Tendo em conta os constantes problemas que apresentasse com os processos de corrosão, o presente trabalho de pesquisa tem como foco principal a alteração nas propriedades de superfície das ligas de alumínio empregadas nas aeronaves, AA2024 e AA7075, utilizando mono e bicamadas baseadas de octadecil-trimetóxi-silano (ODTMS) + poli(anilina-co-3-aminobenzoico/PAni3ABA) a fim de encontrar melhores condições para a redução da corrosão puntiformes. Posteriormente, avalia-se as características protetoras dos filmes através de testes de corrosão, como potencial de circuito aberto, curvas de polarização anódica e espectroscopia de impedância eletroquímica visando a caracterização do comportamento eletroquímico das amostras. Também foram realizadas análises de microscopia óptica para verificar a eficiência de proteção contra a corrosão dos revestimentos propostos antes e após os ensaios de corrosão. Os resultados obtidos demonstram que as camadas utilizadas melhoram a resistência contra a corrosão na seguinte ordem: PAni3ABA > ODTMS + PAni3ABA > ODTMS, sendo a primeira a que apresentou os melhores resultados como maiores deslocamentos do Ecorr para valores mais positivos, diminuição da icorr e menor número de pontos de corrosão após a realização das curvas de polarização. Além de testes de aderência para os filmes também foram efetuadas caracterizações das ligas por MEV. / Taking into account the constant problems that presents with corrosion processes, this research work has focused primarily on the change in surface properties of aluminum alloys used in aircraft, AA2024 and AA7075, with mono and bilayers using as a base octadecyl trimethoxy silane (ODTMS) + poly (aniline-co-3-aminobenzoic / PAni3ABA) to find optimum conditions for reducing corrosion punctiform. Later, it evaluates the protective features of the films through corrosion tests such as open circuit potential, anodic polarization curves and electrochemical impedance spectroscopy in order to characterize the electrochemical behavior of the samples. They were also carried out optical microscopy analysis to verify the efficiency of protection against corrosion of the coatings proposed before and after corrosion testing. The results obtained show that the layers used improve corrosion resistance in the following order: PAni3ABA> ODTMS + PAni3ABA> ODTMS, the first being the one that presented the best results as larger shifts towards more positive values, reduced and fewer corrosion points after performing the polarization curves. In addition to compliance tests for the films were also made characterizations of alloys by SEM.

De nos jours, une gestion optimale de l'énergie électrique est devenue un enjeu majeur. La conversion de l'énergie entre une source et sa charge est réalisée par un élément central : le convertisseur statique utilisé aussi bien pour des faibles puissances (quelques Watts) que pour des très fortes (plusieurs MWatt). La brique élémentaire est la cellule de commutation constituée de semi-conducteurs de puissance (à commutation commandée ou spontanée) généralement réunis au sein d'un " module de puissance ". La nécessaire réduction des volumes dans certaines applications (comme les systèmes embarqués par exemple) ainsi que l'augmentation des calibres de tensions des nouveaux semi- conducteurs grands gaps auront comme conséquence directe d'augmenter les contraintes sur les systèmes d'isolation des convertisseurs. Une répartition contrôlée de ces contraintes dans le volume présente alors un intérêt pour maintenir la fiabilité du système d'isolation. Il est donc nécessaire d'effectuer une caractérisation la plus large possible de l'ensemble des matériaux isolants utilisés dans le packaging des dits " modules de puissance ", ainsi qu'une bonne compréhension de leurs mécanismes de défaillances. Le travail présenté ici consiste en l'étude d'une nouvelle stratégie de répartition du potentiel dans le volume appelée gradation de potentiel. L'isolation de volume développée est un assemblage multicouche constitué d'un matériau à conductivité contrôlée (Epoxy/Graphene) jouant le rôle de gradateur et d'une fine couche isolante (parylène) assurant la tenue en tension. Différents outils, tant théoriques (simulation) qu'expérimentaux, ont été ainsi utilisés pour aider au dimensionnent du système d'isolation électrique. La modélisation par la méthode des éléments finis (MEF) permet-elle de prédéterminer la répartition de la contrainte (potentiel et champ électrique) dans une structure de test prédéfini ou de décrire l'étude de l'influence de la conductivité du matériau gradateur et de l'épaisseur du film sur la répartition des équipotentielles. D'un point de vue expérimental le film sélectionné a été caractérisé pour des épaisseurs comprises entre 10 et 40 µm. Le matériau à conductivité contrôlée a été ensuite élaboré puis caractérisé pour différents taux de chargement. Après l'incorporation du système d'isolation dans différentes structures tests (substrats métallisés et structure double face), différentes méthodes permettant de caractériser le système d'isolation ont été utilisées qu'il s'agisse de mesures directes de la contrainte électrique par sonde à champ nul (potentiel de surface) ou indirectes par des mesures de décharges partielles. L'isolation multi-couches présente des améliorations dans la répartition du potentiel mais aussi des limites d'utilisation en fonction de la conductivité du matériau gradateur. Cette isolation doit donc être dimensionnée au plus près des caractéristiques d'utilisation et offre une approche intéressante pour le dimensionnement des modules de puissances double face. / Nowadays, an optimal management of the electrical energy becomes a key point in electric systems. The conversion of energy is realized by a main component: the power converter. It is used as well for low power (few Watts) as for very high power (MWatts). The elementary block of the converters, is the switching cell made up of semiconductor power devices. The trend to reduce both the volume and the weight in many applications (for example in embedded systems) and the increase of the rating voltage of the new wide band gap semiconductors will have for consequence an increase of the stresses on the electrical insulating systems of the power module . A controlled grading of these electrical constraints in the volume is highly interesting to ensure the reliability of the system. It is therefore necessary to perform a precise characterization of the insulated materials used in the packaging of the power modules, as well as to get a good understanding of their failures mechanisms. The works presented in this dissertation consists in the study of a new strategy for the field gradation in power modules. The proposed insulation is an assembly of multi-layers made up of a thick material of electrically controlled conductivity (Epoxy/Graphene nanocomposite) and of a thin insulating layer (Parylene films). Various tools were used (both theoretical and experimental) to help dimensioning of the Electrical Insulation System (EIS). The Finite Element Method (FEM) was used to simulate the equipotential and field distribution in the structure under study and to analyse on one hand, the influence of the changes in the conductivity values of the Epoxy/Graphene nanocomposite materials and, on the other hand, the impact of the parylene (PA) films thickness on the stress grading. From an experimental point of view, the PA films were characterized for different thicknesses ranging between 10 µm and 40 µm. The Epoxy/Graphene nanocomposites of controlled conductivity were manufactured and characterized (0 to 5 % wt) for various filler contents. The field grading effects were evaluated directly in different structures thanks to surface potential measurements and (indirectly) to partial discharges measurements. The proposed multilayer EIS exhibits some improvements regarding the stress grading but also some limits depending on the conductivity of the nanocomposite. Such an EIS will have to be dimensioned taking into account the rating voltage and could offer an interesting approach for the future design of the power modules.

Este trabalho apresenta a análise de agregados reciclados de telhas de cerâmica vermelha, visando seu emprego em camadas de pavimentos de baixo custo, baseado em estudos de laboratório. A indústria de cerâmica vermelha gera refugos da queima que são tratados como resíduos, mas se constituem em materiais de alto conteúdo energético e matéria prima de qualidade. O quadro da geração desses resíduos foi diagnosticado nas cidades de Monte Carmelo e Ituiutaba, em Minas Gerais. Os dados quantitativos obtidos indicam que é justificável a sua reciclagem. Somente na cidade de Monte Carmelo, as quantidades geradas permitiriam executar 10,8 km de camada de base de pavimento, ao se misturar 40% de solo poderia atingir 32 km por ano. Aproximadamente 10 t destes resíduos foram britadas obtendo-se o agregado reciclado de telha (ART). Estes agregados foram caracterizados mediante os ensaios físicos e mecânicos, e submetidos aos ensaios empregados na pavimentação, como a metodologia tradicional, metodologia MCT, método da pastilha, resistência ao cisalhamento, outros ensaios denominados índices de qualidade, ensaio de módulo resiliente e deformação permanente. Apesar deste material atender aos principais requisitos da metodologia tradicional, identificou-se que ele quebra com a aplicação de energia de compactação e de tensões nos ensaios, e apresenta alta resiliência - grandes deformações resilientes-, o que levaria à perda da capacidade de suporte da estrutura do pavimento, por fadiga. Desenvolveu-se uma metodologia para a determinação da absorção no estado saturado superfície seca, de agregados porosos, com fração fina inclusive, pois os métodos conhecidos não são aplicáveis; esta metodologia pode ser aprimorada para se constituir em norma de ensaio. Estudou-se um método inédito para a otimização do volume compactado da mistura de agregado com solo, baseado na porosidade do material granular, como uma alternativa ao método da estabilização granulométrica que se mostrou inadequado, no caso. As misturas produzidas com solos lateríticos foram avaliadas após a compactação não apresentando mais a quebra dos grãos do agregado, e mostraram ganhos expressivos no valor do módulo de resiliência, chegando em um caso a atingir 288% acima do módulo do agregado. Os resultados dos ensaios de laboratório indicaram ser possível a aplicação deste material em misturas com solos lateríticos, em camadas de pavimentos de baixo custo. / The purpose of this work is to use recycled aggregate of ceramics roofing tiles for low cost pavement layers, based on laboratory studies. The heavy-clay ceramic industry generates wastes, originated from the calcination stage, that are considered as residues which demand resources for its deposition. However they are high energy content materials which can be useful. The generation of these residues in the cities of Monte Carmelo and Ituiutaba, in the State of Minas Gerais indicated that its recycling is valid. For instance, in the city of Monte Carmelo, it is generated such a large amount of residues that it should be enough to execute about 10,8 km of base course of pavement; moreover if 40% of soil is mixed 32 km pavement per year can be produced. For this study, approximately 10 metric tones of these residues had been crushed to produce the recycled aggregate from roofing tile. The aggregates produced had been characterized by physical and mechanical tests. They were also submitted to the tests used for aggregates for pavement, such as the traditional methodology, methodology MCT (tropical compacted miniature), shear strength, resilient module, permanent deformation, and other tests called quality rates. These residues comply with the main requirements of the traditional methodology, however it is necessary to point out that the material breaks with the application of energy for compaction and under the tensions during the mechanical tests, it also presents high resilience, or great resilient deformations, which will lead to the loss of the supporting capacity of the pavement due to fatigue. An appropriate methodology was developed for the porous aggregate absorption measurement, including its fraction, in the saturated dry surface state. As the known methods for absorption are not applicable, this methodology with improvements can be proposed as standard test. A new method to optimize the compacted volume of the mixture was studied, based on the porosity of the granular material, as an alternative to the traditional method of the grain sized stabilization, which is not adequate for this purpose. The mixtures produced with lateritics soils were evaluated after the compacting, they have not presented the broken grains. These mixtures performed very well with significant increase in the value of the resilience module, up to 288% above of the module of the aggregate. The results of the laboratory indicate that it is possible to use these residues in mixtures with laterític soil, for layers of low cost pavements.

Argilominerais são componentes abundantes nas frações < 2 &mu;m solos, com grande papel no controle de processos geoquímicos e de formação de solos. Nos manguezais brasileiros, apesar das caracterizações gerais já realizadas, há ausência de estudos cristaloquímicos detalhados que possam evidenciar mecanismos de formação/transformação envolvendo essas fases. Este trabalho se propõe, através de dois estudos comparativos, aprofundar a caracterização cristaloqímica das frações 2-0,2 &mu;m e < 0,2 &mu;m, sugerir processos de transformação envolvendo os argilominerais dos manguezais e entender quais atributos ambientais estão associados a essas transformações. Esta caracterização se baseia nas técnicas de modelagem de DRX, decomposição de picos 060 de padrões não-orientados de DRX, FTIR, espectroscopia Mössbauer, análises térmicas, análise química da água intersticial e modelagem geoquímica dos componentes químicos em solução. Os resultados, que serão detalhados nos capítulos 2 e 3, sugerem uma série de transformações minerais, via fases interestratificadas, que devem ter importantes implicações para a compreensão dos processos pedogenéticos envolvendo argilominerais, do seu papel no ciclo biogeoquímico dos elementos associados à sua gênese e relação indireta ou direta com componentes bióticos do ecossistema, que podem influenciar nas transformações que envolvem os minerais. / Clay minerals are ubiquitous components in < 2 &mu;m size fraction of soils, having an important role in the control of geochemical processes and soil genesis. Despite of the general characterizations performed in Brazilian mangroves soils there is a lack of a detailed crystal chemical study able to evidence mechanisms of formation/transformation of such minerals. This study aims (by two different comparative works) to enhance the crystal chemical characterization of mineral phases in the 2-0,2 &mu;m and < 0,2 &mu;m size fractions of mangrove soils, suggesting the existence of mineral transformation involving clay phases and comprehending what environmental settings are related to these transformations. This characterization is based on XRD modelling of oriented patterns, peak fitting of 060 peaks in randomly XRD patterns, Mössbauer spectroscopy, thermal analysis, chemical analysis of soil pore water and geochemical modelling of inorganic soluble compounds. The results, which are described in chapters 2 and 3 indicate a sequence of mineral transformations, via mixed-layered clays, which may have important consequences for the comprehension of soil genesis processes involving clay minerals, their role in the biogeochemical cycles of structural elements of clays and a straight relationship with biotic components of mangrove ecosystem.

Le développement de la microélectronique « ultime » requiert la fabrication de structures de type SOI (Silicon-On-Insulator) dotées d’une couche superficielle de Si d’épaisseur très fine (de l’ordre de 10 nm) et uniforme (<+/- 0,5 nm). Une des voies pour relever ce challenge serait d’intégrer, dans la technologie Smart CutTM, des substrats donneurs modifiés permettant de « forcer » l’hydrogène à précipiter, en cours de recuit, dans un plan parallèle à, et proche de, la surface. Dans ce travail, nous étudions les effets de l’implantation ionique d’ions hydrogène et d’un recuit thermique dans des structures de silicium contenant de fines couches « enterrées » de Si:B ou de SiGe. Nous avons tout d’abord identifié les conditions d’implantation et de recuit permettant l’obtention de cloques sur des surfaces libres et donc devant permettre de fracturer la couche en présence d’un raidisseur mécanique, ce que nous avons testé. La couche Si:B permet d’obtenir la fracture pour une dose d’hydrogène implanté plus faible et pour un budget thermique plus faible qu’avec une couche de SiGe. De plus, la rugosité de ces couches après transfert est nettement plus faible qu’obtenue avec le procédé de référence. Nous avons observé (par MET et SIMS) que l’hydrogène se piège dans la couche Si:B, et aux interfaces entre le SiGe et le Si, ce qui suggère que les mécanismes mis en jeu dans ce piégeage sont différents. Nous avons ensuite étudié la redistribution de l’hydrogène après implantation et recuit (par SIMS) ainsi que l’évolution des platelets (par MET) au cours d’un recuit isotherme dans la structure Si/Si:B/Si. En cours de recuit, les platelets formés en dehors de la couche Si:B se dissolvent au profit de ceux, plus grands, formés dans la couche dopée, qui finalement forment des microfissures. Cette croissance est à la base du transfert de l’hydrogène implanté vers la couche piégeante. Cette diffusion est néanmoins lente et tout l’hydrogène implanté n’est finalement pas « pompé » par cette couche piégeante. Un modèle numérique simple a permis de comprendre puis de reproduire qualitativement le phénomène de redistribution observé par SIMS. Ce travail a donc montré que les couches de Si:B sont très prometteuses pour la fabrication de SOI ultrafins. Ce procédé a été optimisé en milieu industriel et une rugosité du film transféré de 2 à 8 Å a été obtenue, ce qui est 10 fois plus faible que la rugosité obtenue avec le procédé Smart CutTM classique. / The development of the advanced microelectronics requires the manufacturing of SOI (Silicon-On-Insulator) wafers with a very thin top Si layer (around 10 nm) and drastic uniformity specification (<+/- 0,5 nm on 300 mm wafers). An interesting way to raise this challenge would be to integrate, in the Smart CutTM technology, modified donors substrates in order to “force” hydrogen to precipitate, during the annealing, in a plane parallel and close to the surface. In this work, we study the potential benefits of the incorporation of thin buried layers of boron doped silicon (Si:B) or SiGe alloy in the donor substrate. We show that Si:B is particularly interesting: fracture is obtained for a lower implanted hydrogen dose and for a lower thermal budget than when using a SiGe buried layer. Moreover, the layer roughness after transfer is obviously lower than that obtained with the reference process. We have shown, using TEM and SIMS, that the mechanisms leading to hydrogen trapping are different in these two types of buried layers. Then, we have studied the hydrogen redistribution after implantation and annealing (by SIMS) and the platelets evolution (by TEM) during isothermal annealing in the Si/Si:B/Si structure. During annealing, the platelets formed outside of the Si:B buried layer dissolved in favor of the ones, larger, formed in the doped layer, which grow and finally form microcracks. This growth results in the transfer of implanted hydrogen towards the trapping layer. Nevertheless, this diffusion is slow and all implanted hydrogen is not finally « pumped » by the trapping layer. A simple numerical model makes it possible to understand then to reproduce qualitatively the redistribution phenomenon observed by SIMS. This work shows that the incorporation of Si:B buried layer in the donor substrate is a very promising technique for the manufacturing of ultrathin SOI. This process was optimized in an industrial environment and transferred films with a post fracture roughness a decade lower compared to the reference process were obtained.

This document addresses problems encountered when establishing the very low air-flow speeds required for experimental investigations of the mechanisms of low-Reynolds-number boundary-layer turbulence. Small-scale motions in the near-wall region are important features of turbulent boundary-layer dynamics, and, if these features are to be resolved by measurements in air with conventionally-sized hot-wire probes, a well-behaved canonical turbulent boundary layer must be developed at free stream flow speeds no higher than 4 m/s. However, at such low speeds, the turbulent boundary layers developed on the walls of a wind tunnel are very susceptible to perturbation by non-turbulent time-dependent flow structures which originate upstream from the test section in the laminar flow at the inlet and in the contraction. Four different non-turbulent flow structures have been identified. The first is a result of quasi-two-dimensional separation of the laminar boundary-layer from the surfaces of the wind-tunnel contraction. Potential flow simulations show that susceptibility to this form of separation is reduced by increasing the degree of axisymmetry in the cross-section geometry and by decreasing the streamwise curvature of the concave surfaces. The second source of time-dependence in the laminar boundary-layer flow is an array of weak streamwise vortices produced by Goertler instability. The Goertler vortices can be removed by boundary-layer suction at the contraction exit. The third form of flow perturbation, revealed by visualisation experiments with streamers, is a weak large-scale forced-vortex swirl produced by random spatial fluctuations of temperature at the wind-tunnel inlet. This can be prevented by thorough mixing of the inlet flow; for example, a centrifugal blower installed at the inlet reduces the amplitude of temperature nonuniformity by a factor of about forty and so prevents buoyancy-driven swirl. When subjected to weak pressure gradients near the start of a wind-tunnel contraction, Goertler vortices in laminar wall layers can develop into three-dimensional separations with strong counter-rotating trailing vortices. These trailing vortices are the fourth source of unsteady flow in the test-section. They can be suppressed by a series of appropriately located screens which remove the low-speed-streak precursors of the three-dimensional separations. Elimination of the above four contaminating secondary flows permits the development of a steady uniform downstream flow and well-behaved turbulent wall layers. Measurements of velocity in the turbulent boundary layer of the test-section have been obtained by hot-wire anemometry. When a hot-wire probe is located within the viscous sublayer, heat transfer from the hot-wire filament to the wall produces significant errors in the measurements of both the mean and the fluctuating velocity components. This error is known as wall-proximity effect and two successful methods are developed for removing it from the hot-wire signal. The first method is based on the observation that, if all experimental parameters except flow speed and distance from the wall are fixed, the velocity error may be expressed nondimensionally as a function of only one parameter, in the form DeltaU^+=f(y^+). The second method, which also accommodates the effect of changing the hot-wire overheat ratio, is based on a dimensional analyis of heat transfer to the wall. Velocity measurements in the turbulent boundary layer at the mid-plane of a nearly square test-section duct have established that, when the boundary-layer thickness is less than one quarter of the duct height, mean-velocity characteristics are indistinguishable from those of a two-dimensional flat-plate boundary layer. In thicker mid-plane boundary layers, the mean-velocity characteristics are affected by stress-induced secondary flow and by lateral constriction of the boundary-layer wake region. A significant difference between flat-plate and duct boundary layers is also observed in momentum-balance calculations. The momentum-integral equation for a duct requires definitions of momentumd and displacement thickness which are different from those given for flat-plate boundary layers. Momentum-thickness growth rates predicted by the momentum-integral equation for a duct agree closely with measurements of the newly defined duct momentum thickness. Such agreement cannot be obtained in terms of standard flat-plate momentum thickness. In duct boundary layers with Reynolds numbers Re_theta between 400 and 2600, similarity in the wake-region distributions of streamwise turbulence statistics has been obtained by normalising distance from the wall with the flat-plate momentum thickness, theta_2. This result indicates that, in contrast with the mean velocity characteristics, the structure of mid-plane turbulence does not depend on the proportion of duct cross-section occupied by boundary layers and is essentially the same as in a flat-plate boundary layer. For Reynolds numbers less than 400, both wall-region and wake-region similarity fail because near-wall turbulence events interact strongly with the free stream flow and because large scale turbulence motions are directly influenced by the wall. In these conditions, which exist in both duct and flat-plate turbulent boundary layers, there is no distinct near-wall or wake region, and the behaviour of turbulence throughout the boundary layer depends on both wall variables and on outer region variables simultaneously. / Thesis (Ph.D.)--School of Mechanical Engineering, 1998.

Cette thèse examine deux façons de diminuer la complexité des problèmes de propagation d'ondes diffractées par un obstacle borné : la diminution des domaines de calcul à l'aide de milieux fictifs absorbants permettant l'adjonction de conditions aux limites exactes et la recherche d'une nouvelle approximation spatiale sous forme polynomiale donnant lieu à des schémas explicites où la stabilité est indépendante de l'ordre choisi. Dans un premier temps, on réduit le domaine de calcul autour de domaines non nécessairement convexes, mais propres aux problèmes de scattering (non trapping), à l'aide de la méthode des Perfectly Matched Layers (PML). Il faut alors considérer des domaines d'exhaustion difféomorphes à des convexes avec des hypothèses "presque" nécessaires. Pour les Equations de type Maxwell et Ondes, l'existence et l'unicité sont montrées dans tout l'espace et en domaine artificiellement borné, tant en fréquentiel qu'en temporel. La décroissance est analysée localement et asymptotiquement et des simulations numériques sont proposées. La deuxième partie de ce travail est une alternative à l'approximation de type Galerkin Discontinu, inspirée des résultats de régularité de J. Rauch, présentant l'avantage de conserver une condition CFL de type Volumes Finis indépendante de l'ordre d'approximation, aussi bien pour des maillages structurés que déstructurés. La convergence de cette méthode est démontrée via la consistance et la stabilité, grâce au théorème d'équivalence de Lax-Richtmyer pour des domaines structurés. En déstructuré, la consistance ne pouvant plus s'établir au moyen de la formulation de Taylor, la convergence n'est plus assurée, mais les premiers tests numériques bidimensionnels donnent d'excellents résultats.

<p>Saab Microwave Systems, SMW is a supplier of radar systems. The circuit boards that are operating in their radars have components which solder joints contains lead. However, the EU directive RoHs and WEEE are causing SMW to prepare for a transition to lead free solder joints. The objective of this thesis is to gain deeper knowledge of lead free solder joints.</p><p>Brittle fractures in solder joints is a type of failure that might increase in a transition to lead free solder joints. The brittle fractures are induced by the creation of the intermetallic phases which are formed during soldering. The amount and composition of the intermetallics affects the mechanical strength of the joint. An intermetallic layer is thickened during heat exposure as during soldering, thermal aging and rework.</p><p>The focus of this thesis was to investigate how rework affect the brittleness of the lead free solder joint and thereby how the intermetallic layers change depending on chemical composition, design and reflow cycles. Two types of components and two types of solder materials (SnPb and SAC305) were studied.</p><p>To study the mechanical properties of the joint a shear testing device was used. This is a way of measuring the reliability of the joint when subjected to mechanical shock. The intermetallic layers were examined in a Scanning Electron Microscope and the fracture surfaces were studied in a optical microscope, a scanning electron microscope and a stereomicroscope. The heat spread over the board where examined by soldering thermocouples to the board and plotting the values of time and temperature.</p><p>The results showed that the rework process did not have any significant impact of the intermetallic growth. The adjecent and distant components were not damaged during rework. A lead free rework process can therefor be preformed successfully at SMW. The intermetallic layers formed at the interface between the a lead free solder and a nickel finish grew faster than an intermetallic layer formed between a leaded solder and a nickel finish. The presence of nickel could therefore have a more negative effect on the intermetallic growth rate for the lead free material compared to the leaded.</p>

The perfectly matched layer (PML) is a novel technique to simulate the absorption of waves in unbounded domains. The underlying equations are often a system of second order hyperbolic partial differential equations. In the numerical treatment, second order systems are often rewritten and solved as first order systems. There are several benefits with solving the equations in second order formulation, though. However, while the theory and numerical methods for first order hyperbolic systems are well developed, numerical techniques to solve second order hyperbolic systems are less complete. We construct a strongly well-posed PML for second order systems in two space dimensions, focusing on the equations of linear elasto-dynamics. In the continuous setting, the stability of both first order and second order formulations are linearly equivalent. We have found that if the so-called geometric stability condition is violated, approximating the first order PML with standard central differences leads to a high frequency instability at most resolutions. In the second order setting growth occurs only if growing modes are well resolved. We determine the number of grid points that can be used in the PML to ensure a discretely stable PML, for several anisotropic elastic materials. We study the stability of the PML for problems where physical boundaries are important. First, we consider the PML in a waveguide governed by the scalar wave equation. To ensure the accuracy and the stability of the discrete PML, we derived a set of equivalent boundary conditions. Second, we consider the PML for second order symmetric hyperbolic systems on a half-plane. For a class of stable boundary conditions, we derive transformed boundary conditions and prove the stability of the corresponding half-plane problem. Third, we extend the stability analysis to rectangular elastic waveguides, and demonstrate the stability of the discrete PML. Building on high order summation-by-parts operators, we derive high order accurate and strictly stable finite difference approximations for second order time-dependent hyperbolic systems on bounded domains. Natural and mixed boundary conditions are imposed weakly using the simultaneous approximation term method. Dirichlet boundary conditions are imposed strongly by injection. By constructing continuous strict energy estimates and analogous discrete strict energy estimates, we prove strict stability.

No description available.