Statistical properties of fractal type dislocation cell structures

Abstract

The dislocation microstructure developing during plastic deformation strongly influences the stress-strain properties of crystalline materials. Resent theoretical investigations based on the 2D continuum theory of straight parallel edge dislocations were able to predict a periodic dislocation microstructure. The results obtained, however, can only be considered as a very first step toward the understanding of the origin of dislocation patterning. One of the most challenging problems is the modeling of the formation of the fractal like dislocation microstructure. So, it is crucial to determine the statistical properties of such a structure developing at ideal multiple slip orientation. In the paper, by x-ray line profile analysis and the method of high resolution electron backscatter diffraction (HR-EBSD) a complex experimental characterization of dislocation microstructure developing in uniaxially compressed Cu single crystals is presented. With these methods, the maps of the internal stress, the Nye tensor, and the geometrically necessary dislocation (GND) density were determined at different load levels. It is found from the fractal analysis of the GND maps that the fractal dimension of the cell structure is decreasing with increasing average spatial dislocation density fluctuation. Moreover, it is shown that the evolution of different types of dislocations can be successfully monitored with the HR-EBSD-based technique.