In this thesis, a hierarchical multiscale method was developed to predict rolling contact fatigue lives of mechanical systems. In the proposed multiscale method, the molecular modeling and simulation of lubricant was conducted to investigate the friction between rolling contact surfaces. The calculated friction coefficient was passed to the continuum model of rolling contact components to predict fatigue lives. Molecular dynamics modeling and simulation of thin film lubrication and lubricated contact surfaces were carried out to investigate mechanisms of hydrodynamic lubrication at nano-scale first. Although various lubricant alkane chains were considered in the molecular model, the chain length of eight united molecules were mainly employed in this thesis. In addition, the effects of temperature and nano-particles (debris) on the friction forces were discussed. It was found that the existing of nano-particles (debris) could increase the friction force between contact surfaces with hydrodynamic lubrication. In the continuum model of the developed multiscale method, finite element analysis was employed to predict rolling contact fatigue life of rolling contact components, including bearing and gear-tooth. Specifically, the fatigue crack initiation of bearing was studied, and then the fatigue crack initiation and propagation in gear-tooth. In addition, the enhancement of gear-tooth fatigue life by using composite patches was discussed as well. It should be noted that the friction coefficient used in the continuum model was calculated in the molecular model. It is one-way message passing in the developed multiscale method. Another continuum method was studied and developed in this thesis to provide alternate methods for the continuum model in the proposed multiscale framework. Peridynamics method has advantages in modeling and simulation of discontinuities, including cracks, over the conventional finite element methods. The applications of Peridynamics in predicting fatigue crack initiation and propagation lives were discussed in this thesis.

The mechanical reliability of electronic components has become harder and harder to predict due to the use of composite materials. One of the key issues is creating an accurate model of the delamination mechanism, which consists in the separation of two different bounded materials. This phenomenon is a very challenging issue that is investigated in the Nano Interface Project (NIP), in which this thesis is involved. The macroscopic adhesion force is governed by several parameters described at different length scales. Among these parameters, the roughness profile of the interface has a pronounced influence. The main difficulty for an accurate delamination characterization is then investigating the effects of this roughness profile and the modifications it implies for the overall cohesion. The objective of the NIP is to develop an interface model for the numerical testing of electronic components in a finite element software. The problem is that a direct modeling of all the mechanisms described previously is really expensive in term of computation time, if possible at all. This difficulty is increased by the huge mismatch of the mechanical properties of the materials in contact. A scale transition method is therefore required, which is provided by homogenization. The idea is to consider the delamination at a wider scale. Rather than modeling the whole roughness profile, the adhesion at the interface will be described by homogenized, or macroscopic, parameters extracted from a representative model at the micro-scale, the RVE. This thesis will deal with the determination of these homogenized parameters.

Physical and chemical heterogeneities cause the porous media transport parameters to vary with scale, and between these two types of heterogeneities geological heterogeneity is considered to be the most important source of scale-dependence of transport parameters. Subsurface processes associated with chemical alterations result in changing reservoir properties with interlinked spatial and temporal scale, and there is uncertainty in the evolution of those properties and the chemical processes. This dissertation provides a framework and procedures to quantify the spatiotemporal scaling characteristics of reservoir attributes and transport processes in heterogeneous media accounting for chemical alterations in the reservoir. Conventional flow scaling groups were used to assess their applicability in scaling of recovery and Mixing Zone Length (MZL) in presence of chemical reactivity and permeability heterogeneity through numerical simulations of CO₂ injection. It was found out that these scaling groups are not adequate enough to capture the scaling of recovery and transport parameters in the combined presence of chemical reactivity and physical heterogeneity. In this illustrative example, MZL was investigated as a function of spatial scale, temporal scale, multi-scale heterogeneity, and chemical reactivity; key conclusions are that 1) the scaling characteristics of MZL distinctly differ for low permeability and high permeability media, 2) heterogeneous media with spatial arrangements of both high and low permeability regions exhibit scaling characteristics of both high and low permeability media, 3) reactions affect scaling characteristics of MZL in heterogeneous media, 4) a simple rescaling can combine various MZL curves by merging them into a single MZL curve irrespective of the correlation length of heterogeneity, and 5) estimates of MZL (and consequently predictions of oil recovery) will fluctuate corresponding to displacements in a permeable medium whose lateral length is smaller than the correlation length of geological formation. We illustrate and extend the procedure of estimating Representative Elementary Volume (REV) to include temporal scale by coupling it with spatial scale. The current practice is to perform spatial averaging of attributes and account for residual variability by calibration and history matching. This results in poor predictions of future reservoir performance. The proposed semi-analytical technique to scale-up in both space and time provides guidance for selection of spatial and temporal discretizations that takes into account the uncertainties due to sub-processes. Finally, a probabilistic particle tracking (PT) approach is proposed to scale-up flow and transport of diffusion-reaction (DR) processes while addressing multi-scale and multi-physics nature of DR mechanisms and also maintaining consistent reservoir heterogeneity at different levels of scales. This multi-scale modeling uses a hierarchical approach which is based on passing the macroscopic subsurface heterogeneity down to the finer scales and then returning more accurate reactive flow response. This PT method can quantify the impact of reservoir heterogeneity and its uncertainties on statistical properties such as reaction surface area and MZL, at various scales. / text

Zirconium and its alloys have been extensively used in both heavy and light water nuclear reactors. Like other Hexagonal Close-Packed (HCP) materials, e.g. magnesium, zirconium alloys develop different textures during manufacturing process which result in highly anisotropic materials with different responses under different loading conditions. Slip and twinning are two major deformation mechanisms during plastic deformation of zirconium. This dissertation uses various experimental techniques and a crystal plasticity scheme in the finite element framework to study deformation mechanisms in HCP materials with an emphasis on twinning in Zircaloy-2. The current study is presented as a manuscript format dissertation comprised of four manuscript chapters. After a literature review in Chapter 2, Chapter 3 reports steps in developing a crystal plasticity finite element user material subroutine for modeling deformation in Zircaloy-2 at room temperature. It is shown in Chapter 3 that the developed rate dependent equations are capable of capturing evolution of key features, e.g., texture, lattice strains, and twin volume fractions, during deformation by twinning and slip. Chapter 4 reports various assumptions and approaches in modeling twinning where results are compared against neutron diffraction measurements from the literature. It is shown in Chapter 4 that the predominant twin reorientation scheme can explain texture development more precisely than the other schemes discussed. Chapter 5 and 6 are two connected chapters where in the first one the formation of twins is studied statistically and in the second one, local inception and propagation of twins is studied. Numerical results of these two chapters are compared with 2D electron backscattered diffraction measurements, both carried out by the author and from the literature. Results from these two connected chapters emphasize the important role of grain boundary geometry and stress concentration sites on twin nucleation and growth. The four manuscript chapters are followed by summarizing conclusions and suggestions for future work in Chapter 7. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2012-04-23 11:50:33.751

Single wall carbon nanotubes (SWCNTs) show a variety of unparalleled properties such as high electrical and thermal conductivity, high specific surface area (SSA) and a large stiffness under axial loads. One of the major challenges in tapping the vast potential of SWCNTs is to fabricate nanotube based macrostructures that retain the unique properties of nanotubes. Pristine SWCNT aerogels are highly porous, isotropic structures of nanotubes mediated via van der Waals (VDW) interactions at junctions. The mechanical behavior of such aerogels is examined in several experimental studies. However, it is necessary to supplement these studies with insights from simulations in order to develop a fundamental understanding of deformation behavior of SWCNT aerogels. In this study, the mechanical behavior of SWCNT networks is studied using a multi-scale modeling approach. The mechanics of an individual nanotube and interactions between few nanotubes are modeled using molecular dynamics (MD) simulations. The results from atomistic simulations are used to inform meso-scale and continuum scale finite element (FE) models. The deformation mechanism of pristine SWCNT networks under large compressive strain is deduced from insights offered by meso-scale simulations. It is found that the elasticity of such networks is governed by the bending deformation of nanotubes while the plastic deformation is governed by the VDW interactions between nanotubes. The stress response of the material in the elastic regime is dictated by the VDW stresses on nanotubes while in the plastic regime, both the VDW and axial deformation stresses on nanotubes drive the overall stress response. In this study, the elastic behavior of a random SWCNT network with any set of junction stiffness and network density is also investigated using FE simulations. It is found that the elastic deformation of such networks can be governed either by the deformation of the nanotubes (bending, axial compression) or deformation of the junctions. The junction stiffness and the network density determine the network deformation mode. The results of the FE study are also applicable to any stiff fiber network.

Phenomenological material models such as Johnson-Cook plasticity are often used in finite element simulations of large deformation processes at different strain rates and temperatures. Since the material constants that appear in such models depend on the material, experimental data, fitting method, as well as the mathematical representation of strain rate and temperature effects, the predicted material behavior is subject to uncertainty. In this dissertation, evidence theory is used for modeling uncertainty in the material constants, which is represented by separate belief structures that are combined into a joint belief structure and propagated using impact loading simulation of structures. Yager’s rule is used for combining evidence obtained from more than one source. Uncertainty is quantified using belief, plausibility, and plausibility-decision functions. An evidence-based design optimization (EBDO) approach is presented where the nondeterministic response functions are expressed using evidential reasoning. The EBDO approach accommodates field material uncertainty in addition to the embedded uncertainty in the material constants. This approach is applied to EBDO of an externally stiffened circular tube under axial impact load with and without consideration of material field uncertainty caused by spatial variation of material uncertainties due to manufacturing effects. Surrogate models are developed for approximation of structural response functions and uncertainty propagation. The EBDO example problem is solved using genetic algorithms. The uncertainty modeling and EBDO results are presented and discussed.

Titanium-7%wt-Aluminum (Ti-7Al) has been of interest to the aerospace industry owing to its good structural and thermal properties. However, extensive research is still needed to study the structural behavior and determine the material properties of Ti-7Al. The homogenized macro-scale material properties are directly related to the crystallographic structure at the micro-scale. Furthermore, microstructural uncertainties arising from experiments and computational methods propagate on the material properties used for designing aircraft components. Therefore, multi-scale modeling is employed to characterize the microstructural features of Ti-7Al and computationally predict the macro-scale material properties such as Young's modulus and yield strength using machine learning techniques. Investigation of microstructural features across large domains through experiments requires rigorous and tedious sample preparation procedures that often lead to material waste. Therefore, computational microstructure reconstruction methods that predict the large-scale evolution of microstructural topology given the small-scale experimental information are developed to minimize experimental cost and time. However, it is important to verify the synthetic microstructures with respect to the experimental data by characterizing microstructural features such as grain size and grain shape. While the relationship between homogenized material properties and grain sizes of microstructures is well-studied through the Hall-Petch effect, the influences of grain shapes, especially in complex additively manufactured microstructure topologies, are yet to be explored. Therefore, this work addresses the gap in the mathematical quantification of microstructural topology by developing measures for the computational characterization of microstructures. Moreover, the synthesized microstructures are modeled through crystal plasticity simulations to determine the material properties. However, such crystal plasticity simulations require significant computing times. In addition, the inherent uncertainty of experimental data is propagated on the material properties through the synthetic microstructure representations. Therefore, the aforementioned problems are addressed in this work by explicitly quantifying the microstructural topology and predicting the material properties and their variations through the development of surrogate models. Next, this work extends the proposed multi-scale models of microstructure-property relationships to magnetic materials to investigate the ferromagnetic-paramagnetic phase transition. Here, the same Ising model-based multi-scale approach used for microstructure reconstruction is implemented for investigating the ferromagnetic-paramagnetic phase transition of magnetic materials. The previous research on the magnetic phase transition problem neglects the effects of the long-range interactions between magnetic spins and external magnetic fields. Therefore, this study aims to build a multi-scale modeling environment that can quantify the large-scale interactions between magnetic spins and external fields. / Doctor of Philosophy / Titanium-Aluminum (Ti-Al) alloys are lightweight and temperature-resistant materials with a wide range of applications in aerospace systems. However, there is still a lack of thorough understanding of the microstructural behavior and mechanical performance of Titanium-7wt%-Aluminum (Ti-7Al), a candidate material for jet engine components. This work investigates the multi-scale mechanical behavior of Ti-7Al by computationally characterizing the micro-scale material features, such as crystallographic texture and grain topology. The small-scale experimental data of Ti-7Al is used to predict the large-scale spatial evolution of the microstructures, while the texture and grain topology is modeled using shape moment invariants. Moreover, the effects of the uncertainties, which may arise from measurement errors and algorithmic randomness, on the microstructural features are quantified through statistical parameters developed based on the shape moment invariants. A data-driven surrogate model is built to predict the homogenized mechanical properties and the associated uncertainty as a function of the microstructural texture and topology. Furthermore, the presented multi-scale modeling technique is applied to explore the ferromagnetic-paramagnetic phase transition of magnetic materials, which causes permanent failure of magneto-mechanical components used in aerospace systems. Accordingly, a computational solution is developed based on an Ising model that considers the long-range spin interactions in the presence of external magnetic fields.

The task of thermal management in electrical systems has never been simple and has only become more difficult in recent years as the power electronics industry pushes towards devices with higher power densities. At the Center for Power Electronic Systems (CPES), a new approach to power electronic design is being implemented with the Integrated Power Electronic Module (IPEM). It is believed that an IPEM-based design approach will significantly enhance the competitiveness of the U.S. electronics industry, revolutionize the power electronics industry, and overcome many of the technology limits in today's industry by driving down the cost of manufacturing and design turnaround time. But with increased component integration comes the increased risk of component failure due to overheating. This thesis addresses the issues associated with the thermal management of integrated power electronic devices. Two studies are presented in this thesis. The focus of these studies is on the thermal design of a DC-DC front-end power converter developed at CPES with an IPEM-based approach. The first study investigates how the system would respond when the fan location and heat sink fin arrangement are varied in order to optimize the effects of conduction and forced-convection heat transfer to cool the system. The set-up of an experimental test is presented, and the results are compared to the thermal model. The second study presents an improved methodology for the thermal modeling of large-scale electrical systems and their many subsystems. A zoom-in/zoom-out approach is used to overcome the computational limitations associated with modeling large systems. The analysis performed in this paper was completed using I-DEAS©,, a three-dimensional finite element analysis (FEA) program which allows the thermal designer to simulate the affects of conduction and convection heat transfer in a forced-air cooling environment. / Master of Science

An alternative formulation of the governing equations of a dynamical system, called the multi-scale localized perturbation method, is introduced and derived for the purpose of solving complex geophysical flow problems. Simulation variables are decomposed into background and perturbation components, then assumptions are made about the evolution of these components within the context of an environmental flow in order to close the system. Once closed, the original governing equations become a set of one-way coupled governing equations called the "delta form" of the governing equations for short, with one equation describing the evolution of the background component and the other describing the evolution of the perturbation component. One-way interaction which arises due to non-linearity in the original differential equations appears in this second equation, allowing the background fields to influence the evolution of a perturbation. Several solution methods for this system of equations are then proposed. Advantages of the delta form include the ability to specify a complex, temporally- and spatially-varying background field separate from a perturbation introduced into the system, including those created by natural or man-made sources, which enhances visualization of the perturbation as it evolves in time and space. The delta form is also shown to be a tool which can be used to simplify simulation setup. Implementation of the delta form of the incompressible URANS equations with turbulence model and scalar transport within OpenFOAM is then documented, followed by verification cases. A stratified wake collapse case in a domain containing a background shear layer is then presented, showing how complex internal gravity wave-shear layer interactions are retained and easily observed in spite of the variable decomposition. The multi-scale localized perturbation method shows promise for geophysical flow problems, particularly multi-scale simulation involving the interaction of large-scale natural flows with small-scale flows generated by man-made structures. / Master of Science / Natural flows, such as those in our oceans and atmosphere, are seen everywhere and affect human life and structures to an amazing degree. Study of these complex flows requires special care be taken to ensure that mathematical equations correctly approximate them and that computers are programmed to correctly solve these equations. This is no different for researchers and engineers interested in studying how man-made flows, such as one generated by the wake of a plane, wind turbine, cruise ship, or sewage outflow pipe, interact with natural flows found around the world. These interactions may yield complex phenomena that may not otherwise be observed in the natural flows alone. The natural and artificial flows may also mix together, rendering it difficult to study just one of them. The multi-scale localized perturbation method is devised to aid in the simulation and study of the interactions between these natural and man-made flows. Well-known equations of fluid dynamics are modified so that the natural and man-made flows are separated and tracked independently, which gives researchers a clear view of the current state of a region of air or water all while retaining most, if not all, of the complex physics which may be of interest. Once the multi-scale localized perturbation method is derived, its mathematical equations are then translated into code for OpenFOAM, an open-source software toolkit designed to simulate fluid flows. This code is then tested by running simulations to provide a sanity check and verify that the new form of the equations of fluid dynamics have been programmed correctly, then another, more complicated simulation is run to showcase the benefits of the multi-scale localized perturbation method. This simulation shows some of the complex fluid phenomena that may be seen in nature, yet through the multi-scale localized perturbation method, it is easy to view where the man-made flows end and where the natural flows begin. The complex interactions between the natural flow and the artificial flow are retained in spite of separating the flow into two parts, and setting up the simulation is simplified by this separation. Potential uses of the multi-scale localized perturbation method include multi-scale simulations, where researchers simulate natural flow over a large area of land or ocean, then use this simulation data for a second, small-scale simulation which covers an area within the large-scale simulation. An example of this would be simulating wind currents across a continent to find a potential location for a wind turbine farm, then zooming in on that location and finding the optimal spacing for wind turbines at this location while using the large-scale simulation data to provide realistic wind conditions at many different heights above the ground. Overall, the multi-scale localized perturbation method has the potential to be a powerful tool for researchers whose interest is flows in the ocean and atmosphere, and how these natural flows interact with flows created by artificial means.

Microstructure reconstruction is a necessary tool for use in multi-scale modeling, as it allows for the analysis of the microstructure of a material without the cost of measuring all of the required data for the analysis. For microstructure reconstruction to be effective, the synthetic microstructure needs to predict what a small sample of measured data would look like on a larger domain. The Markov Random Field (MRF) algorithm is a method of generating statistically similar microstructures for this process. In this work, two key factors of the MRF algorithm are analyzed. The first factor explored is how the base features of the microstructure related to orientation and grain/phase topology information influence the selection of the MRF parameters to perform the reconstruction. The second focus is on the analysis of the numerical uncertainty (epistemic uncertainty) that arises from the use of the MRF algorithm. This is done by first removing the material uncertainty (aleatoric uncertainty), which is the noise that is inherent in the original image representing the experimental data. The epistemic uncertainty that arises from the MRF algorithm is analyzed through the study of the percentage of isolated pixels and the difference in average grain sizes between the initial image and the reconstructed image. This research mainly focuses on two different microstructures, B4C-TiB2 and Ti-7Al, which are a ceramic composite and a metallic alloy, respectively. Both of them are candidate materials for many aerospace systems owing to their desirable mechanical performance under large thermo-mechanical stresses. / Master of Science / Microstructure reconstruction is a necessary tool for use in multi-scale modeling, as it allows for the analysis of the microstructure of a material without the cost of measuring all of the required data for the analysis. For microstructure reconstruction to be effective, the synthetic microstructure needs to predict what a small sample of measured data would look like on a larger domain. The Markov Random Field (MRF) algorithm is a method of generating statistically similar microstructures for this process. In this work, two key factors of the MRF algorithm are analyzed. The first factor explored is how the base features of the microstructures related to orientation and grain/phase topology information influence the selection of the MRF parameters to perform the reconstruction. The second focus is on the analysis of the numerical uncertainty that arises from the use of the MRF algorithm. This is done by first removing the material uncertainty, which is the noise that is inherent in the original image representing the experimental data. This research mainly focuses on two different microstructures, B4C-TiB2 and Ti-7Al, which are a ceramic composite and a metallic alloy, respectively. Both of them are candidate materials for many aerospace systems owing to their desirable mechanical performance under large thermo-mechanical stresses.