Multiscale Modeling of Dislocation and Grain Boundary Mechanics in Small Scale Metals
Metals are of great importance for structural applications due to their high yield strength and fracture toughness. In recent years, efforts have been undertaken to further improve these properties, accelerated by advances in materials research and manufacturing processes. The conventional strategy to achieve high strength is to reduce the average grain size, but this is inevitably followed by the loss of ductility. Deformation mechanisms for plastic flow and ductility are largely dependent on microscopic defects such as dislocations, grain boundaries (GBs), and triple junctions (TJs). It is necessary to obtain a fundamental understanding of the correlation between defect mechanics and macroscopic properties across a variety of time and length scales so as to overcome the strength-ductility trade-off. With this motivation, a computational and theoretical approach has been taken to investigate the complex interplay between defects and macroscopic material response. In the first part of this dissertation (Chapters 2-3), dislocation mechanics within single crystals are examined to understand the role of sample size, crystallographic orientation, and loading conditions on the mechanism response. The focus is drawn to the plastic deformation which occurs at the mesoscale, wherefrom material properties are determined. Chapter 2 reports on DD simulations conducted to examine plastic deformation in single crystalline Cu micropillars subjected to two types of combined loading conditions: tension after torsion and torsion after tension. These combined loadings are then compared with simple tension and pure torsion, respectively. In metallic materials, the activation of one slip system increases the flow strength of other slip systems, which is a phenomenon known as latent hardening. This latent hardening behavior has been understood by the “forest hardening” mechanism arising from mutual dislocation interactions at the continuum length scale. As the size of a sample decreases to the submicron scale, the interactions between dislocations become increasingly sparse, so plastic deformation is instead governed mainly by dislocation sources. We find that there exists a transition from latent hardening to latent softening in intermediately-sized 600 nm samples undergoing the combined tension after torsion loading. The systematic computational and theoretical model described here suggests explosive multiplication causes dislocation density to greatly increase, giving rise to latent softening in those micropillars under tension after torsion. At the continuum length scale, mechanical properties of metals show relatively weak orientation dependence; however, Chapter 3 shows how strong anisotropic behaviors are exhibited as the size of sample decreases to micron and nanometer length scales. DD simulations are performed to investigate the orientation-dependent plasticity in submicron face-centered cubic (FCC) micropillars subjected to torsion. Accommodating results from atomistic modeling, updated surface nucleation schemes in DD models have been developed for three orientations (, , and ), allowing investigation of the dislocation microstructure evolution and the corresponding anisotropic mechanical response upon torsional loading and unloading. The DD simulation results show that the coaxial and hexagonal dislocation networks formed in - and -oriented nanopillars, respectively, exhibited excellent plastic recovery, while the rectangular dislocation network formed in the  crystal orientation was more stable and did not experience as much plastic recovery. Following work on isolated dislocation mechanics within a single crystal, the second part of this dissertation, Chapter 4, transitions into the exploration of defect mechanisms within bicrystals. Mechanical properties of metals such as strength and toughness are strongly correlated to complex interactions between various defects in the crystalline structure. While elementary interactions between these defects have been investigated using recent micro- and nano-characterization techniques, understanding of the detailed interaction mechanisms has hardly been obtained. To model plasticity in polycrystals at larger time and length scales, it is necessary to formulate a general guideline to predict both the interaction type (transmission or reflection) and the dislocation’s subsequent slip system after the interaction. Many criteria based on the geometric alignment of the defects have been developed to predict this phenomenon, but these have not been found to be accurate when applied to general data sets of grain boundaries (GBs). With this motivation, we conduct a systematic study using molecular dynamics (MD) models of bicrystals to analyze defect interaction process between a prismatic dislocation loop and eleven different grain boundaries of the following character: three tilt, three twist, and five mixed. Based on the MD observations, two new prediction methods are developed: the first is a new data-driven parametric score function based on the classical geometric criteria, and the second is by applying Gaussian process machine learning methods to find the probability distribution of a hidden function. The proposed methods could pave a new way to predict the unit interaction of dislocation with various GBs, which could show much higher accuracy compared to pre-existing geometric criteria. Finally, additional work on paving the way to polycrystalline modeling at the mesoscale is detailed, followed by an overall summary in Chapter 5.