STATISTICAL MECHANICS MODELING OF MESOSCALE DEFORMATION IN METALS

The research under this project focused on a theoretical and computational modeling of dislocation dynamics of mesoscale deformation of metal single crystals. Specifically, the work aimed to implement a continuum statistical theory of dislocations to understand strain hardening and cell structure formation under monotonic loading. These aspects of crystal deformation are manifestations of the evolution of the underlying dislocation system under mechanical loading. The project had three research tasks: 1) Investigating the statistical characteristics of dislocation systems in deformed crystals. 2) Formulating kinetic equations of dislocations and coupling these kinetics equations and crystal mechanics. 3) Computational solution of coupled crystal mechanics and dislocation kinetics. Comparison of dislocation dynamics predictions with experimental results in the area of statistical properties of dislocations and their field was also a part of the proposed effort. In the first research task, the dislocation dynamics simulation method was used to investigate the spatial, orientation, velocity, and temporal statistics of dynamical dislocation systems, and on the use of the results from this investigation to complete the kinetic description of dislocations. The second task focused on completing the formulation of a kinetic theory of dislocations that respects the discrete nature of crystallographic slip and the physics of dislocation motion and dislocation interaction in the crystal. Part of this effort also targeted the theoretical basis for establishing the connection between discrete and continuum representation of dislocations and the analysis of discrete dislocation simulation results within the continuum framework. This part of the research enables the enrichment of the kinetic description with information representing the discrete dislocation systems behavior. The third task focused on the development of physics-inspired numerical methods of solution of the coupled dislocation kinetics and crystal mechanics framework. To a large extent, this task has also been successfully started. We have developed a custom finite-element approach with mesh points being a subset of the underlying crystal structure. When used to predict the evolution of the dislocation system, the planar motion of dislocations is naturally captured for all slip systems, thus minimizing numerical errors and providing simple ways to investigate cross slip and dislocation reactions. Preliminary results in this direction show that we are closer than ever in building a predictive framework for dislocation dynamics and mesoscale plasticity based on the first principles of dislocation dynamics. The rest of the report gives and overview of the research performed under this project and highlights the key results and open questions left for future investigations