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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
271

Influência da forma de seção transversal no confinamento de pilares de concreto armado encamisados com PRFC (polímero reforçado com fibras) / Influence of the cross section shape in the confinement of jacketed reinforced concrete columns with CFRP (carbon fiber reinforced polymer)

Alexandre Luis Sudano 31 May 2005 (has links)
O efeito de confinamento do concreto em pilares submetidos à compressão axial traz diversos benefícios ao seu comportamento estrutural, dentre os quais destacam-se o aumento na resistência à compressão axial do concreto pela ação das pressões laterais, e a melhoria da ductilidade do elemento estrutural. Em função destas vantagens, o confinamento é uma das principais técnicas de reforço de pilares de concreto. Porém, dependendo da forma da seção transversal, a eficiência do reforço pode ficar comprometida em função da distribuição da pressão de confinamento. No caso de pilares de seção circular, esta distribuição é uniforme. Já em pilares de seção quadrada e retangular, existe concentração de tensão nos cantos da seção transversal, o que, no caso de reforço por encamisamento com PRFC, pode causar a ruptura prematura da camisa, resultando num reforço ineficiente. Com o intuito de considerar as diferentes configurações da distribuição da pressão de confinamento, utiliza-se um coeficiente de forma, que em seções diferentes da circular (para a qual este coeficiente é igual à unidade), minora o valor da pressão de confinamento, o qual é utilizado na previsão da carga de ruptura do pilar reforçado. Este trabalho tem como objetivo central o estudo de vários tipos de seção transversal com o intuito de avaliar a sua influência na eficiência do reforço e da ductilidade do elemento estrutural. Para tal, foram realizadas simulações experimentais com pilares de seção transversal circular, quadrada e retangular com os cantos arredondados, elíptica e uma seção composta por semicírculos. Os resultados demonstram que uma forma de seção transversal adequada é essencial para um bom desempenho do pilar reforçado, sendo assim, as seções transversais que apresentaram os melhores resultados foram a circular, a elíptica e a composta por semicírculos / The effect of the concrete confinement in columns submitted to the axial compression brings many benefits to its structural behavior, amongst them the increase of the axial compressive strength due to the action of the lateral pressures and the improvement of the ductility. In function of these advantages, the confinement is one of the main techniques for strengthening of concrete columns. However, depending on the shape of the cross section, the efficiency of the reinforcement can be impaired by the non-uniformity of the confinement pressure distribution. In the case of circular cross section columns, this distribution is uniform. Otherwise, in square and rectangular cross section columns, there is a pressure concentration at the cross section corners. In case of CFRP jackets, the pressure concentration leads to a premature rupture of the jacket, resulting in an inefficient reinforcement. Intending to consider the different confinement pressure distributions, a shape coefficient is applied to cross sections with distinguished shape from the circular one (for which this coefficient is equal to the unit), to correct the confinement pressure value. The corrected pressure is applied in theoretical evaluations of the column’s load carrying capacity. The main objective of work is to analyze the structural behavior of strengthened concrete columns with different shape cross-sections, evaluating the influences in the efficiency of the jacketing and in the ductility of the structural element. Experimental simulations were made in columns with the following cross section shapes: circular, square and rectangular with rounded corners, elliptical and a section composed by semicircles. The results demonstrated that an adequate shape of the cross-section is essential for a good performance of the strengthened columns. The cross sections that presented the best results were the circular, the elliptical and the one composed by semicircles
272

Comportamento mecânico do poliuretano derivado de óleo de mamona reforçado por fibra de carbono: contribuição para o projeto de hastes de implante de quadril. / Mechanical behavior of carbon fiber reinforced polyurethane derived from castor oil: contribution for the design of hip implant stems.

Geraldo Dantas Silvestre Filho 27 July 2001 (has links)
Utilizando-se um poliuretano derivado de óleo de mamona desenvolvido para implantes ósseos, aonde este vem demonstrando ser biocompatível e apresentando características fisico-químicas semelhantes às dos ossos, estuda-se o comportamento mecânico deste material quando reforçado por fibra de carbono, juntamente com uma metodologia de fabricação de hastes de implante de quadril. Avaliou-se o efeito da fração volumétrica em fibra nas propriedades mecânicas do compósito, bem como, a influência da realização de um tratamento superficial da fibra de carbono por método químico, visando melhorar a adesão interfacial fibra/matriz. Foram realizados ensaios mecânicos nos corpos de prova em compósitos e nas hastes fabricadas para avaliar a resistência mecânica sob carregamentos quase-estáticos. Também foram realizadas simulações computacionais da haste, juntamente com o dispositivo de ensaio projetado, para comparação com os resultados experimentais. Para isto, utilizou-se o programa ANSYS®, que é um sistema de engenharia auxiliado por computador (Computer Aided Engineering - CAE) e utiliza o Método dos Elementos Finitos como ferramenta de análise estrutural. Resultados satisfatórios foram obtidos nos ensaios mecânicos do poliuretano reforçado por fibra de carbono, viabilizando sua aplicação no projeto de hastes de implante de quadril. / The polyurethane derived from castor oil has demonstrated excellent biocompatibility and similarity to the physical and chemical properties of the human bone. In order to use this material in the design of hip implant stems, this work investigates its mechanical behavior when reinforced by carbon fibers. A manufacturing methodology for hip implant stems is also proposed and validated. The effects of fiber volume fraction and superficial treatments on the carbon fibers are evaluated in terms of the mechanical properties of the polyurethane and of the composite. Mechanical tests were performed in the manufactured stems to evaluate the strength under quasi-static loading. Computational simulations of the stem and testing devices were also performed by using the Finite Element Method and the commercial package ANSYS®. The results obtained are quite satisfactory which validates the application of the carbon fiber reinforced polyurethane in hip implant stems.
273

Análise numérica e experimental de falhas em juntas de materiais compósitos tipo single-lap fixadas por parafusos escareados / Numerical and experimental analysis of a single lap countersunk composite fastened joint

Kim Martineli Souza Gonçalves 03 June 2015 (has links)
Este trabalho trata das falhas que podem ocorrer em uniões e juntas de materiais compósitos unidas mecanicamente por parafusos. O compósito de fibra de carbono (tecido) embutido em resina epoxy foi estudado neste trabalho devido ao amplo uso em estruturas de vários segmentos da indústria. O trabalho apresenta vários critérios de falha, demonstrando as vantagens e desvantagens de cada um para materiais compósitos. A fabricação dos corpos de provas e os ensaios necessários para obtenção de parâmetros e validação de estruturas são descritos. A resistência da junta mostrou-se muito menor do que a da estrutura de compósito, demonstrando a importância de estudos assim. Criou-se um modelo numérico utilizando critérios de falhas como o critério de Hashin e o de máxima tensão. Os resultados da simulação de elementos finitos tiveram uma boa relação com os ensaios experimentais e o modelo foi então validado e considerado representativo. / This work shows failures that can occur in composite mechanically fastened joints. The composite carbon fiber embedded in epoxy resin, used in this study, was chosen due to it\'s wide use in structures of any segment of the industry. Many failure criteria, showing the advantages and disadvantages for each, regarding composite structures are presented in this work. Test specimens\' manufacturing is described along with required tests for parameter definition and structures validation. The countersunk fastened joint strength is much lower than the composite structure itself, demonstrating the necessity of studies like this. A numerical model using criteria like Hashin and maximum stress was created. The finite elements\' simulation results had a close response to the experimental results and the model was validated and considered representative.
274

Définition des indicateurs clés de performance et évaluation multicritère de filières durables de recyclage des polymères renforcés de fibres de carbone issus de l’industrie aéronautique / Definition of key sustainability performance indicators and multicriteria evaluation of recycling sector for carbon fiber reinforced polymers from the aerospace industry

Pillain, Baptiste 30 June 2017 (has links)
La consommation globale de plastique renforcé de fibres de carbone (PRFC) est en constante augmentation, ce qui induit la nécessité de créer un secteur de recyclage capable de traiter l’ensemble des fibres de carbone actuellement consommées et qui représente la quantité de déchets à traiter en devenir. Cette thèse porte sur le développement et l'application d’une méthodologie d’évaluation multicritère du développement durable pour la création d’une filière de recyclage des plastiques renforcés de fibres de carbone (PRFC) issus du secteur aéronautique, mais aussi des autres secteurs consommateurs de fibres de carbone tels que l’automobile et l’éolien. Cette méthodologie a pour but d’identifier les indicateurs les plus pertinents ainsi que les méthodes qui leurs sont associés, c'est-à-dire qu’elle vise à la création et l’adaptation d’indicateurs clé de performance du développement durable pour caractériser au mieux les impacts environnementaux et sociaux-économique de cette filière de recyclage. Le résultat final de ce travail est la création d’une méthodologie d’évaluation du développement durable dédiée à la filière de recyclage des fibres de carbone par la considération des différents aspects de celui-ci. Cette méthodologie, aidant à l’identification et la définition des indicateurs clé de performances du développement durable peut être aussi appliquée à d’autres secteurs souhaitant s’implanter en suivant les principes de ce développement. / The global consumption of carbon-fiber reinforced plastic (CFRP) is constantly growing since the last decade, leading to the need to create a recycling sector able to manage the amount of carbon fibers currently consumed and representing the amount of waste to be treated in the future. This thesis focus on the creation of a methodology for evaluating the sustainability potential for the implementation of a carbon fiber reinforced plastics recycling (CFRP) sector. CFRP coming from the aeronautics sector as well as other sectors such as the automobile and wind-energy industries. This methodology aims at identifying the most relevant indicators and associated methods, but also aims at the creation and adaptation of indicators to best assess the environmental and socioeconomic impacts of this recycling sector. The final result of this work, is the creation of a sustainability assessment methodology dedicated to the carbon fiber recycling sector, considering the different sustainability pillars. However this methodology also define more widely a tool that helps to identify sustainability performance indicators and that can be applied to other sectors if necessary.
275

Influence of metal ions on lignin-based carbon fiber quality

Andersson, Sofia January 2017 (has links)
Carbon fiber is a lightweight, versatile material with many current and potential applications. To be able to expand the market for carbon fiber composites in other areas than special applications the production costs must be reduced. One way of accomplishing this could be to use a less expensive raw material where lignin is a good example as it can be provided at lower cost, is renewable and abundantly available compared to commercially used raw materials today. So far, the mechanical properties of lignin-based carbon fibers are inferior relative to commercial carbon fibers. For lignin-based carbon fibers to enter the commercial market more research is necessary to gain knowledge of the conversion of lignin to carbon fiber. The LightFibre project investigates the possibilities to produce carbon fibers based on a mixture of softwood kraft lignin and cellulose. The kraft lignin is isolated from black liquor in the kraft/sulfate process with the LignoBoost process. This master thesis project was conducted within in the LightFibre project and evaluated whether metal ions generally present in kraft lignin had an influence on the final carbon fiber quality in terms of mechanical properties and morphology. The mechanical properties were determined with tensile testing, the morphology by scanning electron microscopy (SEM) and the relative abundance of studied elements with electron dispersive spectroscopy (EDS). The influence of the chosen metal ions was tested by impregnation of dry-jet wet spun prefibers based on 70 wt.% softwood kraft lignin and 30 wt.% dissolving pulp cellulose. The fibers were impregnated in room temperature with solutions containing Na2SO4, K2SO4, MgSO4, FeSO4 and Al2(SO4)3 salts where the cations were the focus in these trials. The concentrations used for impregnation were 0.2 and 1M of the cations. The obtained mechanical properties of the carbon fibers of the samples impregnated with different metal ions did not deviate significantly from the reference which had a tensile strength of 870 MPa and tensile modulus of 68 GPa. The analysis of morphology with SEM showed no defects or damage of any of the fibers. Therefore, it was concluded that the impregnated metal ions: K+, Na+, Al3+, Mg2+ and Fe2+ at the obtained levels in the fibers cause no effects on the fibers during the stabilization and carbonization that affects the mechanical performance of final carbon fiber.  The amount of potassium in one of the samples was estimated to 0.1 wt.%. From the results of this study it may be suggested that the general recommendation of <0.1 wt.% ash in lignin can be exceeded, for dry-jet wet-spun kraft lignin/cellulose-based carbon fibers.
276

Contribution à l’étude de la résistance à la compression de stratifiés composites à fibres de carbone haut module : cas de chargements statiques et cycliques. / A contribution to the study of the resistance to compression of high modulus carbon fiber reinforced polymer : static and cyclic loading case studies.

Méchin, Pierre-Yves 30 January 2017 (has links)
Cette thèse est une contribution à la compréhension du comportement des composites carbone-époxy en compression par l’étude de l’influence des constituants (fibres et matrices). L’incidence d’un chargement mécanique d’amplitude constante ou variable sur la durabilité est étudiée et un modèle numérique permettant la prédiction de la résistance résiduelle est proposé. Une première partie des travaux s’intéresse aux mécanismes spécifiques engagés dans la résistance en compression. Un modèle analytique est retenu pour une confrontation expérimentale. Ce modèle propose de considérer d’une part le micro-flambage de la fibre comme contenu par le comportement en cisaillement de la matrice (Budiansky et Fleck, 1993). En complément, une partie supplémentaire de structure considérant, entre autres, l’influence du gradient de déformation induit dans une sollicitation en flexion 4 points est étudiée (Grandidier, 2002). Afin de valider la pertinence du modèle, une campagne expérimentale est menée sur six matrices époxy différentes (de fragile à ductile) dans des empilements stratifiés monolithiques identiques réalisés en cuisson autoclave. Ces résultats ont permis de valider la capacité du modèle à prédire l’influence de la rigidité de la matrice sur la résistance en compression. Le partie micro-flambage est validée pour la prise en compte de la matrice. La partie effet de structure (gradient ici) est validée par une comparaison avec des résultats supplémentaires obtenus sur des éprouvettes sandwich sollicitées en flexion. Ces dernières éprouvettes ont fait l’objet d’une conception spécifique afin de favoriser la rupture en compression pure (sans gradient de déformation). Une seconde partie est consacrée à l’étude de la durabilité en compression. Une campagne expérimentale d’essais de fatigue est menée en flexion 4 points sur les éprouvettes sandwich précédemment conçues. Les essais sont conduits à une fréquence de 10 Hz et différents rapports de charge dans une optique de dégager l’évolution de la résistance résiduelle. Un modèle numérique de changement d’échelles (stratifié, plis, constituants) est parallèlement développé, basé sur la dégradation et la plasticité de la matrice. On fait l’hypothèse de simplicité thermo-rhéologique de la matrice pour établir des courbes de maitresses à partir d’une série d’essais identifiés (fluage, relaxation, fatigue…). On utilise les propriétés résiduelles du pli (rigidité, résistance) pour estimer un indicateur d’endommagement. Ce dommage est répercuté dans les propriétés de la matrice au moyen d’une loi de dégradation linéaire. Une loi de cumul de dommage de type Miner est alors introduite pour tenir compte de la variabilité des chargements appliqués. Un solveur micro- mécanique est développé pour extraire le comportement non-linéaire du pli en cisaillement tenant compte de la dégradation. Ce comportement est paramétré par une loi de Ramberg-Osgood utilisée dans le modèle analytique validé précédemment. Les travaux des deux parties permettent donc la mise en place d’un outil de prédiction de la résistance résiduelle des plis sollicités dans un chargement biaxial plan, avec en particulier le traitement de la compression / This PhD dissertation is a contribution to the modelling of Carbon-Fiber-Epoxy-Polymer laminates, undergoing specifically compression loadings, according to components. The aim is to build a design tool for composites structures taking into account this compression specificity for dimensioning racing yachts parts (masts, daggerboards, foils), which is the expertise of HDS/GSea-Design, the company associated to this work. Emphasis was put on the influence of linear or non-linear properties of each phase by varying the type of fibre (from high stiffness to high strength) and the type of matrix (from brittle to ductile). The effect of a mechanical loading, static, constant (creep, relaxation) or variable (fatigue) on durability is studied and a numerical model for predicting the residual strength is proposed. The first part of this work deals with the mechanisms involved in compressive strength. An analytical model is used for an experimental validation. It considers a contribution linked to the micro-buckling of the fibre as contained by the shear behaviour of the matrix (Budiansky et Fleck [1993]). It considers also a contribution of the deformation gradient induced for instance in a bending loading (Gardin et al. [2002]). To validate this model, an experimental campaign was conducted on six different epoxy matrices (from brittle to ductile) on identical monolithic stackings processed in autoclave. The results allowed the validation of the model capability to predict the influence of the matrix stiffness on the compressive strength of unidirectional laminas. Taking into account the matrix behaviour validates the micro-buckling contribution. Regarding the deformation gradient contribution, it is validated through a comparison using additional experimental results on sandwich samples in bending. The latter samples were specifically designed to favour a pure compression fracture (without any deformation gradient). The second part examines durability in compression. Another experimental campaign with fatigue tests was conducted with four points bending tests on the same sandwich samples. Experiments were carried out at 10 Hz and different load ratios were used to study their influence on the compressive residual strength. A numerical model involving different scales (laminate, laminas, fibres and matrix) is developed in parallel (Huang et al. [2012a]), based on the degradation and the plasticity of the matrix. The assumption of thermo-rheological simplicity of the matrix is made to build master curves from dedicated experiments (creep, relaxation). We then use the residual properties (stiffness, strength) of the ply to estimate a damage level. This latter parameter is used to modify the elastic stiffness of the matrix with a linear law. A Miner-type cumulative law is used in fatigue to take into account the different possible loadings. A micro-mechanical solver is developed to extract the non-linear shear behaviour of the ply accounting for this degradation. This behaviour is described by a Ramberg-Osgood law used in the analytical model described in the first part of this work. The joint contributions of these two parts allowed us to program a numerical tool for predicting the residual strength of plies undergoing a biaxial in- plane loading, being monotonous, constant or with a variable amplitude, with emphasis on the particular case of compression loading.
277

MENs Doped Adhesive and Influence on Fracture Toughness

Yang, Kao Z 31 March 2016 (has links)
Composites are in high demand; however, fasteners are often required for joining process and can reduce their advantages. One solution is adhesive bonding, but uncertainty exists regarding long term durability and the ability to interrogate bonds noninvasively. One potential solution to qualify bond integrity over its service life is to dope an adhesive with magneto-electric nanoparticles (MENs). MENs can yield output magnetic signatures that are influenced by bond quality and damage state. In this study, adhesives have been doped with MENs prior to bonding at 1% volume concentration. For optimum implementation, this health monitoring system should be evaluated for effects of the MENs on the mechanical properties. Lap-shear testing was conducted to assess changes in the bond strength from addition of the nanoparticles. End-notched flexure (ENF) tests were also conducted for fracture mechanism evaluation. Results showed an increase of 12% in shear strength as a function of MENs loading concentration. In addition, a feasibility study of output magnetic signature as a function of elevated temperature and humidity were evaluated for MENs doped and un-doped adhesives. Results gave an order of magnitude change in magnetic signal as a function of exposure time.
278

Innovative Modular High Performance Lightweight Decks for Accelerated Bridge Construction

Ghasemi, Sahar 13 November 2015 (has links)
At an average age of 42 years, 10% of the nation’s over 607,000 bridges are posted for load restrictions, with an additional 15% considered structurally deficient or functionally obsolete. While there are major concerns with decks in 75% of structurally deficient bridges, often weight and geometry of the deck further limit the load rating and functionality of the bridge. Traditional deck systems and construction methods usually lead to prolonged periods of traffic delays, limiting options for transportation agencies to replace or widen a bridge, especially in urban areas. The purpose of this study was to develop a new generation of ultra-lightweight super shallow solid deck systems to replace open grid steel decks on movable bridges and as well serve as a viable alternative in bridge deck replacements across the country. The study has led to a lightweight low-profile asymmetric waffle deck made with advanced materials. The asymmetry comes from the arrangement of primary and secondary ribs, respectively perpendicular and parallel to the direction of traffic. The waffle deck is made with ultrahigh performance concrete (UHPC) reinforced with either high-strength steel (HSS) or carbon fiber reinforced polymer (CFRP) reinforcement. With this combination, the deck weight was limited to below 21 psf and its overall depth to only 4 inch, while still meeting the strength and ductility demands for 4 ft. typical stringer spacing. It was further envisioned that the ultra-high strength of UHPC is best matched with the high strength of HSS or CFRP reinforcement for an efficient system and the ductile behavior of UHPC can help mask the linear elastic response of CFRP reinforcement and result in an overall ductile system. The issues of consideration from the design and constructability perspectives have included strength and stiffness, bond and development length for the reinforcement, punching shear and panel action. A series of experiments were conducted to help address these issues. Additionally full-size panels were made for testing under heavy vehicle simulator (HVS) at the accelerated pavement testing (APT) facility in Gainesville. Detailed finite element analyses were also carried out to help guide the design of this new generation of bridge decks. The research has confirmed the superior performance of the new deck system and its feasibility.
279

Fatigue Damage Characterization Of Carbon/Epoxy Laminates Under Spectrum Loading

Sudha, J 01 1900 (has links) (PDF)
Fibre Reinforced Polymer Composites are extensively used in aircraft structures because of its high specific stiffness, high specific strength and tailorability. Though Fibre Reinforced Polymers offer many advantages, they are not free from problems. The damage of different nature, e.g., service mechanical damages, fatigue damage or environmental damage can be observed during operating conditions. Among all the damages, manufacturing or service induced, delamination related damage is the most important failure mechanisms of aircraft-composite structures and can be detrimental for safety. Delamination growth under fatigue loading may take place due to local buckling, growth from free edges and notches such as holes, growth from ply-drops and impact damaged composites containing considerable delamination. Delamination growth can also occur due to interlaminar stresses, which can arise in complex structures due to unanticipated loading. The complex nature of composite failure, involving different failure modes and their interactions, makes it necessary to characterize/identify the relevant parameters for fatigue damage resistance, accumulation and life prediction. An effort has been made in this thesis to understand the fatigue behavior of carbon fibre reinforced epoxy laminates under aircraft wing service loading conditions. The study was made on laminates with different lay-up sequences (quasi-isotropic and fibre dominated) and different geometries (plain specimen, specimen with a hole and ply-drop specimen). The fatigue behaviour of the composite was analyzed by following methods: . Ultrasonic C-Scan was used to characterize the delamination growth. . Dynamic Mechanical Analysis (DMA) was done to study the interfacial degradation due to fatigue loading. In this analysis, the interfacial strength indicator and interfacial damping were calculated. The DMA also provides the storage modulus degradation under fatigue loading. . Scanning electron microscope examination was carried out to understand the fatigue damage mechanisms. . A semi-empirical phenomenological model was also used to estimate the residual fatigue life. This research work reveals that the Carbon Fibre Reinforced Polymer laminates are in the safe limit under service loading conditions, except the specimen with a hole. The specimen with a hole showed delaminations around the hole due to stress concentration and higher interlaminar stresses at the hole edges and this delamination is found to be associated with fibre breakage and fibre pullout. The quasi-isotropic laminate is found to show poorer fatigue behaviour when compared to fibre dominated laminate and ply-drop also shows poor performance due to high stress concentration in the ply-drop region.
280

Análise numérica e experimental de falhas em juntas de materiais compósitos tipo single-lap fixadas por parafusos escareados / Numerical and experimental analysis of a single lap countersunk composite fastened joint

Gonçalves, Kim Martineli Souza 03 June 2015 (has links)
Este trabalho trata das falhas que podem ocorrer em uniões e juntas de materiais compósitos unidas mecanicamente por parafusos. O compósito de fibra de carbono (tecido) embutido em resina epoxy foi estudado neste trabalho devido ao amplo uso em estruturas de vários segmentos da indústria. O trabalho apresenta vários critérios de falha, demonstrando as vantagens e desvantagens de cada um para materiais compósitos. A fabricação dos corpos de provas e os ensaios necessários para obtenção de parâmetros e validação de estruturas são descritos. A resistência da junta mostrou-se muito menor do que a da estrutura de compósito, demonstrando a importância de estudos assim. Criou-se um modelo numérico utilizando critérios de falhas como o critério de Hashin e o de máxima tensão. Os resultados da simulação de elementos finitos tiveram uma boa relação com os ensaios experimentais e o modelo foi então validado e considerado representativo. / This work shows failures that can occur in composite mechanically fastened joints. The composite carbon fiber embedded in epoxy resin, used in this study, was chosen due to it\'s wide use in structures of any segment of the industry. Many failure criteria, showing the advantages and disadvantages for each, regarding composite structures are presented in this work. Test specimens\' manufacturing is described along with required tests for parameter definition and structures validation. The countersunk fastened joint strength is much lower than the composite structure itself, demonstrating the necessity of studies like this. A numerical model using criteria like Hashin and maximum stress was created. The finite elements\' simulation results had a close response to the experimental results and the model was validated and considered representative.

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