Quasi-continuum Reduction of Field Theories and Energetics of Defects in Aluminum.

Defects strongly govern the formation of microstructure in crystalline materials and thus their material properties. Accurate study of defect energetics requires numerical techniques capable of handling a wide range of length scales from the angstrom to the micro-scale by resolution of short-ranged complex atomic re-arrangements at the defect core and long-ranged elastic distortions of the lattice in bulk. We use a three pronged approach to attempt to solve this problem: (a) Orbital Free Density Functional Theory, a fast yet chemically accurate physical model valid for metals with a valence electron density close to a free electron gas (e.g Al, Mg). (b) A real space formulation and a finite element based implementation to naturally couple quantum mechanics with continuum mechanics (c) A coarse grained model that removes cell size restrictions on simulations, thus providing capability to handle millions of atoms. We use this technique to study the defect-core and energetics of an edge dislocation in Aluminum. Our results suggest that the core-size – region with significant contribution of electronic effects to defect energetics – is around ten times the magnitude of the Burgers vector, which is much larger than core-sizes used in continuum studies. The computed core-structure, representing two Shockley partials, is consistent with other electronic structure and atomistic studies. Interestingly, our study indicates that the core-energy of an edge dislocation has a significant and a highly non-linear response to external macroscopic strains. From this core-energy dependence on macroscopic strains, we infer that interactions between dislocations involve an additional short-ranged force beyond the traditional Peach-Koehler force, and that this force is significant in regions of in-homogenous deformations.PhDMechanical Engineering and Scientific ComputingUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/107230/1/mrinal_1.pd

Large Scale Electronic Structure Studies on the Energetics of Dislocations in Al-Mg Materials System and Its Connection to Mesoscale Models

Computational modeling of dislocation behavior is vital for designing new lightweight metallic alloys. However, extraordinary challenges are posed by the multiscale physics ranging over a vast span of interacting length-scales from electronic-structure and atomic-scale effects at the dislocation core ($< 10^{-9} {rm m}$) to long-ranged elastic interactions at the continuum scale ($sim 10 upmu$). In particular, quantification of the energetics associated with electronic-structure effects inside the dislocation core and its interaction with the external macroscopic elastic fields have not been explored due to limitations of current electronic-structure methods based on the widely used plane-wave based discretization. This thesis seeks to address the above challenges by developing computational methodologies to conduct large-scale real-space electronic-structure studies of energetics of dislocations in Aluminum and Magnesium, and use these results to develop phenomenological connections to mesoscale models of plasticity like discrete dislocation dynamics (DDD), which study the collective behavior of the dislocations at longer length scales ($sim$ 1--15 $upmu$). First, a local real-space formulation of orbital-free Density Functional Theory is developed based on prior work, and implemented using finite-element discretization. The local real-space formulation coupled with bulk Dirichlet boundary conditions enables a direct computation of the isolated dislocation core energy. Studies on dislocations in Aluminum and Magnesium suggest that the core-size---region with significant contribution of electronic effects to dislocation energetics---is around seven to eleven times the magnitude of the Burgers vector. This is in stark contrast to prior displacement field based core size estimates of one to three times the magnitude of the Burgers vector. Interestingly, our study further indicates that the core-energy of the dislocations in both Aluminum and Magnesium is strongly dependent on external macroscopic strains with a non-zero slope at zero external strain. Next, the computed dislocation core energetics is used to develop a continuum model for an arbitrary aggregate of dislocations in an infinite isotropic elastic continua. This model, which accounts for the core energy dependence on macroscopic deformation provides a phenomenological approach to incorporate the electronic structure effects into mesoscale DDD simulations. Application of this model to derive nodal forces in a discrete dislocation network, leads to additional configurational forces beyond those considered in existing DDD models. Using case studies, we show that even up to distances of $10-15$ nm between the dislocations, these additional configurational forces are non-trivial in relation to the elastic Peach-Koehler force. Furthermore, the core force model is incorporated into a DDD implementation, where significant influence of core force on elementary dislocation mechanisms in Aluminum such as critical stress of a Frank-Read source and structure of a dislocation binary junction are demonstrated. To enable the above electronic-structure studies of dislocations in generic material systems, calculations using the more accurate and transferable Kohn-Sham Density Functional Theory (KS-DFT) are required. The final part of this thesis extends previous work on real-space adaptive spectral finite-element discretization of KS-DFT to develop numerical strategies and implementation innovations, which significantly reduce the computational pre-factor, while increasing the arithmetic intensity and lowering the data movement costs on both many-core and heterogeneous architectures. This has enabled systematically convergent and massively parallel (demonstrated up to 192,000 MPI tasks) KS-DFT calculations on material systems up to $sim 100,000$ electrons. Using GPUs, an unprecedented sustained performance of 46 PFLOPS (27.8% peak FP64 performance) is demonstrated on a large-scale benchmark dislocation system in Magnesium containing 105,080 electrons.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/153417/1/dsambit_1.pd