Under stress, many crystalline materials exhibit irreversible plastic deformation caused by the motion of lattice dislocations. In plastically deformed microcrystals, internal dislocation avalanches lead to jumps in the stress-strain curves (strain bursts), whereas in macroscopic samples plasticity appears as a smooth process. By combining three-dimensional simulations of the dynamics of interacting dislocations with statistical analysis of the corresponding deformation behavior, we determined the distribution of strain changes during dislocation avalanches and established its dependence on microcrystal size. Our results suggest that for sample dimensions on the micrometer and submicrometer scale, large strain fluctuations may make it difficult to control the resulting shape in a plastic-forming process.

This review examines the size effects observed in the mechanical strength of thin metal films and small samples such as single-crystalline pillars, whiskers, and wires. Experimental results from mechanical testing and electron microscopy studies, as well as recent insights from discrete dislocation dynamics simulations, are presented. The size dependency of deformation may be separated into three regimes: the nanometer regime of roughly 100 nm and below, an intermediate regime between 100 nm and approximately 1 μm, and a bulk-like regime. We argue that there is no scaling law with one universal power-law exponent encompassing the entire range. Instead, there are a number of different mechanisms and underlying effects, e.g., the initial dislocation microstructure or loading conditions. The complex interaction of these mechanisms leads to the typically observed scaling behavior.

A three-dimensional discrete dislocation dynamics plasticity model is presented. The approach allows realistic boundary conditions on the specimen, as both stress and displacement fields of the dislocations are incorporated in the formulation. Emphasis is placed on various technical details in the formulation as well as on the implementation. The current implementation includes features necessary to model conservative motion of dislocations in presence of surfaces. These include details of the discretization of the evolving dislocation structure, the handling of junction formation and destruction, cross-slip and boundary conditions. Special attention is given to the treatment of dislocations that partly glide out of the material, including the treatment of image forces via the finite-element method.

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Realistic dislocation network topologies were generated by relaxing an initially pinning point free dislocation loop structure using three-dimensional discrete dislocation dynamics simulations. Traction-free finite-sized samples were used. Subsequently, these equilibrated structures were subjected to tensile loading and their mechanical behavior was investigated with respect to the initial configuration. A strong mechanical size effect was found. The flow stress at 0.2% plastic deformation scales with specimen size with an exponent between -0.6 and -0.9, depending on the initial structure and size regime. During relaxation, a mechanism, also favored by cross-slip, is identified which leads to rather stable pinning points. These pinning points are comparable to those of the isolated Frank-Read sources often used as a starting configuration in previous discrete dislocation dynamics simulations. These nodes act as quite stable dislocation sources, which can be activated multiple times. The influence of this source mechanism on the mechanical properties of small-scale specimens is discussed

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