ABSTRACT CONTACT MECHANICS OF GRADED MATERIALS WITH TWODIMENSIONAL MATERIAL PROPERTY VARIATIONS G&ouml / kay, Kemal M.S., Department of Mechanical Engineering Supervisor: Asst. Prof. Dr. Serkan Dag September 2005, 62 pages Ceramic layers used as protective coatings in tribological applications are known to be prone to cracking and debonding due to their brittle nature. Recent experiments with functionally graded ceramics however show that these material systems are particularly useful in enhancing the resistance of a surface to tribological damage. This improved behavior is attributed to the influence of the material property gradation on the stress distribution that develops at the contacting surfaces. The main interest in the present study is in the contact mechanics of a functionally graded surface with a two &ndash / dimensional spatial variation in the modulus of elasticity. Poisson&rsquo / s ratio is assumed to be constant due to its insignificant effect on the contact stress distribution [30]. In the formulation of the problem it is assumed that the functionally graded surface is in frictional sliding contact with a rigid flat stamp. Using elasticity theory and semi-infinite plane approximation for the graded medium, the problem is reduced to a singular integral equation of the second kind. Integral equation is solved numerically by expanding the unknown contact stress distribution into a series of Jacobi polynomials and using suitable collocation points. The developed method is validated by providing comparisons to a closed form solution derived for homogeneous materials. Main numerical results consist of the effects of the material nonhomogeneity parameters, coefficient of friction and stamp size and location on the contact stress distribution.

The challenges in the deposition of dissimilar materials are mainly related to the large differences in the physical and chemical properties of the deposited and substrate materials. These differences readily cause residual stresses and intermetallic phases. This has led to the development of functionally graded materials which exhibit spatial variation in composition. Laser direct metal deposition due to its flexibility, it offers wide variety of dissimilar and functionally graded materials deposition. Despite considerable advances in process optimization, there is a rather limited understanding of the role of metallurgical factors in the laser deposition of dissimilar and functionally graded alloys. The aim of this work is to understand and explain mechanisms occurring in diode laser deposition of dissimilar materials and functionally graded materials. The first part of this work addressed diode laser deposition of Inconel 718 nickel alloy to Ti-6Al-4V titanium alloy. Here, the effect of laser pulse parameters and powder mass flow rates on the stress formation and cracking has evaluated by experiment and numerical techniques. Results showed that the clad thickness was an important factor affecting the cracking behaviour. In the second part of this study, an image analysis technique has been developed to measure the surface disturbance and the melt pool cross section size during laser direct metal deposition of Inconel 718 on a Ti-6Al-4V thin wall. It was noted that under tested conditions the overall melt pool area increased with the increase in powder flow rate; the powder carrier gas flow rates also seemed to play important roles in determining the melt pool size. In the third part of this study, a parametric study on the development of Inconel 718 and Stainless steel 316L continuously graded structure has been carried out. Results suggested that microstructure and other mechanical properties can be selectively controlled across the deposited wall. The results presented in this dissertation can be used as a metallurgical basis for further development of dissimilar and functionally graded manufacturing using LDMD technique, guiding future manufacturing engineers to produce structurally sound and microstructurally desirable laser deposited samples.

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.

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.

No description available.

O objetivo precípuo deste estudo é a implementação computacional de modelos constitutivos elásticos e elastoplásticos para materiais com gradação funcional em regime de grandes deslocamentos e elevadas deformações. Para simular numericamente um problema estrutural, são empregados aqui elementos finitos sólidos (tetraédrico e hexaédrico) com ordem de aproximação polinomial qualquer. Grandezas da Mecânica Não Linear do Contínuo, como deformação e tensão, são utilizadas na formulação deste estudo. Para reproduzir os grandes deslocamentos, é empregada a análise não linear geométrica. A descrição adotada aqui é a Lagrangiana total, e o equilíbrio da estrutura é expresso pelo Princípio da Mínima Energia Potencial Total. Com relação à resposta elástica do material, são usadas leis constitutivas hiperelásticas, nas quais a relação tensão-deformação é obtida a partir de um potencial escalar. O comportamento elastoplástico do material é definido pela decomposição da deformação nas parcelas elástica e plástica, pelo critério de plastificação de von-Mises, pela lei de fluxo associativa, pelas condições de consistência e de complementaridade, pelo parâmetro de encruamento isotrópico e pelo tensor das tensões inversas, relacionado ao encruamento cinemático. Duas formulações elastoplásticas são utilizadas aqui: a de Green-Naghdi, na qual a deformação é decomposta de forma aditiva; e a hiperelastoplástica, em que o gradiente é decomposto de forma multiplicativa. É empregado também o conceito de material com gradação funcional (GF), a qual é definida como a variação gradual (contínua e suave) das propriedades constitutivas do material. A solução numérica do equilíbrio de forças é feita via método iterativo de Newton-Raphson. Para satisfazer o critério de plastificação, são utilizadas as estratégias de previsão elástica, e de correção plástica via algoritmos de retorno. Basicamente foram desenvolvidos cinco programas computacionais: o gerador automático das funções de forma; o gerador de malhas de elementos finitos sólidos; o código para análise de materiais em regime elástico; o código para análise de materiais em regime elastoplástico; e o programa de pós-processamento. Além desses, o aluno teve contato com os programas EPIM3D e DD3IMP ao longo de seu estágio de doutorado na Universidade de Coimbra (Portugal). Os programas EPIM3D e DD3IMP são empregados para analisar, respectivamente, materiais em regime elastoplástico, e processos de conformação de metais. Para o problema da barra sob tração uniaxial uniforme, são descritas equações e soluções analíticas para materiais homogêneos e com GF em regime elastoplástico. Para reduzir o tempo de simulação, foi empregada a programação em paralelo. De acordo com os resultados das simulações numéricas, as principais conclusões são: o refinamento da malha de elementos finitos melhora a precisão dos resultados para materiais em regimes elástico e elastoplástico; as formulações elastoplásticas de Green-Naghdi e hiperelastoplástica parecem ser equivalentes para pequenas deformações; a formulação hiperelastoplástica é equivalente ao modelo mecânico dos programas EPIM3D e DD3IMP para materiais em regime de pequenas deformações elásticas; foram constatados ganhos significativos, em termos de tempo de simulação, com a paralelização dos códigos computacionais de análise estrutural; e os programas desenvolvidos são capazes de simular - com precisão - problemas complexos, como a membrana de Cook e o cilindro fino transversalmente tracionado. / The main objective of this study is the computational implementation of elastic and elastoplastic constitutive models for functionally graded materials in large deformation regime. In order to numerically simulate a structural problem, the finite elements used are solids (tetrahedric and hexahedric) of any order of approximation. Entities from Nonlinear Continnum Mechanics, as strain and stress, are used in the present formulation. To reproduce the finite displacements, the geometrically nonlinear analysis is employed. The description adopted here is the total Lagrangian, and the structural equilibrium is expressed by means of the Principal of Minimum Total Potential Energy. Regarding the elastic material response, hyperelastic constitutive laws are used, in which the stress-strain relation is obtained from a scalar potential. The elastoplastic material behavior is defined by the strain decomposition in the elastic and plastic parts, by the von-Mises yield criterion, by the associative flow law, by the consistency and complementarity conditions, by the isotropic hardening parameter, and by the backstress tensor, related to the kinematic hardening. Two elastoplastic formulations are used here: the Green-Naghdi one, in which the strain is additively decomposed; and the hyperelastoplasticiy, in which the gradient is multiplicatively decomposed. The concept of functionally graded (FG) material, in which the constitutive properties vary gradually (continuous and smoothly), is also used. The numerical solution of the forces equilibrium is obtained via Newton-Raphson iterative procedure. In order to satisfy the yield criterion, the strategies of elastic prediction and plastic correction (via return algorithms) are used. Basically, five computer codes have been developed: the automatic shape functions generator; the solid mesh generator; the code for analysis of materials in the elastic regime; the code for analysis of materials in the elastoplastic regime; and the post-processor. Besides these, the student had contact with the programs EPIM3D and DD3IMP during his doctoral stage in the University of Coimbra (Portugal). The programs EPIM3D and DD3IMP are employed to analyze, respectively, materials in the elastoplastic regime, and sheet-metal forming processes. For the problem of the bar under uniform uniaxial tension, equations and analytical solutions are described for homogeneous and FG materials. To reduce the simulation time, the parallel programming has been employed. According to the numerical simulation results, the main conclusions are: the results accuracy is improved with mesh refinement for materials in the elastic and elastoplastic regimes; the Green-Naghdi elastoplastic formulation and the hyperelastoplasticity appear to be equivalent for small strains; the hyperelastoplastic formulation is equivalent to the mechanical model of the programs EPIM3D and DD3IMP for materials the small elastic strains regime; simulation time reduction has been obtained with the parallelization of the computer codes for structural analysis; the developed programs are capable of simulating, precisely, complex problems, such as the Cook\'s membrane and the pulled thin cylinder.