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During plastic flow of crystalline solids, dislocations self-organize in the form of patterns, with a wavelength that is inversely proportional to stress. After four decades of investigations, the origin of this property is still under discussion. We show that dislocation patterns verifying the principle of similitude can be obtained from dynamics simulations of double slip. These patterns are formed in the presence of long-and short-range interactions, but they are not significantly modified when only short-range interactions are present. This new insight into dislocation patterning phenomena has important implications regarding current models. DOI: 10.1103/PhysRevLett.96.125503 PACS numbers: 61.72.Lk, 62.20.Fe, 82.20.Wt, 89.75.Da During plastic flow of crystalline solids, dislocations, the linear defects that carry plasticity at the microscopic scale, move and multiply. In parallel, dislocation microstructures tend to self-organize in the form of patterns containing dislocation-rich and dislocation-poor regions. As elementary dislocation processes are reasonably well understood [1], this collective behavior constitutes a major obstacle to a physical modeling of the mechanical response. In monotonic deformation and in multislip conditions, the patterns consist of three-dimensional cells bounded by cell walls. A wealth of experimental observations [2] shows that during plastic deformation, the average spacing between cell walls shrinks like the inverse of the recorded stress, the flow stress. This property is known under the name of principle of similitude [3]. After many controversies about how to model the formation of dislocation cells (see Ref.[4] for a review), it was realized 20 years ago that dislocation patterning is an example of self-organization in a system driven far from equilibrium. In the models that were further developed, the main difficulty consists in accounting for long-range interaction stresses between dislocations, which were assumed to be at the origin of patterning phenomena [5,6]. The specific features of such models are, however, still under discussion, as they do not account for a few essential properties of dislocations.Dislocation dynamics simulations constitute a natural tool for investigating this type of collective behavior. However, 3D simulations are still too demanding in terms of computational load to allow investigating the similitude principle. A study of 3D patterns in face-centered cubic (fcc) crystals has, nevertheless, confirmed that three main mechanisms, which are currently implemented in these simulations, participate to pattern formation [7]. The reactions between intersecting dislocations, or junctions, are strong obstacles which pin the cell walls. Elastic interactions between dislocations, which are long-ranged, also necessarily play a role. The cross-slip of screw dislocations stabilizes dislocation tangles, accounts for the threedimensional dissemination of slip, and governs the selforganization kinetics.Dislocation patterns can be more easily obtained in 2...

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The possibility of the influence of segregation-induced local electric fields in the bulk diffusion of the species controlling the plastic deformation of nanocrystalline materials has been pointed out. Until now, there is only a model applicable to the case of a monodimensional system. In spite of its simplicity, it predicts a significative influence of a local electric field in creep. Our work develops a different model applicable to three-dimensional systems. It takes as a starting point the diffusional model, and it can be generalized to those systems in which the grain-boundary sliding model accommodated by diffusional processes accurately describes plasticity in the submicron range of grain size. The range of validity, as well as the different behavior of nanocrystalline materials from the submicron ones is discussed. Preliminary results are in good agreement with the published data for yttria tetragonal zirconia ͑YTZP͒ nanocrystalline ceramics.