Using experimental data obtained from standard fracture test configurations, theoretical and numerical tools are developed to mathematically describe non-self-similar progression of cracks without specifying an initial crack. A cohesive-decohesive zone model, similar to the cohesive zone model known in the fracture mechanics literature as the Dugdale-Barenblatt model, is adopted to represent the degradation of the material ahead of the crack tip. This model unifies strength-based crack initiation and fracture-mechanics-based crack progression. The cohesive-decohesive zone model is implemented with an interfacial surface material that consists of an upper and a lower surface that are connected by a continuous distribution of normal and tangential nonlinear elastic springs that act to resist either Mode I opening, Mode II sliding, Mode III sliding, or a mixed mode. The initiation of fracture is determined by the interfacial strength and the progression of the crack is determined by the critical energy release rate. The adhesive is idealized with an interfacial surface material to predict interfacial fracture. The interfacial surface material is positioned within the bulk material to predict discrete cohesive cracks. The interfacial surface material is implemented through an interface element, which is incorporated in ABAQUS using the user defined element (UEL) option. A procedure is established to formulate a rate dependent model based on experiments carried out on compact tension test specimens. The rate dependent model is incorporated into the interface element approach to capture the unstable crack growth observed in experiments under quasi-static loading conditions. The compact tension test gives the variation of the fracture toughness with the rate of loading, this information is processed and a relationship between the fracture toughness and the rate of the opening displacement is established. The cohesive-decohesive zone model is implemented through a material model to be used in an explicit code (LS-DYNA). Dynamic simulations of the standard test configurations for Mode I (Double Cantilever Beam) and Mode II (End Load Split) are carried out using the explicit code. Verification of these coupon tests leads to the crash analysis of realistic structures like the square composite tube. Analyses of bonded and unbonded square tubes are presented. These tubes shows a very uncharacteristic failure mode: the composite material disintegrates on impact, and this has been captured in the analysis. Disadvantages of the interface element approach are well documented in the literature. An alternative method, known as the Extended Finite Element Method (XFEM), is implemented here through an eight-noded quadrilateral plane strain element. The method, based on the partition-of-unity, is used to study simple test configuration like the three-point bend problem and a double cantilever beam. Functionally graded materials are also simulated and the results are compared to the experimental results available in the literature. / Ph. D.

The coatings produced by an atmospheric plasma spray process (APSP) must be of uniform quality. However, the complexity of the process and the random introduction of noise variables such as fluctuations in the powder injection rate and the arc voltage make it difficult to control the coating quality that has been shown to depend upon mean values of powder particles' temperature and speed, collectively called mean particles' states (MPSs), just before they impact the substrate. Here we use a science-based methodology to develop an adaptive controller for achieving consistent MPSs. We first identify inputs into the APSP that significantly affect the MPSs, and then formulate a relationship between these two quantities. When the MPSs deviate from their desired values, the adaptive controller based on the model reference adaptive controller (MRAC) framework is shown to successfully adjust the input parameters to correct them. The performance of the controller is tested via numerical experiments using the software, LAVA-P, that has been shown to well simulate the APSP. The developed adaptive process controller is further refined by using sigma (σ) adaptive laws and including a low-pass filter that remove high-frequency oscillations in the output. The utility of the MRAC controller to achieve desired locations of NiCrAlY and zirconia powder particles for generating a 5-layered coating is demonstrated. In this case a pure NiCrAlY layer bonds to the substrate and a pure zirconia makes the coating top. The composition of the intermediate 3 layers is combination of the two powders of different mass fractions. By increasing the number of intermediate layers, one can achieve a continuous through-the-thickness variation of the coating composition and fabricate a functionally graded coating. / Doctor of Philosophy / Canned food sold in a grocery store have cans' interior surface coating with a polymer to increase the shelf life of the food. Similarly, many parts in an automobile have coatings to protect them from corrosion and possibly wear and tear. A process used to produce these coatings is rather complex and involves several variables. An undesired change these variables affects the coating quality. Automatically controlling a coating process is like a cruise control in a car. It should detect which variables have changed and either take appropriate corrective actions or shut down the process if it cannot be corrected or alert an operator to stop the process. In this work we have developed a controller to adaptively adjust the input parameters for an atmospheric plasma spray process (APSP) often used to produce thermal barrier coatings in gas turbines and blades of aircraft jet engines. These coatings hinder the flow of heat from the hot exhaust gases to the blades thereby prolonging their life span.

The goal of this research was to create a microstructure graded glass-ceramic and investigate the resulting properties as a function of crystallization processing. The desired glass-ceramic was a lithium disilicate material that has a crystallization gradient across the sample, leading to functionally graded properties as a result of the microstructure gradient. Samples were prepared by melting and pouring glass at 1400°C, annealing at 400°C for 48 hours, and nucleating at 480°C for 2 hours. To ensure that crystallization would not occur homogeneously throughout the sample, a temperature gradient was imposed during crystallization. Samples were crystallized on a self-constructed resistance wire furnace that was open to air. Several crystallization processing parameters were tested, including high temperature for a short time and low temperature for a long time. Samples were ground and polished to 0.25 microns before characterization methods were performed. Scanning electron microscopy (SEM) showed the microstructure transition across the sample cross section, with crystals present on the crystalline side and only nuclei present on the glassy side. Raman spectroscopy showed a transformation of the characteristic spectra across the sample cross section, with defined, high-intensity peaks on the crystalline side and broad, low-intensity peaks on the glassy side. Microhardness showed a slight transition in hardness values across the sample cross section, however the variability was too great to draw any conclusions. The characterization methods showed that the desired material was created and the resulting properties were a function of the crystallization processing parameters. / Master of Science

Curved beams such as arches find ubiquitous applications in civil, mechanical and aerospace engineering, e.g., stiffened floors, fuselage, railway compartments, and wind turbine blades. The analysis of free vibrations of curved structures plays a critical role in their design to avoid transient loads with dominant frequencies close to their natural frequencies. One way to increase their areas of applications and possibly make them lighter without sacrificing strength is to make them of Functionally Graded Materials (FGMs) that are composites with continuously varying material properties in one or more directions. In this thesis, we study free vibrations of FGM circular beams by using a logarithmic shear deformation theory that incorporates through-the-thickness logarithmic variation of the circumferential displacement, and does not require a shear correction factor. The radial displacement of a point is assumed to depend only upon its angular position. Thus the beam theory can be regarded as a generalization of the Timoshenko beam theory. Equations governing transient deformations of the beam are derived by using Hamilton's principle. Assuming a time harmonic variation of the displacements, and by utilizing the generalized differential quadrature method (GDQM) the free vibration problem is reduced to solving an algebraic eigenvalue problem whose solution provides frequencies and the corresponding mode shapes. Results are presented for different spatial variations of the material properties, boundary conditions, and the aspect ratio. It is found that the radial and the circumferential gradation of material properties maintains their natural frequency within that of the homogeneous beam comprised of a constituent of the FGM beam. Furthermore, keeping every other variable fixed, the change in the beam opening angle results in very close frequencies of the first two modes of vibration, a phenomenon usually called mode transition. / Master of Science / Curved and straight beams of various cross-sections are one of the simplest and most fundamental structural elements that have been extensively studied because of their ubiquitous applications in civil, mechanical, biomedical and aerospace engineering. Many attempts have been made to enhance their material properties and designs for applications in harsh environments and reduce weight. One way of accomplishing this is to combine layerwise two or more distinct materials and take advantage of their directional properties. It results in a lightweight structure having overall specific strength superior to that of its constituents. Another possibility is to have volume fractions of two or more constituents gradually vary throughout the structure for enhancing its performance under anticipated applications. Functionally graded materials (FGMs) are a class of composites whose properties gradually vary along one or more space directions. In this thesis, we have numerically studied free vibrations of FGM circular beams to enhance their application domain and possibly use them for energy harvesting.

A key advantage of Additive Manufacturing (AM) is the opportunity to design and fabricate complex structures that cannot be made via traditional means. However, this potential is significantly constrained by the use of a facet-based geometry representation (e.g., the STL and the AMF file formats); which do not contain any volumetric information and often, designing/slicing/printing complex geometries exceeds the computational power available to the designer and the AM system itself. To enable efficient design and fabrication of complex/multi-material complex structures, several algorithms are presented that represent and process solid models as a set of voxels (three-dimensional pixels). Through this, one is able to efficiently realize parts featuring complex geometries and functionally graded materials. This thesis specifically aims to explore applications in three distinct fields namely, (i) Design for AM, (ii) Design for Manufacturing (DFM) education, and (iii) Reverse engineering from imaging data wherein voxel-based representations have proven to be superior to the traditional AM digital workflow. The advantages demonstrated in this study cannot be easily achieved using traditional AM workflows, and hence this work emphasizes the need for development of new voxel based frameworks and systems to fully utilize the capabilities of AM. / MS / Additive Manufacturing(AM) (also referred to as 3D Printing) is a process by which 3D objects are constructed by successively forming one-part cross-section at a time. Typically, the input file format for most AM systems is in the form of surface representation format (most commonly. STL file format). A STL file is a triangular representation of a 3-dimensional surface geometry where the part surface is broken down logically into a series of small triangles (facets). A key advantage of Additive Manufacturing is the opportunity to design and fabricate complex structures that cannot be made easily via traditional manufacturing techniques. However, this potential is significantly constrained by the use of a facet-based (triangular) geometry representation (e.g., the STL file format described above); which does not contain any volumetric (for e.g. material, texture, color etc.) information. Also, often, designing/slicing/printing complex geometries using these file formats can be computationally expensive. To enable more efficient design and fabrication of complex/multi-material structures, several algorithms are presented that represent and process solid models as a set of voxels (three-dimensional pixels). A voxel represents the smallest representable element of volume. For binary voxel model, a value of ‘1’ means that voxel is ‘on’ and value of 0 means voxel is ‘off’. Through this, one is able to efficiently realize parts featuring complex geometries with multiple materials. This thesis specifically aims to explore applications in three distinct fields namely, (i) Design for AM, (ii) Design for Manufacturing (DFM) education, and (iii) Fabricating models (Reverse engineering) directly from imaging data. In the first part of the thesis, a software tool is developed for automated manufacturability analysis of a part that is to be produced by AM. Through a series of simple computations, the tool provides feedback on infeasible features, amount of support material, optimum orientation and manufacturing time for fabricating the part. The results from this tool were successfully validated using a simple case study and comparison with an existing pre-processing AM software. Next, the above developed software tool is implemented for teaching instruction in a sophomore undergraduate classroom to improve students’ understanding of design constraints in Additive Manufacturing. Assessments are conducted to measure students’ understanding of a variety of topics in manufacturability both before and after the study to measure the effectiveness of this approach. The third and final part of this thesis aims to explore fabrication of models directly from medical imaging data (like CT Scan and MRI). A novel framework is proposed which is validated by fabricating three distinct medical models: a mouse skull, a partial human skull and a horse leg directly from corresponding CT Scan data. The advantages demonstrated in this thesis cannot be easily achieved using traditional AM workflows, and hence this work emphasizes the need for development of new voxel based frameworks and systems to fully utilize the capabilities of AM.

Functionally graded structures have material properties that continuously vary in one or more directions. Examples include human teeth, seashells, bamboo stems and human organs, where the varying volume fraction of fibers and their orientations optimize functionality. Deformations of such structures typically involve bending, stretching, and shearing. An everyday example of shearing deformation is the twisting of wet fabrics to extract water. In this study, we analytically examine the large deformations of functionally graded Mooney-Rivlin circular cylinders, focusing on how radial grading of material moduli can be beneficially utilized. We investigate the finite deformations caused by pressures applied to the bounding surfaces and axial loads or twisting moments on the end faces. We also simulate residual stresses in a hollow cylinder either by inverting it inside out or by closing a longitudinal wedge opening parallel to the cylinder axis through axisymmetric deformation before other loads are applied. It is observed that the maximum shear stress in an initially stress-free Mooney-Rivlin cylinder can occur at an interior point. In the absence of axial forces on the end faces, the cylinder elongates when twisted, with the degree of elongation depending on the grading of the material moduli. These findings should aid numerical analysts in verifying their algorithms for simulating large deformations of rubber-like materials modeled by the Mooney-Rivlin relation. / Master of Science / Functionally graded materials (FGMs) are composites whose properties vary in one or more directions to exploit the functionality of the individual components. An example would be a sheet of material that is fully metallic on one side and fully ceramic on the other, with properties changing gradually through the thickness. The Mooney-Rivlin model is used to capture the stress-strain response of rubber-like materials. Therefore, functionally graded Mooney-Rivlin cylinders are rubber-like composite cylinders whose properties change throughout their thickness. Functionally graded cylinders have a wide array of applications, including in pressure vessels, vibration damping systems and tires. Therefore, having a thorough understanding of the stresses induced in these cylinders when subjected to loads is essential for safe and reliable designs. This research aims to investigate the effects of material inhomogeneity on the stresses induced in functionally graded cylinders subjected to torsion, radial expansion, eversion, and various combinations of these. Furthermore, realizing that stresses induced during the fabrication process cannot be easily quantified, we study a problem in which these induced stresses can be determined and analyze their effect on subsequent deformations of the cylinder when subjected to torsion and radial expansion. To achieve this aim, we use a member of Ericksen's third family of universal deformations, which mathematically describes torsion, inflation, and eversion, along with the Mooney-Rivlin model to determine the stress state resulting from deformation. The results show that for cylinders of the same geometry in the stress-free undeformed state subjected to identical surface tractions, material inhomogeneities greatly influence the stresses in the cylinder. It was also found that the magnitude of the normal and shear stresses, axial stretch, and the geometry of the cylinder after deformation depend on the type of deformation and functional grading. Additionally, the results indicate that the normal stresses induced in an initially stressed cylinder are much greater than those in a cylinder that is initially stress-free when subjected to the same boundary conditions.

Total Hip Arthroplasty (THA) is an orthopaedic procedure that is performed to reduce pain and restore the functionality of hip joints that are affected by degenerative diseases. The outcomes of THA are generally good. However, the stress shielding of the periprosthetic femur is a factor that can contribute towards the premature loosening of the femoral stem. In order to improve the stress shielding characteristics of metallic femoral stems, stiffness configurations that offer more flexibility should be considered. This research has investigated the potential of more flexible and lightweight cobalt chromium molybdenum (CoCrMo) femoral stems that can be manufactured using Selective Laser Melting (SLM). Square pore cellular structures with compressive properties that are similar to human bone have been presented and incorporated into femoral stems by utilising fully porous and functionally graded designs. A three dimensional finite element model has been developed to investigate and compare the load transfer to the periprosthetic femur when implanted with femoral stems offering different stiffness configurations. It was shown that the load transfer was improved when the properties of the square pore cellular structures were incorporated into the femoral stem designs. Factors affecting the manufacturability and production of laser melted femoral stems have been investigated. A femoral stem design has been proposed for cemented or cementless fixation. Physical testing has shown that a functionally graded stem can be repeatedly manufactured using SLM, which was 48% lighter and 60% more flexible than a traditional CoCrMo prosthesis. The research presented in this thesis has provided an early indication of utilising SLM to manufacture lightweight CoCrMo femoral stems with levels of flexibility that have the potential to reduce stress shielding in the periprosthetic femur.

O objetivo deste trabalho é controlar a incidência de fissuras em fibrocimentos aplicando o conceito de materiais com gradação funcional através da protensão química gerada pela aplicação de silicato de sódio alcalino entre as camadas dos fibrocimentos. Atualmente é bastante comum os fibrocimentos apresentarem fissuras ao longo das bordas devido aos gradientes de umidade gerados durante a estocagem das pilhas de telhas no pátio das indústrias. O potencial da protensão química foi avaliado através da porosidade total, da quantificação das fases hidratadas, da retração por secagem e do desempenho mecânico. A aplicação de silicato de sódio alcalino no ligante CPII F provocou retração por secagem 1,5 vezes maior que a referência aos 91 dias. O módulo de ruptura (MOR) não sofreu alteração, mas o limite de proporcionalidade da matriz (LOP) aumentou em torno de 95%. O módulo de elasticidade dinâmico foi 13 % maior. O aumento da retração por secagem e o ganho de desempenho mecânico apontam o potencial da protensão química para o controle da fissuração em fibrocimentos produzidos pelo processo Hatschek. / The objective of this work is controlling the incidence of cracks in fiber cement, using the concept of functionally graded materials through the chemical prestressing, generated by application of alkaline sodium silicate among fiber cement layers. Currently, its very common the fiber cements present cracks along the edges due to moisture gradients, caused during storage of piles of tiles in the courtyard of the industry. The chemical prestressing potential was evaluated through of the total porosity, the quantification of hydrate phases, the drying shrinkage and the mechanical performance. The application of alkaline sodium silicate in the cement CPII F caused drying shrinkage 1,5 times greater than the reference to 91 days. The modulus of rupture (MOR) didnt suffer change, but the proportional limit of matrix (LOP) increased by around 95%. The dynamic modulus of elasticity was 13% higher. The increase of drying shrinkage and the mechanical performance gain indicate the chemical prestressing potential to control the cracking in fiber cement produced by the process Hatschek.

The properties of composite materials in which spherical inclusions are embedded in a matrix of some kind, have been studied for many decades and many analytical models have been developed which measure these properties. There has been a steady progression in the complexity of models over the years, providing greater insight into the nature of these materials and improving the accuracy in the measurement of their properties. Some of the properties with which this thesis is concerned are, the elastic, thermal and electrical properties of such composites. The size of the spherical inclusion which acts as the reinforcing phase, has a major effect on the overall properties of composite materials. Once an inclusion is embedded into a matrix, a third region of different properties between the inclusion and matrix is known to develop which is called the interphase. It is well known in the composite community that the smaller the inclusion is, the larger the interphase region which develops around it. Therefore, with the introduction of nanoparticles as the preferred reinforcing phase for some composites, the interphase has a major effect on its properties. It is the aim of this thesis to consider the role of the interphase on the properties of composites by modeling it as an inhomogeneous region. There is much scientific evidence to support the fact that the interphase has an inhomogeneous nature and many papers throughout the thesis are cited which highlight this. By modeling the inhomogeneous properties by arbitrary mathematical functions, results are obtained for the various properties in terms of these general functions. Some specific profiles for the inhomogeneous region are considered for each property in order to demonstrate and test the models against some established results.

In this study the plane linear elastic problem of a functionally graded layer which contains periodic cracks is considered. The main objective of this study is to determine the thermal stress intensity factors for edge cracks. In order to find an analytic solution, Young&rsquo / s modulus and thermal conductivity are assumed to be varying exponentially across the thickness, whereas Poisson ratio and thermal diffusivity are taken as constant. First, one dimensional transient and steady state conduction problems are solved (heat flux being across the thickness) to determine the temperature distribution and the thermal stresses in a crack free layer. Then, the thermal stress distributions at the locations of the cracks are applied as crack surface tractions in the elasticity problem to find the stress intensity factors. By defining an appropriate auxiliary variable, elasticity problem is reduced to a singular integral equation, which is solved numerically. The influence of such parameters as the grading, crack length and crack period on the stress intensity factors is investigated.