Dislocation patterning - meso-scale interactive behavior of dislocations studied through dislocation density-function dynamics

Abstract

The formation of dislocation patterns ranging from highly ordered to fractal-like morphologies as metals deform plastically is strong manifestation of the group interactive behavior of dislocations in the meso scale. Past attempts to understanding dislocation patterning include the analytical models of the Walgraef-Aifantis type that consider the diffusive transport of dislocation density in one dimension. From a statistical mechanics point of view, dislocation patterning has also been interpreted as a result of the balance between the interactive energy and configurational entropy of the dislocations, and as a noise factor akin to the thermal temperature increases, the dislocation distribution is predicted to transit from being homogeneous to regular cellular and then to irregular cellular. The application of discrete dislocation dynamics to predict dislocation patterns has been hampered by the high quantities of dislocations involved. In this talk, a new simulator based on the dynamics of dislocation-density functions is used to predict the formation of dislocation subcells under oscillatory loading conditions. This simulator adopts an “all-dislocation” approach in which the flux, production and annihilation, as well as the Taylor and elastic interactions between dislocation densities are considered without distinguishing between geometrically necessary (GNDs) and statistically stored dislocations (SSDs). Elastic interactions between dislocations in 3D are treated in full accordance with Mura’s formulation for eigen stress. Dislocation generation is considered as a consequence of dislocations to maintain their connectivity. For an FCC model corresponding to Al, softening during vibrational loadings as well as enhanced cell formation are predicted. The simulations reveal that subcells form during oscillatory loadings due to the enhanced elimination of SSDs by the oscillatory stress, leaving behind GNDs with low Schmid factors which then form the subgrain walls. The oscillatory stress helps the depletion of the SSDs, because the chance for them to meet up and annihilate is increased with reversals of dislocation motions.