Phase-field (PF) models are one of the most powerful tools to simulate microstructural evolution in metallic materials, polymers, and ceramics. However, existing PF approaches rely on rigorous mathematical model development, sophisticated numerical schemes, and high-performance computing for accuracy. Although recently developed surrogate microstructure models employ deep-learning techniques and reconstruction of microstructures from lower-dimensional data, their accuracy is fairly limited as spatio-temporal information is lost in the pursuit of dimensional reduction. Given these limitations, a novel data-driven emulator (DDE) for extrapolation prediction of microstructural evolution is presented, which combines an image-based convolutional and recurrent neural network (CRNN) with tensor decomposition, while leveraging previously obtained PF datasets for training. To assess the robustness of DDE, the emulation sequence and the scaling behavior with phase-field simulations for several noisy initial states are compared. In conclusion, the effectiveness of the microstructure emulation technique is explored in the context of accelerating runtime, along with an emphasis on its trade-off with accuracy.Meanwhile, an interpolation DDE has also been tested, which is based on obtaining a low-dimensional representation of the microstructures via tensor decomposition and subsequently predicting the microstructure evolution in the low-dimensional space using Gaussian process regression (GPR). Once the microstructure predictions are obtained in the low-dimensional space, a hybrid input-output phase retrieval algorithm will be employed to reconstruct the microstructures. As proof of concept, the results on microstructure prediction for spinodal decomposition are presented, although the method itself is agnostic of the material parameters. Results show that GPR-based DDE model are able to predict microstructure evolution sequences that closely resemble the true microstructures (average normalized mean square of 6.78 × 10−7) at time scales half of that employed in obtaining training data. This data-driven microstructure emulator opens new avenues to predict the microstructural evolution by leveraging phase-field simulations and physical experimentation where the time resolution is often quite large due to limited resources and physical constraints, such as the phase coarsening experiments previously performed in microgravity. Future work will also be discussed and demonstrate the intended utilization of these two approaches for 3D microstructure prediction through their combined application.

The design of energy absorbing structures is driven by application specific requirements like the amount of energy to be absorbed, maximum transmitted stress that is permissible, stroke length, and available enclosing space. Cellular structures like foams are commonly leveraged in nature for energy absorption and have also found use in engineering applications. With the possibility of manufacturing complex cellular shapes using additive manufacturing technologies, there is an opportunity to explore new topologies that improve energy absorption performance. This thesis aims to systematically understand the relationships between four key elements: (i) unit cell topology, (ii) material composition, (iii) relative density, and (iv) fields; and energy absorption behavior, and then leverage this understanding to develop, implement and validate a methodology to design the ideal cellular structure energy absorber. After a review of the literature in the domain of additively manufactured cellular materials for energy absorption, results from quasi-static compression of six cellular structures (hexagonal honeycomb, auxetic and Voronoi lattice, and diamond, Gyroid, and Schwarz-P) manufactured out of AlSi10Mg and Nylon-12. These cellular structures were compared to each other in the context of four design-relevant metrics to understand the influence of cell design on the deformation and failure behavior. Three new and revised metrics for energy absorption were proposed to enable more meaningful comparisons and subsequent design selection. Triply Periodic Minimal Surface (TPMS) structures were found to have the most promising overall performance and formed the basis for the numerical investigation of the effect of fields on the energy absorption performance of TPMS structures. A continuum shell-based methodology was developed to analyze the large deformation behavior of field-driven variable thickness TPMS structures and validated against experimental data. A range of analytical and stochastic fields were then evaluated that modified the TPMS structure, some of which were found to be effective in enhancing energy absorption behavior in the structures while retaining the same relative density. Combining findings from studies on the role of cell geometry, composition, relative density, and fields, this thesis concludes with the development of a design framework that can enable the formulation of cellular material energy absorbers with idealized behavior.

High-entropy alloys (HEAs) is a new class of materials which have been studied heavily due to their special mechanical properties. HEAs refers to alloys with multiple equimolar or nearly equimolar elements. HEAs show exceptional and attractive properties currently absent from conventional alloys, which make them the center of intense investigation. HEAs obtain their properties from four core effects that they exhibit and most of the work on them have been dedicated to study their mechanical properties. In contrast, little or no research have gone into studying the functional or even thermal properties of HEAs. Some HEAs have also shown exceptional or very high melting points. According to the definition of HEAs, Si-Ge-Sn alloys with equal or comparable concentrations of the three group IV elements belong to the category of HEAs. Thus, the equimolar components of Si-Ge-Sn alloys probably allow their atomic structures to display the same fundamental effects of metallic HEAs. The experimental fabrication of such alloys has been proven to be very difficult, which is mainly due to differences between the properties of their constituent elements, as indicated from their binary phase diagrams. However, previous computational studies have shown that SiGeSn HEAs have some very interesting properties, such as high electrical conductivity, low thermal conductivity and semiconducting properties. In this work, going for a complete characterization of the SiGeSn HEA properties, the melting point of this alloy is studied using classical molecular dynamics (MD) simulations and density functional theory (DFT) calculations. The aim is to investigate the effects of high Sn content in this alloy on the melting point compared with the traditional SiGe alloys. Classical MD simulations results strongly indicates that none of the available empirical potentials is able to predict accurate or reasonable melting points for SiGeSn HEAs and most of its subsystems. DFT calculations results show that SiGeSn HEA have a melting point which represent the mean value of its constituent elements and that no special deviations are found. This work contributes to the study of SiGeSn HEA properties, which can serve as guidance before the successful experimental fabrication of this alloy.

The increasing availability of data and advances in computation have spurred the development of data-driven approaches for modeling complex dynamical systems. These approaches are based on the idea that the underlying structure of a complex system can be discovered from data using mathematical and computational techniques. They also show promise for addressing the challenges of modeling high-dimensional, nonlinear systems with limited data. In this research expository, the state of the art in data-driven approaches for modeling complex dynamical systems is surveyed in a systemic way. First the general formulation of data-driven modeling of dynamical systems is discussed. Then several representative methods in feature engineering and system identification/prediction are reviewed, including recent advances and key challenges.

Microstructure refinement and alloy additions are considered potential routes to increase high temperature performance of existing metallic superalloys used under extreme conditions. Nanocrystalline (NC) Cu-10at%Ta exhibits such improvements over microstructurally unstable NC metals, leading to enhanced creep behavior compared to its coarse-grained (CG) counterparts. However, the low melting point of Cu compared to other FCC metals, e.g., Ni, might lead to an early onset of diffusional creep mechanisms. Thus, this research seeks to study the thermo-mechanical behavior and stability of hierarchical (prepared using arc-melting) and NC (prepared by collaborators through powder pressing and annealing) Ni-Y-Zr alloys where Zr is expected to provide solid solution and grain boundary strengthening in hierarchical and NC alloys, respectively, while Ni-Y and Ni-Zr intermetallic precipitates (IMCs) would provide kinetic stability. Hierarchical alloys had microstructures stable up to 1100 °C with ultrafine eutectic of ~300 nm, dendritic arm spacing of ~10 μm, and grain size ~1-2 mm. Room temperature hardness tests along with uniaxial compression performed at 25 and 600 °C revealed that microhardness and yield strength of hierarchical alloys with small amounts of Y (0.5-1wt%) and Zr (1.5-3 wt%) were comparable to Ni-superalloys, due to the hierarchical microstructure and potential presence of nanoscale IMCs. In contrast, NC alloys of the same composition were found to be twice as hard as the hierarchical alloys. Creep tests at 0.5 homologous temperature showed active Coble creep mechanisms in hierarchical alloys at low stresses with creep rates slower than Fe-based superalloys and dislocation creep mechanisms at higher stresses. Creep in NC alloys at lower stresses was only 20 times faster than hierarchical alloys, with the difference in grain size ranging from 10^3 to 10^6 times at the same temperature. These NC alloys showed enhanced creep properties over other NC metals and are expected to have rates equal to or improved over the CG hierarchical alloys with ECAP processing techniques. Lastly, the in-situ wide-angle x-ray scattering (WAXS) measurements during quasi-static and creep tests implied stresses being carried mostly by the matrix before yielding and in the primary creep stage, respectively, while relaxation was observed in Ni5Zr for both hierarchical and NC alloys. Beyond yielding and in the secondary creep stage, lattice strains reached a steady state, thereby, an equilibrium between plastic strain rates was achieved across different phases, so that deformation reaches a saturation state where strain hardening effects are compensated by recovery mechanisms.

Intelligent engineering designs require an accurate understanding of material behavior, since any uncertainties or gaps in knowledge must be counterbalanced with heightened factors of safety, leading to overdesign. Therefore, building better structures and pushing the performance of new components requires an improved understanding of the thermomechanical response of advanced materials under service conditions. This dissertation provides fundamental investigations of several advanced materials: thermoset polymers, a common matrix material for fiber-reinforced composites and nanocomposites; aluminum alloy 7075-T6 (AA7075-T6), a high-performance aerospace material; and ceramic matrix composites (CMCs), an advanced composite for extreme-temperature applications. To understand matrix interactions with various interfaces and nanoinclusions at their fundamental scale, the properties of thermoset polymers are studied at the atomistic scale. An improved proximity-based molecular dynamics (MD) technique for modeling the crosslinking of thermoset polymers is carefully established, enabling realistic curing simulations through its ability to dynamically and probabilistically perform complex topology transformations. The proximity-based MD curing methodology is then used to explore damage initiation and the local anisotropic evolution of mechanical properties in thermoset polymers under uniaxial tension with an emphasis on changes in stiffness through a series of tensile loading, unloading, and reloading experiments. Aluminum alloys in aerospace applications often require a fatigue life of over 109 cycles, which is well over the number of cycles that can be practically tested using conventional fatigue testing equipment. In order to study these high-life regimes, a detailed ultrasonic cycle fatigue study is presented for AA7075-T6 under fully reversed tension-compression loading. The geometric sensitivity, frequency effects, size effects, surface roughness effects, and the corresponding failure mechanisms for ultrasonic fatigue across different fatigue regimes are investigated. Finally, because CMCs are utilized in extreme environments, oxidation plays an important role in their degradation. A multiphysics modeling methodology is thus developed to address the complex coupling between oxidation, mechanical stress, and oxygen diffusion in heterogeneous carbon fiber-reinforced CMC microstructures.

Electromigration, the net atomic diffusion associated with the momentum transfer from electrons moving through a material, is a major cause of device and component failure in microelectronics. The deleterious effects from electromigration rise with increased current density, a parameter that will only continue to increase as our electronic devices get smaller and more compact. Understanding the dynamic diffusional pathways and mechanisms of these electromigration-induced and propagated defects can further our attempts at mitigating these failure modes. This dissertation provides insight into the relationships between these defects and parameters of electric field strength, grain boundary misorientation, grain size, void size, eigenstrain, varied atomic mobilities, and microstructure.First, an existing phase-field model was modified to investigate the various defect modes associated with electromigration in an equiaxed non-columnar microstructure. Of specific interest was the effect of grain boundary misalignment with respect to current flow and the mechanisms responsible for the changes in defect kinetics. Grain size, magnitude of externally applied electric field, and the utilization of locally distinct atomic mobilities were other parameters investigated. Networks of randomly distributed grains, a common microstructure of interconnects, were simulated in both 2- and 3-dimensions displaying the effects of 3-D capillarity on diffusional dynamics. Also, a numerical model was developed to study the effect of electromigration on void migration and coalescence. Void migration rates were found to be slowed from compressive forces and the nature of the deformation concurrent with migration was examined through the lens of chemical potential. Void migration was also validated with previously reported theoretical explanations. Void coalescence and void budding were investigated and found to be dependent on the magnitude of interfacial energy and electric field strength. A grasp on the mechanistic pathways of electromigration-induced defect evolution is imperative to the development of reliable electronics, especially as electronic devices continue to miniaturize. This dissertation displays a working understanding of the mechanistic pathways interconnects can fail due to electromigration, as well as provide direction for future research and understanding.

Fatigue fracture is one of the most common types of mechanical failures seen in structures. Considering that fatigue failures usually initiate on surfaces, it is accepted that surface roughness has a detrimental effect on the fatigue life of components. Irregularities on the surface cause stress concentrations and form nucleation sites for cracks. As surface conditions are not always satisfactory, particularly for additively manufactured components, it is necessary to develop a reliable model for fatigue life estimation considering surface roughness effects and assure structural integrity. This research study focuses on extending a previously developed subcycle fatigue crack growth model to include the effects of surface roughness. Unlike other models that consider surface irregularities as series of cracks, the proposed model is unique in the way that it treats the peaks and valleys of surface texture as a single equivalent notch. First, an equivalent stress concentration factor for the roughness was estimated and introduced into an asymptotic interpolation method for notches. Later, a concept called equivalent initial flaw size was incorporated along with linear elastic fracture mechanics to predict the fatigue life of Ti-6Al-4V alloy with different levels of roughness under uniaxial and multiaxial loading conditions. The predicted results were validated using the available literature data. The developed model can also handle variable amplitude loading conditions, which is suggested for future work.