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

Abstract: 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.