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In continuum models of dislocations, proper formulations of short-rangeelastic interactions of dislocations are crucial for capturing various types ofdislocation patterns formed in crystalline materials. In this article, thecontinuum dynamics of straight dislocations distributed on two parallel slipplanes is modelled through upscaling the underlying discrete dislocationdynamics. Two continuum velocity field quantities are introduced to facilitatethe discrete-to-continuum transition. The first one is the local migrationvelocity of dislocation ensembles which is found fully independent of theshort-range dislocation correlations. The second one is the decoupling velocityof dislocation pairs controlled by a threshold stress value, which is proposedto be the effective flow stress for single slip systems. Compared to the almostubiquitously adopted Taylor relationship, the derived flow stress formulaexhibits two features that are more consistent with the underlying discretedislocation dynamics: i) the flow stress increases with the in-plane componentof the dislocation density only up to a certain value, hence the derivedformula admits a minimum inter-dislocation distance within slip planes; ii) theflow stress smoothly transits to zero when all dislocations becomegeometrically necessary dislocations. A regime under which inhomogeneities indislocation density grow is identified, and is further validated throughcomparison with discrete dislocation dynamical simulation results. Based on thefindings in this article and in our previous works, a general strategy forincorporating short-range dislocation correlations in continuum models ofdislocations is proposed.

Continuum dynamics of the formation, migration and dissociation of self-locked dislocation structures on parallel slip planes