[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 .

Functional polymer foams are considered as a promising field which could potentially produce foams with added value. Specifically, functionally graded foams are materials which are expected to provide better mechanical properties while preserving low density in comparison with regular foams. In this thesis, a preparation process of such foams is designed, examination of prepared structure and comparison of mechanical properties with regular foams is performed. The obtained results are discussed and further research in this field is proposed.

In this investigation, the fabrication of functionally graded structures of SS316L to Ni-based alloys were studied, using the novel technique 3D plasma metal deposition. Two Ni-based alloys were used, a heat resistance alloy Ni80-20 and the solid-solution strengthened Ni625. Different configurations were analyzed, for the Ni80-20 a hard transition and a smooth transition with a region of 50% SS316L/50% Ni80-20. Regarding the structures with Ni625, a smooth transition configuration and variations in the heat input were applied. The effect of the process parameters on the geometry of the structures and the microstructures was studied. Microstructure examinations were carried out using optical and scanning electron microscopy. In addition, microhardness analysis were made on the interfaces. In general, the smooth transition of both systems showed a gradual change in the properties. The microstructural results for the SS316L (both systems) showed an austenite matrix with δ-phase. For the mixed zone and the Ni80-20 an austenite (γ) matrix with some M7C3 precipitates and laves phase were recognized. The as-built Ni625 microstructure was composed of an austenite (γ) matrix with secondary phases laves and δ-Ni3Nb, and precipitates M7C3. The mixed zone exhibited the same phases but with changes in the morphology.

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.

Cette étude vise à bien comprendre puis à modéliser le comportement mécanique dans une large plage de vitesse de déformation des tôles d’acier austénitique AISI304 ayant subis un traitement d'attrition mécanique de la surface (SMAT). Ces tôles ainsi traités sont des matériaux multicouches avec un gradient de propriétés. Les principaux résultats obtenus sont résumés comme suit：(1) La sensibilité globale à la vitesse déformation des tôles d’acier austénitique AISI304 traités avec SMAT est caractérisée par des essais de double cisaillement sous chargements quasi-statiques et dynamiques, qui permet d’atteindre une grande déformation sans instabilité géométrique. Des essais de double cisaillement sous impact sont réalisés à l’aide des barres de Hopkinson de grande diamètre et un système d’attache qui a une même impédance acoustique que la barre. Une sensibilité significative a été révélée et on observe ce renforcement n’a pas induit une réduction importante de la ductilité.(2) Dans le but d’un meilleur dépouillement de ces essais de double cisaillement, leur conditions d’essai est analysé dans le détaillé. Le modèle numérique avec le système d’attache a été construit pour étudier l’influence du système d’attache au début de chargement. On trouve un effet limité pour les diverses conditions imparfaites des essais comme la souplesse de système d’attache, des champs mécaniques non-homogènes, l’état de non-équilibre, etc. Par contre, les études numérique et analytique ont démontré que l’hypothèse simple de petites perturbations habituellement utilisé pour le dépouillement de ces essais n’est pas suffisamment précise. La déformation Eulérien cumulée doit être utilisée pour obtenir un résultat numérique correct. A partir de ce résultat, la sensibilité à la vitesse déformation des tôles d’acier austénitique AISI304 traités avec SMAT obtenue expérimentalement a été retouchée.(3) Un modèle multicouche elasto-plastique en dommageable a été proposé pour décrire le comportement des tôles d’acier austénitique AISI304 traités avec SMAT. Les paramètres sont identifiées à partir des essai de traction. La partie elasto-plastique est calée par une loi d’écrouissage de type Ludwig. Par contre, les paramètres d’endommagement sont obtenus avec une méthode d’identification inverse sur la base de simulation numérique de ces essais de traction. Pour valider ce modèle multi-couche elasto-plastique dommageable, un essai d’indentation/perforation est réalisé sur des tôles d’acier austénitique AISI304 traités avec SMAT. Des simulations numériques correspondantes montres que ce modèle multi-couche elasto-plastique en dommageable une prédiction plutôt précise de ces essais de d’indentation/perforation.(4) Pour évaluer la performance anti-perforation des tôles d’acier austénitique AISI304 traités avec SMAT, des essais de perforation sous impact a été réalisés avec des barres de Hopkinson. Des simulations numériques de ces essais de perforation sous impact sont réalisées avec un modèle numérique comparable avec le cas quasi-statique. ́tant donne que la sensibilité globale à la vitesse déformation des tôles d’acier austénitique AISI304 traités avec SMAT est caractérisée par des essais de double cisaillement, la sensibilité à la vitesse a été introduite dans le modèle multi-couche elasto-plastique en dommageable. Le résultat numérique correspond bien à la mesure expérimentale, ce qui indique non seulement l’efficacité du modèle numérique mais aussi celle du modèle multicouche elasto-plastique en dommageable. / This Ph.D dissertation aimed at the comprehensive understanding and the constitutive modeling of the mechanical behaviours of the surface mechanical attrition treatment (SMAT) treated AISI304 stainless steel sheet under a large range of loading rates. SMAT treated AISI304 stainless steel sheets are multi-layered functionally graded materials (FGM). The main research results and conclusions are summarized as followed:(1) The overall rate sensitivity SMAT treated AISI304 stainless steel sheet is characterized by the double shearing test under quasi-static and dynamic loading where a large strain can be achieved without geometry instability. Impact double shear test are performed with a large diameter Hopkinson bar system and an adapted equal-impedance clamping device. Significant rate sensitivity is found. It is also observed that such a rate enhancement does not induce an important reduction of the ductility.(2) In order to extract accurate material information from the double shear tests, their testing conditions are thoroughly analyzed using numerical simulation. Numerical models including clamping devices have been built to investigate the influence of this clamping device at the early stage of loading. A limited effect was found for various imperfect testing conditions such as the clamping device stiffness, non-homogeneous stress and strain fields, non-equilibrium state, etc. On the contrary, numerical and analytical study shows that the simple small strain assumption usually used in double shear tests are not accurate enough. Eulerian cumulated strain definition should be used to get consistent numerical results. From this finding, the experimental rate sensitivity obtained for the SMAT treated AISI304 stainless steel sheet are recalculated.(3) A multi-layers elastic plastic damageable constitutive model is proposed to model SMAT treated AISI304 stainless steel sheet. The parameters are identified using tensile testing results. The elastic plastic behavior is curve fitted with a simple Ludwig hardening model. However, the damage parameters should be identified using an inverse method on the basis of numerical simulation of these tensile tests. In order to validate this multi-layer elastic plastic damageable constitutive model, indentation/piercing tests on SMAT treated AISI304 stainless steel sheet are performed. Numerical simulation of this indentation/piercing tests is also realized. It is found that the identified multi-layer elastic plastic damageable constitutive model allows for a quite accurate prediction of the experimental piercing tests.(4) In order to evaluate the impact anti-piercing capacity of the SMAT treated AISI304 stainless steel sheet, the impact perforation tests using Hopkinson bar are carried out. Numerical simulation of these impact perforation tests are realized with a similar FEM model as the quasi-static case. As the rate sensitivity of SMAT treated AISI304 stainless steel sheet is experimentally characterized with double shear test, a rate sensitive multi-layer elastic plastic damageable constitutive model is introduced. The numerical results agree well with the experimental ones, which indicates the effectiveness of the numerical model as well as the rate sensitive multi-layer elastic plastic damageable constitutive model.

Das 1K- und das 2K-Spritzgießverfahren dienen zur Herstellung thermoplastischer Sandwichstrukturen, deren Deck- und Kernschicht aus einer kurzglasfaserverstärkten Polypropylen-Folie sowie entweder kompaktem oder geschäumtem Polypropylen besteht. Zudem erfolgt die Herstellung der Schäume durch das CELLMOULD®-Verfahren mit einem physikalischen Treibmittel. Eine geeignete kurzfaserverstärkte PP-Folie wird aufgrund ihrer mikroskopischen, rheologischen und mechanischen Eigenschaften ausgewählt. Beim Schaumspritzgießen ermittelt die Drei-Wege-ANOVA den Einfluss der Werkzeugtemperatur, der Eingasungsmenge und der Einspritzgeschwindigkeit auf die Dichte sowie die Zelldichte und die Zellgröße der eingespritzten Schäume. Funktional gradierte Sandwichstrukturen lassen sich durch die Mikrostruktur-untersuchung evaluieren. Die mechanischen und spezifischen mechanischen Eigenschaften der eingespritzten Proben werden in der Arbeit durch die Biegeprüfung bestimmt. Die Ergebnisse zeigen, dass sich faserverstärkte konventionelle PP-Folien mit 30 Gew.-% am besten für die Deckschichten eignen. Beim Schaumspritzgießen beeinflusst lediglich die Werkzeugtemperatur die Zelldichte und die Zellgröße. Funktional gradiertes Material ergibt sich bei der Sandwichstruktur, die durch 1K-Spritzgießen hergestellt wird. Aufgrund des Vorhandenseins einer geschäumten Lage, kompakter Lagen und kurzglasfaserverstärkter Lagen findet die Gradierung sich von der Mitte bis zu den Rändern der Proben statt. Das Vorhandensein von Schaumstrukturen verringert den Biegemodul und die Biegefestigkeit. Die Biegedehnung bei maximaler Biegespannung nimmt signifikant mit den vorhandenen Glasfasern ab. Die Sandwichstrukturen führen lediglich zur Erhöhung des Biegemoduls und der Biegefestigkeit gegenüber kompaktem und geschäumtem PP. Die Biegedehnung bei maximaler Biegespannung verhält sich bei den Sandwichstrukturen umgekehrt zum Biegemodul und der Biegefestigkeit. Beim Vergleich mittels unterschiedlicher Spritzgießverfahren produzierter Sandwichstrukturen haben die durch das 1K-Spritzgießverfahren hergestellten Proben einen niedrigeren Biegemodul und eine geringere Biegefestigkeit als die durch das 2K-Spritzgießverfahren produzierten. Jedoch zeigen die Sandwichstrukturen aus dem 1K-Spritzgießverfahren mit geschäumtem Kern den höheren spezifischen Biegemodul und die höhere spezifische Biegefestigkeit in Y-Richtung im Vergleich zu jenen aus dem 2K-Spritzgießverfahren. Außerdem weisen die verschiedenen Versagensarten der Sandwichstrukturen bei der Biegeprüfung und der Bestimmung der interlaminaren Scherfestigkeit keine Delamination zwischen Deck- und Kernschicht auf. Bei der Berechnung durch den modifizierten Gonzales-Ansatz und die Paralleltheorie zeigt sich, dass der E-Modul der Schäume und der Sandwichstrukturen fast identisch mit jenem aus den Experimenten ist. Allerdings ist die Berechnung der faserverstärkten Proben nicht möglich, daher wird der E-Modul aus den Experimenten verwendet, um die Durchbiegung im Rahmen einer Balkentheorie zu bestimmen. Die nahezu identische Durchbiegung aus dem Experiment und der Berechnung lässt sich auch durch die Euler-Bernoulli-Balkentheorie nachweisen. Die Arbeit zeigt auf, dass die Sprünge in der Steifigkeit und Festigkeit in jeder Lage von 1K-und 2K-spritzgegossenen Sandwichstrukturen abnehmen. Auf diese Weise lässt sich die Vermeidung der Delamination zwischen Deck- und Kernschicht erreichen. Die Dichte und die Materialmenge der Sandwichstrukturen reduzieren sich ohne signifikante Abnahme des spezifischen Biegemoduls und der spezifischen Biegefestigkeit. Mit der Verwendung von mechanischen Eigenschaften von Teilkomponenten der Sandwich-struktur können die Biegeeigenschaften der gradierten Sandwich-strukturen durch eine Berechnung vorausgesagt werden.:1 Einführung 2 Stand der Technik 3 Motivation und Ziel 4 Versuchsdurchführung 5 Ergebnisse und Diskussion 6 Zusammenfassung und Ausblick / The 1-component and 2-component injection moulding processes are employed to produce thermoplastic sandwich structures of which the skin and core layers comprise a short glass fibre-reinforced polypropylene film and either compact or foamed polypropylene, respectively. In addition, the foams are produced using the CELLMOULD® process with a physical blowing agent. A suitable short fibre reinforced PP film is selected on the basis of its microscopic, rheological and mechanical properties. In foam injection moulding, the three-way ANOVA determines the influence of the mould temperature, gas content and injection speed on the density as well as the cell density and cell size of the injected foams. Functionally graded sandwich structures can be proven by using the microstructure investigation. The mechanical properties and specific mechanical properties of the injected samples are determined by the three-point bending test. The results show that fibre-reinforced conventional PP films with 30 wt% are the most suitable for the skin layers. In the case of foam injection moulding, only the mould temperature influences the cell density and cell size of the injected foams. Functionally graded material results from the sandwich structure, which is produced by 1-component injection moulding process, because a foamed layer, compact layers and short glass fibres reinforced layers occur from the middle to the edges of these samples. The presence of foam structures reduces the flexural modulus and the flexural strength. The bending elongation at maximum bending stress decreases significantly with the existing glass fibres. The sandwich structures only increase the flexural modulus and the flexural strength compared to compact and foamed PP. The bending elongation at maximum bending stress behaves in the opposite way in the sandwich structures compared to the flexural module and the flexural strength. When comparing sandwich structures produced using different injection moulding processes, the sandwich structures produced by the 1-component injection moulding process have a lower flexural modulus and a lower flexural strength than those produced by the 2-component injection moulding process. However, the sandwich structures with foamed core from the 1-component injection moulding process show the higher specific flexural modulus and the higher specific flexural strength in Y-direction compared to those in the same direction from the 2-component injection moulding process. In addition, the various types of failure of the sandwich structures during the bending test and the determination of the interlaminar shear strength provide no delamination between the skin and core layers. The calculation suggests that the modulus of elasticity of the foams and the sandwich structures, calculated by the modified Gonzales approach and the parallel theory, respectively, is almost identical to that from the experiments. Nevertheless, the calculation of the fibres-reinforced samples cannot be achieved, hence, the modulus of elasticity of the fibres-reinforced samples from the experiments is used to determine the deflection based on a beam theory. The almost identical deflection from the experiment and the calculation can also be demonstrated by the Euler-Bernoulli beam theory.The work shows that the significant change in rigidity and strength decrease in each layer of 1-component and 2-component injection moulded sandwich structures. Thus, the avoidance of delamination between the skin and core layers can be achieved. The density and the amount of material in the sandwich structures are reduced without a significant decrease in the specific flexural modulus and the specific flexural strength. With the use of mechanical properties of subcomponents of the sandwich structure, the bending properties of the graded sandwich structures can be predicted by a calculation.:1 Einführung 2 Stand der Technik 3 Motivation und Ziel 4 Versuchsdurchführung 5 Ergebnisse und Diskussion 6 Zusammenfassung und Ausblick

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