  Progress toward a first-principles theory of plasticity and work-hardening is
currently impeded by an insufficient picture of dislocation kinetics (the
dynamic effect of driving forces in a given dislocation theory). This is
because present methods ignore the short-range interaction of dislocations.
This work presents a kinetic theory of continuum dislocation dynamics in a
vector density framework which takes into account the short-range interactions
by means of suitably defined correlation functions. The weak line bundle
ensemble of dislocations is defined, whereby the treatment of dislocations by a
vector density is justified. It is then found by direct averaging of the
dislocation transport equation that additional driving forces arise which are
dependent on the dislocation correlation. A combination of spatial
coarse-graining and statistical averaging of discrete dislocation systems are
used to evaluate the various classes of tensorial dislocation correlations
which arise in the line bundle kinetic theory. A novel, chiral classification
of slip system interactions in FCC crystals is used to define proper and
improper rotations by which correlation functions corresponding to six
interaction classifications can be evaluated. The full set of these six
dislocation correlations are evaluated from discrete data. Only the
self-correlations (for densities of like slip system) are found to be highly
anisotropic. All six classes of correlation functions are found to decay within
2-4 times the coarse-graining distance. The correlations corresponding to the
coplanar interactions are found to be negligible. Implications of the evaluated
correlations for the implementation of vector density continuum dislocation
dynamics are discussed, especially in terms of an additional correlation
component of the driving force and a gesture toward a coarse-grained
dislocation mobility.
