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Progress toward a first-principles theory of plasticity and work-hardening iscurrently impeded by an insufficient picture of dislocation kinetics (thedynamic effect of driving forces in a given dislocation theory). This isbecause present methods ignore the short-range interaction of dislocations.This work presents a kinetic theory of continuum dislocation dynamics in avector density framework which takes into account the short-range interactionsby means of suitably defined correlation functions. The weak line bundleensemble of dislocations is defined, whereby the treatment of dislocations by avector density is justified. It is then found by direct averaging of thedislocation transport equation that additional driving forces arise which aredependent on the dislocation correlation. A combination of spatialcoarse-graining and statistical averaging of discrete dislocation systems areused to evaluate the various classes of tensorial dislocation correlationswhich arise in the line bundle kinetic theory. A novel, chiral classificationof slip system interactions in FCC crystals is used to define proper andimproper rotations by which correlation functions corresponding to sixinteraction classifications can be evaluated. The full set of these sixdislocation correlations are evaluated from discrete data. Only theself-correlations (for densities of like slip system) are found to be highlyanisotropic. All six classes of correlation functions are found to decay within2-4 times the coarse-graining distance. The correlations corresponding to thecoplanar interactions are found to be negligible. Implications of the evaluatedcorrelations for the implementation of vector density continuum dislocationdynamics are discussed, especially in terms of an additional correlationcomponent of the driving force and a gesture toward a coarse-graineddislocation mobility.

Dislocation correlations and the continuum dynamics of the weak line bundle ensemble