Functionally graded materials (FGMs) are inhomogeneous materials in which the material properties vary with respect to space. Research has been done by scientific community in developing techniques like photothermal radiometry (PTR) to measure the thermal conductivity and volumetric heat capacity of FGMs. One of the problems involved in the technique is to solve the inverse problem, i.e., estimating the thermal properties after the frequency scan has been obtained. The present work involves finding the unknown thermal conductivity and volumetric heat capacity of the FGMs by using finite volume method. By taking the flux entering the sample as periodic and solving the discretized 1-D thermal wave field equation at a frequency domain, one can obtain the complex temperatures at the surface of the sample for each frequency. These complex temperatures when solved for a range of frequencies gives the phase vs frequency scan which can then be compared to original frequency scan obtained from the PTR experiment by using a residual function. Brute force and gradient descent optimization methods have been implemented to estimate the unknown thermal conductivity and volumetric specific heat of the FGMs through minimization of the residual function. In general, the spatial composition profile of the FGMs can be approximated by using a smooth curve. Three functional forms namely Arctangent curve, Hermite curve, and Bezier curve are used in approximating the thermal conductivity and volumetric heat capacity distributions in the FGMs. The use of Hermite and Bezier curves gives the flexibility to control the slope of the curve i.e. the thermal property distribution along the thickness of the sample. Two-layered samples with constant thermal properties and three layered samples in which one of the layer has varying thermal properties with respect to thickness are considered. The program is written in Fortran and several test runs are performed. Results obtained are close to the original thermal property values with some deviation based on the stopping criteria used in the gradient descent algorithm. Calculating the gradients at each iteration takes considerable amount of time and if these gradient values are already available, the problem can be solved at a faster rate. One of the methods is extending automatic differentiation to complex numbers and calculating the gradient values ahead; this is left for future work.

Composite materials and hybrid materials such as fiber-metal laminates, and functionally graded materials are increasingly common in application in aerospace structures. However, adhesive bonding of dissimilar materials makes these materials susceptible to delamination. The use of integrated Sinc methods for predicting interlaminar failure in laminated composites and hybrid material systems was examined. Because the Sinc methods first approximate the highest-order derivative in the governing equation, the in-plane derivatives of in-plane strain needed to obtain interlaminar stresses by integration of the equilibrium equations of 3D elasticity are known without post-processing. Interlaminar stresses obtained with the Sinc method based on Interpolation of Highest derivative were compared for the first-order and third-order shear deformable theories, the refined zigzag beam theory and the higher-order shear and normal deformable beam theory. The results indicate that the interlaminar stresses by the zigzag theory compare well with those obtained by a 3D finite element analysis, while the traditional equivalent single layer theories perform well for some laminates. The philosophy of the Sinc method based on Interpolation of Highest Derivative was extended to create a novel weak form based approach called the Integrated Local Petrov-Galerkin Sinc Method. The Integrated Local Petrov-Galerkin Sinc Method is easily utilized for boundary-value problem on non-rectangular domains as demonstrated for analysis of elastic and elastic-plastic plane-stress panels with elliptical notches. The numerical results showed excellent accuracy compared to similar results obtained with the finite element method. The Integrated Local Petrov-Galerkin Sinc Method was used to analyze interlaminar debonding of composite and fiber-metal laminated beams. A double-cantilever beam and a fixed-ratio mixed mode beam were analyzed using the Integrated Local Petrov-Galerkin Sinc Method and the results were shown to correlate well with those by the finite element method. An adaptive Sinc point distribution technique was implemented for the delamination analysis which significantly improved the methods accuracy for the present problem. Delamination of a GLARE, plane-strain specimen was also analyzed using the Integrated Local Petrov-Galerkin Sinc Method. The results correlate well with 2D, plane-strain analysis by the finite element method, including interlaminar stresses obtained by through-the-thickness integration of the equilibrium equations of 3D elasticity. / Ph. D.

Submitted by Angela Maria de Oliveira (amolivei@uepg.br) on 2019-02-27T11:49:16Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Gustavo Antoniacomi de Carvalho.pdf: 6310308 bytes, checksum: 8e1efd9d86bc5a1adf80b45bba2a3985 (MD5) / Made available in DSpace on 2019-02-27T11:49:16Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Gustavo Antoniacomi de Carvalho.pdf: 6310308 bytes, checksum: 8e1efd9d86bc5a1adf80b45bba2a3985 (MD5) Previous issue date: 2018-01-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Cerâmicas porosas vêm ganhando visibilidade devido a algumas aplicações tecnológicas interessantes, tais como a utilização em eletrólitos sólidos, ânodos de células a combustível, filtros cerâmicos e reposição óssea e dental. Dentre elas, há especial atenção ao estudo de materiais porosos com porosidade graduada, nos quais a quantidade de poros e a morfologia dos mesmos se alteram pelo volume do material. Nesse trabalho foi realizado o processamento e caracterização de materiais cerâmicos de alumina com porosidade graduada a partir das técnicas de freeze casting e colagem de barbotina, utilizando hidróxido de alumínio e amido de arroz como fases de sacrifício. Após a conformação das amostras por esses métodos, a porosidade foi caracterizada por microscopia eletrônica de varredura, pelas medidas de porosidade aparente feita pelo Princípio de Arquimedes e pela distribuição de tamanho de poros feita pela técnica de porosimetria de mercúrio. Foi avaliada também a resistência mecânica das amostras a partir de ensaio de compressão. Foi confirmada a relação entre as amostras processados isoladamente e suas respectivas camadas nas amostras graduadas. Foi observada também uma boa interação interfacial entre cada uma das camadas das amostras graduadas. A porosidade das amostras com porosidade graduada se manteve próxima do esperado, o valor esperado foi determinado a partir da média das amostras processadas isoladamente em relação às camadas do material com porosidade graduada. O ensaio mecânico demonstrou que não houve influência das interfaces dos materiais graduados na sua resistência à compressão. / Porous ceramics have been gaining visibility due to some interesting technological applications, such as its use as solid electrolytes, fuel cell anodes, ceramic filters and bone and dental reposition. Among them, there is special care in studying graded porosity materials, where the quantity of pores and pore morphology changes through the material volume. In this work the processing and characterization of alumina ceramic materials with functionally graded porosity by freeze casting and slip casting techniques using aluminum hydroxide and rice starch as sacrificial template was performed. After conformation, the porosity was characterized through electron scanning microscopy, apparent porosity through Archimedes method and median pore size through mercury porosimetry. The mechanical resistance was also obtained by compression testing. The analysis allowed to confirm the relation between each of the isolated samples’ microstructure and its respective layer in each of the graded materials, also, the graded materials shown good interfacial interaction between each of the layers. The porosity in graded materials kept close to the expected value, which was determined by the medium value of the porosities of the isolated samples respective to the graded material. Mechanical testing shown that there was no influence of the graded material interfaces in its compressive strength.

La plupart des problèmes d'ingénierie des deux derniers siècles ont été résolus grâce à des modèles structuraux pour poutres, plaques et coques. Les théories classiques, tels que Euler-Bernoulli, Navier et de Saint-Venant pour les poutres, et Kirchhoff-Love et Mindlin-Reissner pour plaques et coques, ont permis de réduire le problème générique 3-D, dans le problème unidimensionnel pour les poutres et deux dimensionnelle pour les coques et les plaques. Théories raffinés d'ordre supérieur ont été proposées au cours du temps, comme les modèles classiques ne consentez pas à d'obtenir une complète domaine des contraintes et des déformations. La Carrera Unified Formulation (UF) a été proposé au cours de la dernière décennie, et permet de développer un grand nombre de théories structurelles avec un nombre variable d'inconnues principales au moyen d'une notation compacte et se référant à des nuclei fondamentales. Cette formulation unifiée permet de dériver carrément des modèles structurels d'ordre supérieur, pour les poutres, plaques et coques. Dans ce cadre, cette thèse vise à étendre la formulation pour l'analyse des structures fonctionnellement gradués (FGM), en introduisant aussi le problème thermo-mécanique, dans le cas des poutres fonctionnellement gradués. Suite à la formulation unifiée, les variables génériques déplacements sont écrits en termes de fonctions de base, qui multiplie les inconnues. Dans la deuxième partie de la thèse, de nouvelles fonctions de bases pour la modélisation des coques, qui représentent une approximation trigonométrique des variables déplacements, sont pris en compte / Most of the engineering problems of the last two centuries have been solved thanks to structural models for both beams, and for plates and shells. Classical theories, such as Euler-Bernoulli, Navier and De Saint-Venant for beams, and Kirchhoff-Love and Mindlin- Reissner for plates and shells, permitted to reduce the generic 3-D problem, in onedimensional one for beams and two-dimensional for shells and plates. Refined higher order theories have been proposed in the course of time, as the classical models do not consent to obtain a complete stress/strain field. Carrera Unified Formulation (UF) has been proposed during the last decade, and allows to develop a large number of structural theories with a variable number of main unknowns by means of a compact notation and referring to few fundamental nuclei. This Unified Formulation allows to derive straightforwardly higher-order structural models, for beams, plates and shells. In this framework, this thesis aims to extend the formulation for the analysis of Functionally Graded structures, introducing also the thermo-mechanical problem, in the case of functionally graded beams. Following the Unified Formulation, the generic displacements variables are written in terms of a base functions, which multiplies the unknowns. In the second part of the thesis, new bases functions for shells modelling, accounting for trigonometric approximation of the displacements variables, are considered.

[pt] O presente trabalho trata do desenvolvimento de uma modelagem numérica para estruturas cilíndricas com materiais compósitos. Uma classe especial de materiais compósitos, os materiais com gradação funcional (FGM), também é investigada. O modelo constitutivo adotado para o material compósito é baseado na regra das misturas. Esta metodologia é aplicada na análise de reparo e reforço de dutos, considerando as solicitações usuais de campo, notadamente as decorrentes da variação de temperatura e das pressões internas, bem como os efeitos da interação solo-estrutura. O sistema duto-reforço é modelado como elemento de viga conforme o método dos elementos finitos, e as tensões na seção são integradas numericamente. Para tanto, o material, tanto do duto quanto da camada de reforço, é admitido com comportamento elastoplástico. Alguns exemplos, simulando as condições típicas, são apresentados e discutidos, de maneira a avaliar o comportamento dos dutos recuperados com materiais compósitos, e a propor a solução mais eficiente no dimensionamento da camada de reforço, inclusive em termos do material com gradação funcional. / [en] This work presents a numerical model for the investigation of pipe constituted by composite materials. A special class of composite materials, functionally graded materials (FGM), is considered. The composite material model is based on the rule of mixture and an elastoplastic material behavior is incorporated. A finite element model based on the beam element discretization is employed, by which the section integration allows the representation of the non-linear material behavior. This methodology is applied to the analysis of reinforced and repaired pipelines. The soilstructure interaction, accomplished through transversal and longitudinal springs, besides transversal, axial and pressure loading are incorporated. Some examples, simulating the conditions in field, are shown and discussed in order to evaluate the behavior of reinforced pipes, proposing the soluction more efficient in modeling of the reinforcement, included in terms of the functionally graded materials .

El propósito del presente trabajo es desarrollar un modelo matemático que permita el análisis de estabilidad de una viga compuesta de materiales funcionalmente graduados sometida a una carga de compresión axial. La finalidad es analizar el comportamiento de una viga heterogénea y calcular las cargas y los modos de pandeo. En el desarrollo de la investigación se describe vectorialmente el campo de desplazamiento de la viga para obtener las ecuaciones de gobierno de la estructura; de este modo, mediante principios energéticos, se pueda desarrollar el modelo de elementos finitos y buscar una solución vectorial propia. El modelo matemático se divide en dos partes: formulación simbólica y modelo numérico computacional. En el modelo matemático, los materiales funcionalmente graduados afectan el módulo de elasticidad debido a la particularidad del material; y la energía potencial total es afectada por dos estados: estado fundamental (deformación de membrana o de pre-pandeo) y estado incremental (estado de perturbación arbitraria de equilibrio). Los resultados obtenidos fueron verificados con ejercicios benchmarking encontrados en la literatura, para corroborar la eficacia del modelo planteado; validados con informes de pruebas de laboratorio, para revisar la precisión; y estudiados paramétricamente, para analizar la influencia de las variables. / The purpose of the present work is to develop a mathematical model that allows the stability analysis of a beam composed of functionally graded materials subjected to an axial compressive load. The objective is to analyze the behavior of a heterogeneous beam and calculate the buckling loads and modes. In the development of the investigation, the field of displacement of the beam is described in vectors to obtain the governing equations of the structure. In this way, by energetic principles, the finite element model can be developed, and the solution can be found by eigenvalue and eigenvector exercise. The mathematical model is divided in two parts: symbolic formulation and computational numerical model. In the model, the functionally graded materials affect the modulus of elasticity due to the particularity of the material; and the total potential energy is affected by two states: fundamental state (membrane deformation or pre-buckling) and incremental state (arbitrary perturbation of the equilibrium). The results obtained were verified with benchmarking exercises found in literature, to corroborate the effectiveness of the proposed model; validated with lab test-reports, to check its accuracy; and studied parametrically, to analyze the influence of the variables. / Tesis

Traditional methods for increasing the energy absorption of a structure involve using a stronger material or increasing the volume of the structure, resulting in a higher cost or additional weight. Additive manufacturing (AM) can be used to maximize the energy absorption of materials with the ability to create complex geometries such as cellular structures. Previous work has shown that the energy absorption of additively manufactured parts can be improved through functionally graded cellular structures; however, this strategy has not been applied to ultra-high strength steel materials. This work characterizes the effect of multiple functional-grading strategies (e.g. uniform, rod-graded, size-graded) on the energy absorption to weight ratio of laser powder bed fusion (L-PBF) produced M300 maraging steel lattice structures. Each structure is designed with the same average relative density to analyze the structures on an equal mass basis, to evaluate manufacturability, mechanical response, and compare experimental results with numerical simulation.

This thesis describes the design, manufacture and characterisation of thick vacuum plasma sprayed tungsten (W) coatings on steel substrates. Fusion is a potentially clean, sustainable, energy source in which nuclear energy is generated via the release of internal energy from nuclei. In order to fuse nuclei the Coulomb barrier must be breached - requiring extreme temperatures or pressures – akin to creating a ‘star in a box’. Tungsten is a promising candidate material for future fusion reactors due to a high sputtering threshold and melting temperature. However, the large coefficient of thermal expansion mismatch with reactor structural steels such as the low activation steel Eurofer’97 is a major manufacturing and in-service problem. A vacuum plasma spraying approach for the manufacture of tungsten and tungsten/steel graded coatings has been developed successfully. The use of graded coatings and highly textured 3D interface surfi-sculpt substrates has been investigated to allow the deposition of thick plasma sprayed tungsten coatings on steel substrates. Finite element models have been developed to understand the residual stresses that develop in W/steel systems and made use of experimental measurements of coating thermal history during manufacture and elastic moduli measured by nano-indentation. For both the graded and surfi-sculpt coating, the models have been used to understand the mechanism of residual stress redistribution and relief in comparison with simple W on steel coatings, particularly by consideration of stored strain energy. In the case of surfi-sculpt W coatings, the patterned substrate gave rise to regular stress concentrating features, and allowed 2mm thick W coatings to be produced reproducibly without delamination. Preliminary through thickness residual stress measurements were compared to model predictions and provided tentative evidence of significant W coating stress relief by regulated coating segmentation.