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separate elastic energies. Consideration of specific cases indicates that, for a given
Burgers vector and for isotropic elasticity:
1. Parallel screw dislocations always attract or repel each other, depending on
whether they are of unlike or like sign, respectively.
2. Parallel edge dislocations of like sign attract or repel each other if the plane
joining them is inclined at greater or less than 45 to the slip plane, respec-
tively; these interactions are reversed for unlike signs.
More general rules can be found for mixed and inclined dislocations and for
those of different Burgers vector (Hirth and Lothe 1982 , Chap. 5; Weertman and
Weertman 1964 , Chap. 3). The repulsive effect determines the spacing of suc-
cessive dislocations of like sign in a pile-up in a given slip plane in which the
leading dislocation is immobilized. The attractive effect underlies the stability of
dipoles, which are pairs of parallel dislocations of opposite sign lying close to each
other in parallel slip planes, and of tilt subgrain boundaries, which are arrays,
normal to the slip plane, of edge dislocations of like sign.
In the case of dislocations steeply inclined to each other, the long-range elastic
interactions may lead to some local distortion of the dislocations but, on the whole,
they may be of less importance than short-range interactions and the effects of the
actual mutual intersection of the dislocations. Relative to a given dislocation
moving in its slip plane, the inclined dislocations crossing the slip plane are
commonly described as forest dislocations and their intersection by the moving
dislocation as forest cutting. Two short-range interaction effects may be specially
mentioned. The first is the formation of an attractive junction due to the moving
and forest dislocations being locally deviated into parallelism and then reacting to
form a product dislocation segment of lower energy; the result is to tend to pin the
moving dislocation at the junction and to contribute to the building up of a three-
dimensional network. The second effect is to introduce an offset in each of the
dislocation lines as a result of their intersection, each offset being identical with the
Burgers vector of the other dislocation and constituting either a kink or a jog which
may influence the future mobility of the dislocation cut. The intersection process
may be thermally activated since the formation of the kinks or jogs requires energy
which may be in part provided by thermal fluctuation.
6.4 Dislocation Velocity
Since crystal plasticity arises from the motion of dislocations, it is important to
understand the factors affecting their velocity, especially in relation to creep.
The dislocation velocity is focussed upon as one of the primary quantities in the
microdynamical approach to the theory of crystal plasticity, but it may well be
involved in any rate-dependent aspects of deformation.
Since it is the glide of dislocations that usually accounts for most of the strain,
the glide velocity is the dynamical aspect most studied. However, cross-slip and
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