  Coarse-grained descriptions of dislocation motion in crystalline metals
inherently represent a loss of information regarding dislocation-dislocation
interactions. In the present work, we consider a coarse-graining framework
capable of re-capturing these interactions by means of the
dislocation-dislocation correlation functions. The framework depends on a
coarse-graining length to define slip-system-specific dislocation densities.
Following a statistical definition of this coarse-graining process, we define a
spatial correlation function which will allow relative positions of dislocation
pairs, and thus the strength of their interactions at short range, to be
recaptured into a mean field description of dislocation dynamics. Through a
statistical homogeneity argument, we present a method of evaluating this
correlation function from discrete dislocation dynamics simulations. Finally,
results of this evaluation are shown in the form of self-correlation of
dislocation densities on the same slip-system. These correlation functions are
seen to depend weakly on plastic strain (and, in turn, the total dislocation
density), but are seen to depend strongly on the coarse-graining length.
Implications of these correlation functions in regard to continuum dislocation
dynamics as well as future directions of investigation are also discussed.
