Computational Modeling of Elastic Fields in Dislocation Dynamics

In the present work, we investigate the internal fields generated by the dislocation structures that form during the deformation of copper single crystals. In particular, we perform computational modeling of the statistical and morphological characteristics of the dislocation structures obtained by dislocation dynamics simulation method and compare the results with X-ray microscopy measurements of the same data. This comparison is performed for both the dislocation structure and their internal elastic fields for the cases of homogeneous deformation and indentation of copper single crystals. A direct comparison between dislocation dynamics predictions and X-ray measurements plays a key role in demonstrating the fidelity of discrete dislocation dynamics as a predictive computational mechanics tool and in understanding the X-ray data. For the homogeneous deformation case, dislocation dynamics simulations were performed under periodic boundary conditions and the internal fields of dislocations were computed by solving an elastic boundary value problem of many-dislocation system using the finite element method. The distribution and pair correlation functions of all internal elastic fields and the dislocation density were computed. For the internal stress field, the availability of such statistical information paves the way to the development of a density-based mobility law of dislocations in continuum dislocation dynamics models, by correlating the internal-stress statistics with dislocation velocity statistics. The statistical analysis of the lattice rotation and the dislocation density fields in the deformed crystal made possible the direct comparison with X-ray measurements of the same data. Indeed, a comparison between the simulation and experimental measurements has been possible, which revealed important aspects of similarity and differences between the simulation results and the experimental data. In the case of indentation, which represents a highly inhomogeneous deformation, a contact boundary value problem was solved in conjunction with a discrete-dislocation dynamics simulation model; the discrete dislocation dynamics simulation was thus enabled to handle finite domains under mixed traction/displacement boundary conditions. The load-displacement curves for indentation experiments were analyzed with regard to cross slip, indentation speed and indenter shape. The lattice distortion fields obtained by indentation simulations were directly compared with their experimental counterparts. Other indentation simulations were also carried out, giving insight into different aspects of micro-scale indentation deformation.