Geology Reference
In-Depth Information
dislocation crosses the boundary (Friedel
1964
, p. 46; Nabarro
1967
, p. 282). This
interaction does not greatly impede the dislocation emergence at a free surface
when only surface energy has to be supplied in forming the step (no effect at all
would be expected for a screw dislocation in this case). However, when there is
strong material on the other side of the boundary that also has to take part in the
step formation, there may be a large resistance to the emergence. This effect could
be important in affecting mechanical properties when surface films are present on
specimens. In the case of ionic crystals, there may also be charge effects where
dislocations emerge at surfaces, and in any material the point of emergence tends
to be a preferred site for chemical activity.
Even within an imperfect crystal, planar defects such as faults and antiphase
boundaries (surfaces at which there is an ordering discontinuity in an ordered
structure) may act as boundaries to interact with a dislocation. There will in
general be no image forces involved but some resistance to passage of the dis-
location will arise from the creation of additional boundary energy through the
formation of a step (in the case that the dislocation has an edge component) or of a
shear discontinuity (in case of a screw component).
When a sufficiently large repulsive interaction exists, the dislocation will be
arrested at the boundary and so prevent subsequent dislocations on the same slip
plane from reaching the boundary. This effect leads to a pile-up of dislocations of
like sign in the given slip plane. The dislocations themselves interact repulsively in
the pile-up. We therefore now consider the mutual interaction of dislocations.
6.3.4 Mutual Interactions Between Dislocations
Mutual interactions between dislocations are thought to underlie much of the
observed plastic behavior of crystals in both athermal and thermal regimes,
especially where strain hardening is involved and Peierls stress effects are not
dominant. The variety of effects, both observed and envisaged in theories, is very
large and has given rise to a large and confusing literature, the most complex in
dislocation theory. Here, and in
Sects. 6.6.3
and
6.6.6
, we can only attempt to
indicate the essential elements in this theoretical plethora.
Broadly, the mutual interaction can be a long-range effect arising from the
overlap of the long-range elastic stress fields of the dislocations, or a short-range
effect involving intersection or reaction. The long-range interactions tend to be
more important for dislocations that are more or less parallel to each other and the
short-range for those more nearly normal to each other.
Parallel dislocations may either attract or repel each other, depending on their
relative positions and Burgers vectors and on their edge or screw character. The
attraction or repulsion is determined by whether, when superimposing the stress
fields, as given by (
6.3a
,
b
) or a combination of these for mixed dislocations, the
total elastic strain energy is, respectively, less or greater than the sum of the
