Geology Reference
In-Depth Information
6.3.2 Interaction with Dispersed Second Phases
Dispersed second phases, commonly formed as fine precipitates, can play a very
important role in obstructing dislocation motion. The effects are widely exploited
technologically for the strengthening of materials.
The resistance to the motion of a dislocation presented by a distribution of small
second phase particles may be expected to resemble in some respects that pre-
sented by immobile atoms in solid solution but the individual interactions will, in
general, be much stronger. The actual interaction forces will vary widely
according to the natures of the particles and of the processes whereby the dislo-
cation cuts through the particles or circumvents them. The latter distinction, of
cutting or bypassing, is important in determining the overall nature of the inter-
action and its consequences for the macroscopic mechanical behavior. The
behavior may also involve quite different considerations at low and high tem-
peratures, depending on whether thermal activation is playing a significant role in
assisting the cutting or bypassing. (See further,
Sects. 6.6.3
and
6.6.7
).
The particle size is a very important variable in determining the nature and
intensity of the influence of a given dispersed second phase. The respective bar-
riers to a dislocation cutting through particles and circumventing them are com-
monly such that there is a maximum hardening effect at an intermediate particle
size (often submicron) in the range of practical particle sizes (see
Sect. 6.6.2
).
Eventually, at large particle sizes, the second phase can be regarded as simply
providing boundaries with which dislocations in the matrix phase interact, as we
shall next discuss.
6.3.3 Interaction with Boundaries
The energy of a dislocation, which, as already pointed out, consists mainly of the
elastic strain energy in the long-range stress field, is modified when the dislocation
is situated sufficiently near a boundary that part of the long-range stress field is
located on the other side of the boundary. If the latter region consists of an
elastically softer material or of free space, the dislocation near the boundary will
have a lower energy than one further away and hence will be subject to an image
force attracting it toward the boundary. Conversely, if the second region consists
of elastically harder material, the image force will be a repulsive one. For the
theory of image forces, Friedel (
1964
, p. 44), Nabarro (
1967
, Chap. 5), Haasen
(
1978
, p. 252) and Hirth and Lothe (
1982
, Chaps. 3 and 5) can be consulted. The
image force tends to deflect a dislocation line as it approaches to intersect a
surface. Thus, it may influence the configuration of dislocations in the thin foils
viewed in transmission electron microscopy if the dislocations are sufficiently
freely mobile.
There is also a short-range interaction of a dislocation with a boundary since the
boundary has to be cut to produce a step or shear discontinuity when the
