Geology Reference
In-Depth Information
The movement of a dislocation line out of the slip plane is called climb. Since
climb generally requires the removal or supply of substance along the dislocation
path, it is referred to as nonconservative dislocation motion, in contrast to the
conservative motion in slip. The volume DV of substance added or removed during
the climb of a dislocation segment of length l through a distance s normal to the
slip plane is given by
DV
¼
lbs sin h
ð
6
:
5
Þ
where b is the magnitude of the Burgers vector and h its inclination to the slip line
in the slip plane. In the case of a pure screw dislocation, for which the directions of
Burgers vector and dislocation line are parallel, no unique slip plane is defined and
so the dislocation can move conservatively in any plane; this motion is referred to
as cross-slip when the plane is not the primary slip plane.
The application of stress to the region containing a dislocation has a mobilizing
tendency that is equivalent to applying a force normal to the dislocation line. From
work considerations it follows that the component of this force in the slip plane,
the glide force, F
g
;
is
F
g
¼
sbl
ð
6
:
6a
Þ
where s is the resolved shear stress in the slip plane, b the magnitude of the
Burgers vector and l the length of the dislocation segment concerned. Corre-
spondingly, the component of the force in the plane normal to the slip plane, the
climb force, F
c
;
is
F
c
¼
rbl sin h
ð
6
:
6b
Þ
where r is the deviatoric normal-stress component parallel to the Burgers vector
and h the angle between the slip line and the Burgers vector. Thus, the climb force
arising from the stress component r is rbl for a pure edge dislocation and zero for
a pure screw dislocation. For a more general treatment of the force acting on a
dislocation, see Weertman and Weertman (
1964
, pp. 54-61) and Hirth and Lothe
(
1982
, Chap. 3).
6.2.2 The Energy of a Dislocation
The energy of a dislocation can be considered in two parts, associated with the
core and the long-range elastic stress field, respectively. The core is the cylindrical
region of radius r
0
immediately surrounding the dislocation line, within which the
crystal structure is disrupted or distorted beyond the limits of linear elasticity; r
0
is
usually taken to be several times b in magnitude. The region of the long-range
elastic stress field is taken as extending from the cylinder of radius r
0
to the surface
of the crystal or, more usually, to a radius R beyond which the internal stress field
