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Three-dimensional (3D) discrete dislocation dynamics simulations are used to analyze the size effect on the fractal dimension of two-dimensional (2D) and 3D dislocation microstructure. 2D dislocation structures are analyzed first, and the calculated fractal dimension ( n 2 ) is found to be consistent with experimental results gleaned from transmission electron microscopy images. The value of n 2 is found to be close to unity for sizes smaller than 300 nm, and increases to a saturation value of ≈1.8 for sizes above approximately 10 microns. It is discovered that reducing the sample size leads to a decrease in the fractal dimension because of the decrease in the likelihood of forming strong tangles at small scales. Dislocation ensembles are found to exist in a more isolated way at the nano- and micro-scales. Fractal analysis is carried out on 3D dislocation structures and the 3D fractal dimension ( n 3 ) is determined. The analysis here shows that ( n 3 ) is significantly smaller than ( n 2 + 1 ) of 2D projected dislocations in all considered sizes. 

Plasticity in body centered cubic (BCC) crystals is shown to be controlled by slow screw dislocation motion, owing to the thermally-activated process of kink pair nucleation and migration. Through three dimensional discrete dislocation dynamics simulations, this work unravels the mystery of how such slow screw dislocation behavior contributes to extremely rapid strain bursts in submicron BCC tungsten (W) pillars, which is typical of BCC metals. It is found that strain bursts are dominated by the motion of non-screw dislocations at low strain rate, but are more influenced by screw dislocations at high strain rate. The total, and partial strain burst magnitude due to screw dislocations alone, are found to exhibit rate dependence following a power law statistics with exponent of 0.65. Similar power law statistics are also obeyed for the standard deviation of the corresponding plastic strain rate. The role of screw dislocations is attributed to the changing nature of dislocation source operation at different strain rates. The corresponding spatial distribution of plastic deformation is also discussed based on the uniqueness of the simulation method in reproducing the distribution of slipped area and plastic strain with very high spatial resolution.