relative importance of the t
0
and t
g
terms, a complex phenome-
nology can be expected, preventing simple interpretation of the empirical
expressions in Eqs. (
6.15
) and (
6.16
) and making theoretical prediction difficult,
although some attempt has been made by Morris and Martin (
1984a
,
b
).
6.4.2 Cross-Slip Velocity of Screw Dislocations
For undissociated dislocations, motion in the cross-slip plane will be controlled by
the same factors as that in the primary slip plane, apart from the effects of change
in the resolved shear stress and of any change in the Peierls stress or other crys-
tallographically controlled factor in cases in which the cross-slip plane is not
equivalent crystallographically to the primary plane. However, when dissociation
of the screw dislocations occurs, the relative case of their movement into or within
the cross-slip plane may be strongly affected. Effects of this kind have been
especially studied in metals (see Vitek
1985
, for a recent review) but they are
probably widespread; for example, Poirier and Vergobbi (
1978
) suggest such an
effect in olivine.
Thus, if the dissociation yields a partial dislocation having a Burgers vector
nonparallel to the cross-slip plane, then separate movement of this partial dislo-
cation in the cross-slip plane would be very difficult and result in forming a high-
energy fault surface. In order for movement to occur in the cross-slip plane, the
partial dislocations in such a case need to be recombined locally during the
