The main objective of this study is to evaluate mixed mode stress intensity factors for inclined embedded cracks in functionally graded materials. Fracture analysis of inclined cracks requires the calculation of both Mode I and Mode II stress intensity factors ( I K , II K ). In this study, k J -integral is used to calculate I K and II K . Equivalent domain integral approach is utilized to evaluate the k J - integral around the crack tip. The present study aims at developing a finite element model to study inclined crack problems in graded media under thermomechanical loading. A two dimensional finite element model is developed for inclined cracks located in a functionally graded medium. Structural and thermal problems are solved using two dimensional finite elements namely 8- noded triangles. Material properties are sampled directly at the integration points of the elements, as required by the numerical integral evaluation. The main results of the study are the stress intensity factors at the crack tip for functionally graded materials subjected to thermomechanical loading.

In this thesis, the Generalized Finite Difference (GFD) method is applied to analyze the elastoplastic deformation behavior of a long functionally graded (FGM) tube subjected to internal pressure. First, the method is explained in detail by considering the elastic response of a rotating FGM tube. Then, the pressurized tube problem is treated. A long FGM tube with fixed ends (axially constrained ends) is taken into consideration. The two cases in which the modulus of elasticity only and both the modulus of elasticity and the yield limit are graded properties are analyzed. The plastic model here is based on incremental theory of plasticity, Tresca&#039 / s yield criterion and its associated flow rule. The numerical results are compared to those of analytical ones. Furthermore, the elastic response of an FGM tube with free ends is studied considering graded modulus of elasticity and Poisson&#039 / s ratio. The results of these computations are compared to those of Shooting solutions. In the light of analyses and comparisons stated above, the applicability of the GFD method to the solution of similar problems is discussed. It is observed that, in purely elastic deformations the accuracy of the method is sufficient. However, in case of elastic-plastic deformations, the discrepancies between numerical and analytical results may increase in determining plastic displacements. It is also noteworthy that the predictions for tubes with two graded properties, i. e. the modulus of elasticity and the yield limit, turn out to be better than those with one graded property in this regard.

In this study, it is aimed to investigate the mixed-mode fracture behavior of orthotropic functionally graded material (FGM) coatings bonded to a homogeneous substrate through a homogeneous bond-coat. Analytical and computational methods are used to solve the embedded cracking problems under mechanical or thermal loading conditions. It is assumed that the material property gradation of the FGM coating is in the thickness direction and cracks are parallel to the boundaries. The principal axes of orthotropy are parallel and perpendicular to the boundaries. A single embedded crack in the orthotropic FGM coating is investigated analytically assuming that crack surfaces are subjected to either uniform normal or uniform shear stresses. Using Fourier transformations, the problem is reduced to a couple of singular integral equations that are solved numerically to obtain the mixed-mode stress intensity factors, energy release rate and crack opening displacements. To investigate the analytically untractable problems without restrictive assumptions, a computational approach is employed. The adopted computational approach is based on finite element method and displacement correlation technique. Using the computational approach, fracture parameters are obtained considering single and periodic embedded cracking conditions in the orthotropic FGM coatings under mechanical or thermal loads. The results obtained in this study show the effects of material nonhomogeneity, material orthotropy and geometric variables on the fracture behavior of the structure.

An elastic FGM layer bonded to a semi-infinite linear elastic, isotropic, homogeneous half plane is considered. The half plane contains periodic cracks perpendicular to the interface. Mechanical loading is applied through crack surface pressure, resulting in a mode I crack problem. The plane elasticity problem described above is formulated by using Fourier transforms and Fourier series. A singular integral equation is obtained for the auxiliary variable, namely derivative of the crack surface displacement. Solution is obtained, and stress intensity factors are calculated for various values of crack period, crack length, crack location, layer thickness and material gradation.

The preliminary goal of this study is to determine the effects of processing conditions, compositions and microstructural morphologies of the constituents on the physical and thermo-mechanical properties of alumina (Al_2O_3) reinforced aluminum (Al) composites. Composites with 0, 5, 10, 20 and 25 vol% Al_2O_3 were manufactured using powder metallurgy method. The elastic properties (Young's and shear modulus) and the coefficient of thermal expansion (CTE) of the composites were determined using Resonant Ultrasound Spectroscopy (RUS) and Thermo Mechanical Analyzer (TMA) respectively at various temperatures. Increasing compacting pressure improved relative density (or lowered porosity) of the composites. Furthermore, increasing the Al_2O_3 vol% in the composite increased the elastic moduli and reduced the CTE of the composites. Increasing the testing temperature from 25 to 450 oC, significantly reduced the elastic moduli of the composites, while the CTE of the composites changed only slightly with temperatures. Secondly, the goal of this study is to determine the effect of microstructures on the effective thermo-mechanical properties of the manufactured Al-Al_2O_3 composites using finite element (FE) method. Software OOF was used to convert the SEM micrographs of the manufactured composites to FE meshed models, which were then used to determine the effective elastic modulus and CTE. It was observed that, effective modulus dropped by 19.7% when porosity increased by 2.3%; while the effective CTE was mildly affected by the porosity. Additionally, the effect of residual stress on the effective thermo-mechanical properties was studied, and the stress free temperature of the composites was determined. Another objective of this study is to examine the stress-strain response of Al-Al_2O_3 composites due to compressive loads at various temperatures. Elastic modulus, yield stress and strain hardening parameters were determined from the stress-strain curves and their dependency on temperature, porosity and volume fraction were studied. The experimental results were compared with the numerical results. It was observed that high-localized stresses were present near the pores and at the interfaces between Al and Al_2O_3 constituents. Finally, functionally graded materials (FGMs) with varying Al_2O_3 concentration (0, 5and 10 vol%) in Al were manufactured; and their stress-strain response and CTE were determined at various temperatures.

The focus of this dissertation is on the development of an additive manufacturing system and methodology for fabricating structures with functionally graded porous internal properties and complex three-dimensional external characteristics. For this purpose, a multi-scale three-dimensional printing system was developed, with capabilities and fabrication methodologies refined in the context of, but not limited to, manufacturing of porous bone substitutes. Porous bone implants are functionally graded structures, where internally, the design requires a gradient in porosity and mechanical properties matching the functional transition between cortical and cancellous bone regions. Geometrically, the three-dimensional shape of the design must adhere to the anatomical shape of the bone tissue being replaced. In this work, control over functionally graded porous properties was achieved by integrating specialized modules in a custom-made additive manufacturing system and studying their effect on fabricated constructs. Heterogeneous porous properties were controlled by: (i) using a micro-syringe deposition module capable of embedding sacrificial elements with a controlled feature size within the structure, (ii) controlling the amount of binder dispersed onto the powder substrate using a piezoelectric printhead, (iii) controlling the powder type or size in real-time, and/or (iv) selecting the print layer stacking orientation within the part. Characterization methods included differential scanning calorimetry (DSC)-thermo gravimetric analysis (TGA) to establish the thermal decomposition of sacrificial elements, X-ray diffraction (XRD) and dispersive X-ray spectroscopy (EDAX) to investigate the chemical composition and crystallinity, scanning electron microscopy (SEM) and optical microscopy to investigate the physical and structural properties, uniaxial mechanical loading to establish compressive strength characteristics, and porosity measurements to determine the bulk properties of the material. These studies showed that the developed system was successful in manufacturing embedded interconnected features in the range of 100-500 $ \mu m $, with a significant impact on structural properties resulting in bulk porosities in the range of 30-55% and compressive strength between 2-50 MPa. In this work, control over the the three-dimensional shape of the construct was established iteratively, by using a silhouette extraction image processing technique to determine the appropriate anisotropic compensation factors necessary to offset the effects of shrinkage in complex-shaped parts during thermal annealing. Overall shape deviations in the range of +/- 5-7 % were achieved in the second iteration for a femoral condyle implant in a sheep model. The newly developed multi-scale 3DP system and associated fabrication methodology was concluded to have great potential in manufacturing structures with functionally graded properties and complex shape characteristics.

Functionally graded materials processed by the thermal spray techniques such as electron beam physical vapor deposition and plasma spray forming are known to have an orthotropic structure with reduced mechanical properties. Debonding related failures in these types of material systems occur due to embedded cracks that are perpendicular to the direction of the material property gradation. These cracks are inherently under mixed-mode loading and fracture analysis requires the extraction of the modes I and II stress intensity factors. The present study aims at developing semi-analytical techniques to study embedded crack problems in graded orthotropic media under various boundary conditions. The cracks are assumed to be aligned parallel to one of the principal axes of orthotropy. The problems are formulated using the averaged constants of plane orthotropic elasticity and reduced to two coupled integral equations with Cauchy type dominant singularities. The equations are solved numerically by adopting an expansion - collocation technique. The main results of the analyses are the mixed mode stress intensity factors and the energy release rate as functions of the material nonhomogeneity and orthotropy parameters. The effects of the boundary conditions on the mentioned fracture parameters are also duly discussed.

The objective of this study is to develop crack growth analysis methods for functionally graded materials under mode I cyclic loading by using finite element technique. The study starts with the analysis of test specimens which are given in ASTM standard E399. The material properties of specimens are assumed to be changing along the thickness direction according to a presumed variation function used for the modeling of functionally graded materials. The results of the study reveal the influence of different material variation functions on the crack growth behavior. In the second part, the growth of an elliptical crack which is a common case in engineering applications is analyzed. First, mode I cycling loading is applied perpendicular to the crack plane and crack growth profiles for a certain number of cycles are obtained for homogeneous materials. Then, the code is extended for the analysis functionally graded materials. The material properties are assumed to vary as an exponential function along the major or minor axis direction of the crack. The results can be used to examine the crack profile and material constants&rsquo / influence for a certain number of cyclic loading.

Submitted by DAYANA CAMPANELLI DE MORAIS null (dayanacampanelli@gmail.com) on 2017-12-22T03:50:36Z No. of bitstreams: 1 para impressão final.pdf: 3931660 bytes, checksum: d52b37974d258d1d9c1647f7cca67f54 (MD5) / Approved for entry into archive by Silvana Alvarez null (silvana@ict.unesp.br) on 2018-01-04T18:53:29Z (GMT) No. of bitstreams: 1 morais_dc_me_sjc.pdf: 3931660 bytes, checksum: d52b37974d258d1d9c1647f7cca67f54 (MD5) / Made available in DSpace on 2018-01-04T18:53:29Z (GMT). No. of bitstreams: 1 morais_dc_me_sjc.pdf: 3931660 bytes, checksum: d52b37974d258d1d9c1647f7cca67f54 (MD5) Previous issue date: 2017-11-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O presente estudo teve como objetivo desenvolver vitrocerâmicas de dissilicato de lítio com gradiente funcional de densidade, inspirado no gradiente natural que existe entre o esmalte e a dentina. Primeiramente o vidro de composição: 33,33% mol de Li2O e 66,67% mol de SiO2 foi obtido pelo método fusão/resfriamento. Em seguida foram preparadas amostras com estruturas homogêneas do vidro a base de dissilicato de lítio para determinação dos melhores parâmetros de sinterização. Três diferentes tratamentos térmicos, determinados com base no resultado da análise diferencial de calorimetria foram utilizados: 850 °C/3h; 900 °C/3h e 950 °C/3h. A caracterização desses materiais foi realizada através da difração de raios X, microscopia eletrônica de varredura, método de Arquimedes e ensaio de flexão biaxial (n=10). O tratamento térmico de 950 oC obteve os melhores resultados, sendo o escolhido para a realização das próximas etapas do estudo. Com a finalidade de otimizar a estética, foi adicionada cerâmica feldspática (VITAVM®9) ao vidro SiO2-Li2O na proporção de 10%, 15% e 20% (n=30). Foi observado que a adição de 10% de VM9 não alterou a resistência do material, e quanto maior a quantidade de VM9, maior foi a translucidez e menor foram o módulo elástico e a densidade. Com isso, foram preparadas vitrocerâmicas bioinspiradas com gradiente funcional de densidade nas seguintes sequências de camadas: uma com 10% de VM9, outra com 15% e a última com 20%. Não houve diferença na resistência à flexão biaxial do grupo com gradiente, quando a camada mais densa estava voltada para o lado de tração, com o grupo com 15% de VM9 com estrutura homogênea. A translucidez do grupo com gradiente foi equivalente ao grupo homogêneo mais translúcido, com 20% de VM9. Concluiu-se que foi possível sintetizar uma vitrocerâmica de dissilicato de lítio funcionalmente graduada, onde uma boa resistência mecânica e uma boa translucidez foram unidas.

Made available in DSpace on 2016-12-08T17:19:39Z (GMT). No. of bitstreams: 1 pre-textuais.pdf: 99837 bytes, checksum: 26af6e9b202afa9fa60be43b442df83a (MD5) Previous issue date: 2011-07-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The finite element method has been traditionally applied in solving problems of elasticity and heat transfer, being widely used in cases with homogeneous isotropic materials. With the advent of new technologies, it has been more frequent to use components with more than one material, aiming to get the most out of each phase. A common example is the application of coating films, with optimal properties, on a substrate. These coating films may be homogeneous or functionally graded (FGM). The latter presents a continuous variation of properties through the geometry, allowing to reduce differences at the interface with the substrate. It is important to analyze the behavior of stresses along the interface between film and substrate, a region prone for the occurrence of failure. As current commercial finite element programs have limitations to handle FGM's, especially at the interfaces, one of the motivations of this dissertation is to develop a method for stress and flux nodal recovery, adequate to work with this type of material. The work presents the analysis of a component made of steel or aluminum coated with a titanium nitride film (homogeneous or FGM) under thermo-mechanical loading. The thermal part of the problem is set in an Eulerian description, leading to heat transfer by conduction and convection in the solid. The mechanical (elasticity) part is set in the usual Lagrangean description. A staggered thermo-mechanical approach is implemented and promising results are obtained. / O método de elementos finitos tem sido tradicionalmente aplicado na solução de problemas de elasticidade e transferência de calor, sendo amplamente utilizado em casos com materiais homogêneos e isotrópicos. Com o advento de novas tecnologias tem sido mais freqüente a utilização de componentes com mais de um material, onde se procura obter o máximo proveito de cada fase. Um exemplo comum é a aplicação de filmes de revestimento com propriedades ótimas sobre um substrato. Estes filmes de revestimento podem ser homogêneos ou funcionalmente gradados (FGM), sendo que o último tem variação continua de propriedades ao longo da geometria, permitindo atenuar diferenças na interface com o substrato. A análise do comportamento das tensões ao longo da interface entre filme e substrato é de suma importância, pois esta é uma região potencial para ocorrência de falhas. Dado que programas comerciais de elementos finitos atuais apresentam limitações para lidar com FGM s, principalmente na região de interface, uma das motivações desta dissertação é desenvolver um método de pós-processamento de tensões e fluxos capaz de trabalhar adequadamente com este tipo de material. O trabalho apresenta a análise de um componente de aço ou alumínio revestido com filme de nitreto de titânio (homogêneo ou funcionalmente gradado), sob carregamento termomecânico. A parte térmica do problema é descrita usando uma abordagem Euleriana, que resulta em condução de calor por convecção e condução no sólido. A parte mecânica (elasticidade) é descrita pela tradicional abordagem Lagrangeana. Um procedimento de solução termomecânica aninhada (staggered) é implementado e resultados promissores são obtidos.