<p>The resilient modulus and Poisson's ratio of granular materials used in flexible pavement structures is highly nonlinear, stress/strain path and direction-dependent. Resilient properties are very important for realistic flexible pavement design. By far, several important aspects, such as the effect of stress path, major principal stress rotation, initial stress state and inherent fabric, on the cross-anisotropic resilient properties are not fully understood. The main objective of this thesis was to study the cross-anisotropic resilient properties of granular materials along various stress paths from both initial isotropic and initial anisotropic stress states. Extensive resilient modulus stress path tests were performed for this purpose. </p> <p> In this research, the resilient behaviour of the test material for initial isotropic stress states along various stress paths was investigated first, with particular interest in the stress/strain path dependency. New resilient modulus equations were then developed, by taking into account the effect of confining pressure and resilient strains. These equations can be used to estimate the cross-anisotropic resilient modulus corresponding to initial isotropic stress states. Selection of Poisson's ratio was also investigated. </P> <p> The effect of initial stress state on the resilient responses was studied through a series of stress path tests with constant confining pressure and constant vertical stress, respectively. Based on the experimental findings, revised equations for resilient modulus and Poisson's ratio were proposed to account for the effect of ratio of initial horizontal stress to vertical stress (Kini). The proposed equations can predict the cross-anisotropic resilient properties for various stress paths corresponding to initial isotropic/anisotropic stress conditions. </p> <p> In order to provide a more comprehensive insight into the complex resilient properties of granular materials along different stress/strain paths for various initial stress states, a micromechanics approach was introduced to back-calculate the degree of fabric anisotropy. The variations of fabric with stress path, initial stress state and final stress state (i.e., state which corresponds to the peak stress during cyclic loading) were investigated. To provide a reliable prediction of initial/inherent fabric anisotropy and fabric evolution in constitutive s with embedded microstructure, an evolution law of fabric anisotropy was developed. </p> / Thesis / Doctor of Philosophy (PhD)

<p> The spectra of depolarized light scattered from Isotropic and anisotropic liquids were Investigated In order to obtain information on both the reorientational and collisional motions of the liquid molecules. </p> <p> The liquid spectra taken at 22°C on a Coderg spectrometer (1 cm. ^-1 slits) were decomposed into relaxational and collisional components using least squares fitting techniques. Integrated Intensities and depolarization ratios in the zero em -1 (1 cm ^-1= 3 x 10^10 hz.) frequency sjift region as well as in the less than 5 cm^-1 region are reported. </p> <p> The Isotropic liquid spectra from 5 cm ^-1 consisted of a narrow Lorentz and a broader coliisional component which was exponential at shifts > 10 cm^-1. The anisotropic spectra also consisted of relaxational and collisional components; however, the Integrated Intensity of the relaxational and the collisional components Increased by a factor of 20 and 10 respectively from the isotropic liquids. </p> <p> A simple model based on frame distortion Induced anisotropy was constructed to predict the relative Intensity ratios of the collisional component for both Isotropic and anisotropic liquids. </p> <p> The relaxation time of the Lorentz component was Interpreted for both isotropic and anisotropic liquids as being the average time between collisions. It was, found to vary as μ^((3/4)/p), where μ is the reduced mass of two colliding molecules and p the liquid density.</p> <p> The line width parameter 1/vo for all the collisional components was interpreted as being a measure of the duration of a collision and was found to vary as μ^1/2 independent of the density P. </p> / Thesis / Master of Science (MSc)

The texturing of ultra-high temperature ceramics (UHTCs) using weak magnetic fields is studied and developed for the first time. Textured UHTCs were prepared by magnetically assisted slip casting (MASC) in weak magnetic field (B ~ 0.5 T). Analytical calculations describing the balance of torques acting on the suspended particles suggested that texture would form at such low magnetic fields. The calculations include a novel contribution of Stokes drag arising from the inhomogeneous velocity profile of the fluid during slip casting. Experimental proof-of-concept of the theoretical calculations was successfully demonstrated. Calculations of Lotgering orientation factor (LOF) based on the intensities of the (00l) family of peaks measures by XRD revealed strong c-axis crystalline texture in TiB2 (LOF = 0.88) and ZrB2 (LOF = 0.79) along the direction of the magnetic field. Less texture was achieved in HfB2 (LOF = 0.39). In all cases, the density of the textured materials was less than that of control untextured materials, indicating that texturing hindered the densification. The findings from this work confirm the potential for more cost-effective, simple, and flexible processes to develop crystalline texture in UHTCs and other advanced ceramics and give new insight into the mechanisms of magnetic alignment of UHTCs under low magnetic fields. The microstructural evolution during slip casting and pressureless sintering is investigated. The interplay between magnetic alignment and particle packing was investigated using XRD and SEM. During MASC, the suspended particles rotate into their aligned configuration. Particles that deposit at the bottom of the mold near the plaster of Paris substrate have their alignment slightly disrupted over a ~220 μm-thick region. The aligned suspended particles lock into an aligned configuration as they consolidate, leading to a uniform degree of texturing across the entire sample height of several millimeters upon full consolidation of the particle network. If the magnetic field is removed before the particles fully consolidate, the suspended particles re-randomize their orientation. Grain size measurements done using the ASTM E112 line counting method on SEM images revealed anisotropic microstructures in green and sintered textured ZrB2 materials. Smaller effective grain sizes were observed in the direction of c-axis texture than the directions perpendicular to the texture. Grain aspect ratios of 1.20 and 1.13 were observed in materials where the c-axis texture directions were parallel (PAR) and perpendicular (PERP) to the slip casting direction, respectively. Constraint of the preferred a-axis grain growth direction in the textured materials inhibited their densification compared to the untextured material. The PERP material with the preferred grain growth direction constrained along the casting direction had smaller average grain sizes than the PAR material which contained the preferred grain growth directions in the circular plane normal to the casting direction. Compression testing suggests a trend towards higher strength and stiffness in materials with higher density. Classical catastrophic brittle failure was observed in the untextured materials, but in the textured materials some samples exhibited a multiple failure mode. The PERP material tended to exhibit superior strength and stiffness to the PAR material in the classical brittle failure mode due to the orientation of the stiffer a-axis along the loading direction and smaller average grain size in the plane normal to the loading direction in the PERP condition. In the multiple failure mode, the PAR material tended to reach higher strength values after the initial failure and reach slightly higher strains before ultimate failure due to the orientation of the compliant c-axis along the loading direction and ability of the grains elongated in the plane normal to the loading direction to rearrange themselves after initial failure(s). Regardless of density or texture condition, all ZrB2 samples survived thermal shock resistance (TSR) testing. Samples were heated to 1500°C in air, held for 30 minutes, then quenched in room temperature air. After TSR testing, oxide layers formed on the surface of the materials. The specific mass gain and oxide layer thickness tended to increase with increasing porosity and were dramatically increased when open porosity was dominant as in the CTRL 1900 condition. After TSR testing, the compressive strength and strain at failure were both higher compared to the as-sintered materials. The increases in the average compressive strength were 20%, 76%, and 57% in the CTRL, PAR, and PERP conditions, respectively. The combination of the presence of the oxide layer shifting the onset of macroscale damage to higher strain values, the dissipation of load in the more porous region near the oxide layer, and the constraining effect of the oxide layer acting against the expansion of the material contributed to reinforcement of the samples after TSR testing. The CTRL material outperformed the textured materials on average in terms of strength and stiffness due to the higher density. The results suggest that reinforcement was more effective in the PAR condition than the PERP, which may be caused by the formation of a homogenous oxide layer on the PAR while the PERP formed an anisotropic layer. The work presented in this dissertation lays the foundation for affordable, energy efficient preparation of UHTCs and other ceramic materials. Equipment costs are reduced by 3 orders of magnitude, and the operating costs and energy consumption are greatly reduced. Facilitation of the preparation of textured materials opens the door to renewed investigations into their processing and performance. This work describes in detail for the first time the relationships between processing, microstructure, and properties of a textured UHTC part, providing a model for future research. Finally, the findings in this work can be used to guide process optimization, exploration of complex shapes and microstructures, and design of manufacturing schemes to create specialty textured parts for demanding structural and functional applications. / Doctor of Philosophy / Textured ultra-high temperature ceramics (UHTCs), special materials with melting temperatures above 3000°C and potential for use in thermal protection of Mach 5+ aircraft and spacecraft, were prepared by magnetically assisted slip casting (MASC) in a weak magnetic field for the first time. The magnetic field was supplied by commercially available permanent magnets which was applied to a liquid-like slurry with UHTC particles floating in it to orient the UHTC particles with their c-crystal axis along the magnetic field direction. Calculations which described the balance of rotational forces acting to align or misalign the suspended particles suggested that the UHTC particles would align in the weak magnetic field. This prediction was realized. After the liquid in the slurry was removed during MASC to leave behind an aligned particle network, the samples were densified by heating in the absence of air to 2100°C for one hour. In titanium diboride (TiB2) and zirconium diboride (ZrB2), two of the most relevant UHTC materials, strong texture was achieved; 88% and 79% of the crystals in the material were aligned along the original magnetic field direction. This is the first time that this has been reported in the scientific literature. In hafnium diboride (HfB2), only 39% of the grains were aligned. The textured materials all had lower density than the untextured materials prepared alongside them using conventional slip casting. The relationship between magnetic alignment and particle packing was investigated by observing the microstructure. During MASC, the suspended particles rotate into their aligned configuration. Particles that deposit at the bottom of the mold near the plaster of Paris substrate have their alignment slightly disrupted over a ~220 μm-thick region. The aligned suspended particles lock into an aligned configuration as they consolidate, leading to a uniform degree of texturing over across the entire sample height of several millimeters upon full consolidation of the particle network. If the magnetic field is removed before the particles fully consolidate, the suspended particles re-randomize their orientation. The findings from this work confirm the potential for more cost-effective, simple, and flexible processes to develop crystalline texture in UHTCs and other advanced ceramics and give new insight into the mechanisms of magnetic alignment of UHTCs under low magnetic fields. Because of the magnetic alignment of the particles, it is expected that the microstructure would show some difference along and across the direction that the alignment formed along the applied magnetic field. In order to determine that, the size of the grains (particles joined to each other during densification) in the materials are measured along different directions in the sample chosen for their orientational relationship to the magnetic field and casting directions. Smaller effective grain sizes were observed along the direction of magnetically aligned crystalline texture than the directions perpendicular to the texture. Because of how the crystal axes of the particles are aligned, there are differences in how the particles join each other during densification, and that results in an anisotropic microstructure where different grain sizes as a function of the magnetic field direction and the texture direction. Compression testing conducted by squeezing the samples at a fixed rate suggests a trend that indicates the samples are stronger and stiffer when the density is higher, as expected. Untextured samples abruptly failed after reaching their maximum strength value in a manner typical of brittle ceramics. Some textured samples failed in this way, but some failed at low strength values then climbed back up in strength repeatedly until they eventually gave out completely, in a crumbly mode. In the classical brittle failure mode, the PERP material with c-axis texture aligned along the sample diameter, perpendicular to the loading direction, tended to exhibit superior strength and stiffness to the PAR material with c-axis texture oriented along the height and loading directions of the sample because the stiffer crystal axis was oriented along the loading direction and the average grain size seen by the load head was smaller. In the crumbly mode, the PAR material tended to reach higher strength values after initial failure and ultimately fail later in a crumblier mode because the more compliant crystal axis was oriented along the loading direction and the grains elongated in the plane perpendicular to the loading direction could rearrange themselves better after initial failure(s) to bear more load. Regardless of density or texture condition, all ZrB2 samples survived thermal shock resistance (TSR) testing, meaning that the samples remained fully intact after experiencing a big difference in temperature in very short time. Samples were heated in a furnace to 1500°C in air, held for 30 minutes, removed from the furnace, and cooled in air. After TSR testing, the samples developed an oxide layer on the outside, in a similar manner to rust forming on a piece of metal. How much it oxidized per unit area and how thick that oxide layer was increased with increasing porosity. These quantities increased dramatically when the pores connected the interior of the sample to the outside, as in the CTRL 1900 condition. After TSR testing, the samples were stronger by 20%, 76%, and 57% in the CTRL, PAR, and PERP conditions, respectively, indicating that the oxide layer was responsible for an enhancement in strength. The results suggest that increase of strength of the oxide layer was more effective in the PAR condition than the PERP, which is believed to be caused by the formation of a homogenous oxide layer on the PAR while the PERP formed an anisotropic layer. The work presented in this dissertation reduces the start-up equipment costs associated with magnetic alignment processes by 1000 times and lays the foundation for affordable, energy efficient preparation of UHTCs and other ceramic materials. The simplicity of this technique makes it easier for future researchers to study textured materials. This work describes in detail for the first time the relationships between processing, microstructure, and properties of a textured UHTC part, providing a model for future research. Finally, the findings in this work can be used to guide process optimization, exploration of complex shapes and microstructures, and design of manufacturing schemes to create specialty textured parts for demanding applications.

In this work, understanding the microstructural effects of monotonic and cyclic failure of wrought 7075-T651 and cast A356 aluminum alloys were examined. In particular, the structure-property relations were quantified for the plasticity/damage model and two fatigue crack models. Several types of experiments were employed to adapt an internal state variable plasticity and damage model to the wrought alloy. The damage model was originally developed for cast alloys and thus, the model was modified to account for void nucleation, growth, and coalescence for a wrought alloy. In addition, fatigue experiments were employed to determine structure-property relations for the cast alloy. Based on microstructural analysis of the fracture surfaces, modifications to the microstructurally-based MultiStage fatigue model were implemented. Additionally, experimental fatigue crack results were used to calibrate FASTRAN, a fatigue life prediction code, to small fatigue-crack-growth behavior. Lastly, a set of experiments were employed to explore the damage history effect associated with cast and wrought alloys and to provide motivation for monotonic and fatigue modeling efforts.

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This dissertation proposes a new framework to characterize the nonlinear behavior of anisotropic materials in an on-line manner. The proposed framework applies recursive estimation and a multi-linear model to characterize the nonlinear behavior of anisotropic materials on-line using full-field strains, which are capable of capturing the multi-axial information of anisotropic materials. A stochastic method is developed to characterize the linear behavior of anisotropic materials under the influence of full-field strain measurement noise. This method first derives stochastic equations based on the formulas of energy-based characterization that utilizes the principle of ener-gy conservation, and then recursively estimates elastic constants at every acquisition of measure-ment using a Kalman filter (KF). Since the measurement model is expressed nonlinearly, the KF utilizes a Kalman gain, which is newly derived in this dissertation through variance minimization, to achieve optimal characterization. The aforementioned method, namely stochastic linear characteri-zation in this dissertation, becomes a basis of the multi-linear characterization method. This method utilizes a multi-linear model, which is defined by partitions, to characterize the nonlinear constitu-tive relations. The multi-linear characterization scales up the number of estimates and identifies the coefficients of each linear partition using the previously derived KF. The recursive updates in measurements not only removes uncertainty through sensor measurements, but also enables the on-line capability of the nonlinear characterization of anisotropic materials. A series of numerical and experimental studies were performed to demonstrate the performance of the proposed framework in characterizing the nonlinear behavior of anisotropic materials. The validity and applicability of the proposed framework were confirmed by the comparison with the known values of the characterized constitutive relations. It was found that the proposed framework identified elastic constants that were in good agreement with known values irrespective of the spec-imen geometry. The results of the multi-linear characterization method were well correlated with known nonlinear stress-strain relations and concluded that the proposed framework is capable of characterizing adequate nonlinear behavior on-line. / Ph. D.