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In this paper, we present a dislocation-density-based three-dimensional continuum model, where the dislocation substructures are represented by pairs of dislocation density potential functions (DDPFs), denoted by ϕ and ψ . The slip plane distribution is characterized by the contour surfaces of ψ , while the distribution of dislocation curves on each slip plane is identified by the contour curves of ϕ which represents the plastic slip on the slip plane. By using DDPFs, we can explicitly write down an evolution equation system, which is shown consistent with the underlying discrete dislocation dynamics. The system includes (i) a constitutive stress rule, which describes how the total stress field is determined in the presence of dislocation networks and applied loads; (ii) a plastic flow rule, which describes how dislocation ensembles evolve. The proposed continuum model is validated through comparisons with discrete dislocation dynamics simulation results and experimental data. As an application of the proposed model, the “smaller-being-stronger” size effect observed in single-crystal micro-pillars is studied. A scaling law for the pillar flow stress σ flow against its (non-dimensionalized) size D is derived to be σ flow ∼ log ( D ) / D . [ABSTRACT FROM AUTHOR]

Abstract: Micro-pillars of anodic aluminium oxide with nano-sized honeycomb channels along the pillar axis exhibit compressive stress–strain response with large excursions corresponding to discrete, inhomogeneous deformation events. Each excursion is found to associate with the severe distortion of a material layer at the pillar’s head, whereas the remaining of the pillar remains intact. The stresses at which these excursions occur do not exhibit any significant dependence on the pillar size. A simple model is proposed to describe the response of pillars under compression, which energetically, as well as kinetically, explains as to why the localized deformation always takes place at the pillar head. Predictions on the occurrence of instability events from this model also quantitatively agree with the experimental observations. [ABSTRACT FROM AUTHOR]