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Void content computation using optical microscopy for carbon fiber composites / Beräkning av kavitetshalter för kolfiberkompositer med optisk mikroskopiFanni, Saman January 2020 (has links)
Three different void content calculation techniques using optical microscopy werecompared in multiple-user trials. The three methods studied comprised of a selection,thresholding, and semi-automatic machine learning method. The techniques wereapplied to micrographs of three carbon fiber-epoxy composite plates manufacturedin-house, where one plate had reduced void content by means of debulking priorto curing. The users performed the techniques on the sets of micrographs and thestandard deviation between the users void content results were measured.The advantages of the three methods were discussed and their practical applications wereproposed. The trials showed agreement between users on what are voids and not as well asshowing that uncertainties in void content are specimen-specific and not attributed todifferent users or methods applied. All three methods showed satisfying precision incalculating void content compared to void content quality levels provided by literature.It was found that thresholding, which is the current standard method of void contentcalculation using microscopy, inhabits an unscientific bias which compromises the legitimacyof the method. The study formulates a manual selection-based method usingedge-detection selection tools intended to benchmark void content in images, as wellas proposing a route to the automation of void content analysis using microscopy. / Tre olika beräkningstekniker för kavitetshalter med hjälp av mikroskopi jämfördes genom fleranvändar-tester. De tre metoderna innefattade en selektions-metod, tröskelvärdesmetod, och en övervakad maskininlärningsmetod. Metoderna applicerades på mikrografer av tre kolfiber-epoxi kompositplattor tillverkade internt, varav en platta hade reducerad kavitetshalt genom en avbulkningsprocess innan härdning. Användarna genomförde metoderna på mikrograferna och standardavvikelsen mellan användarnas resulterande kavitetshalter mättes. För- och nackdelarna hos de tre metoderna diskuterades och deras praktiska applikationer föreslogs. Testerna visade en överensstämmelse mellan användare om vad som omfattar kaviteter och inte, samt en påvisning på att osäkerheter kring kavitetshalter är provbitberoende och inte användar- eller metodberoende. Alla tre metoder uppvisade en tillfredsställande precision i kavitethaltsberäkning jämfört med kvalitetsnivåer av kavitethalter erhållna från litteratur. Det konstaterades att tröskelvärdesmetoden, vilket är nuvarande standardmetoden för kavitethaltsberäkning med mikroskopi, innehar en bias som sätter validiteten av metoden i fråga. Studien formulerar även en manuell selektions-metod som använder selektions-verktyg för randdetektering, ämnad för att hitta referensvärden för kavitetshalter. Förslag ges även kring tillvägagångssättet till att uppnå automatiserade metoder för kavitethaltsberäkning.
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Multiple Wave Scattering and Calculated Effective Stiffness and Wave Properties in Unidirectional Fiber-Reinforced CompositesLiu, Wenlung 05 August 1997 (has links)
Analytic methods of elastic wave scattering in fiber-reinforced composite materials are investigated in this study to calculate the effective static stiffness (axial shear modulus, m) and wave properties (axially shear wave speed, B and attenuation, Y) in composites. For simplicity only out-of-plane shear waves are modeled propagating in a plane transverse to the fiber axis. Statistical averaging of a spatially random distribution of fibers is performed and a simultaneous system of linear equations are obtained from which the effective global wave numbers are numerically calculated. The wave numbers, K=Re(K)+iIm(K), are complex numbers where the real parts are used to compute the effective axial shear static stiffness and wave speed; the imaginary parts are used to compute the effective axial shear wave attenuation in composites.
Three major parts of this study are presented. The first part is the discussion of multiple scattering phenomena in a successive-events scattering approach. The successive-events scattering approach is proven to be mathematically exact by comparing the results obtained by the many-bodies-single-event approach. Scattering cross-section is computed and comparison of the first five scattering orders is made. Furthermore, the ubiquitous quasi-crystalline approximation theorem is given a justifiable foundation in the fiber-matrix composite context. The second part is to calculate m, B and Y for fiber-reinforced composites with interfacial layers between fibers and matrix. The material properties of the layers are assumed to be either linearly or exponentially distributed between the fibers and matrix. A concise formula is obtained where parameters can be computed using a computationally easy-to-program determinant of a square matrix. The numerical computations show, among other things, that the smoother (more divisional layers), or thinner, the interfacial region the less damped are the composite materials. Additionally composites with exponential order distribution of the interfacial region are more damped than the linear distribution ones. The third part is to calculate m, B and Y for fiber-reinforced composites with interfacial cracks. The procedures and computational techniques are similar to those in the second part except that the singularity near the crack tip needs the Chebychev function as a series expansion to be adopted in the computation.
Both the interfacial layers and interfacial crack cases are analyzed in the low frequency range. The analytic results show that waves in both cases are attenuated and non-dispersive in the low frequency range. The composites with interfacial layers are transversely isotropic, while composites with interfacial cracks are generally transversely anisotropic. / Ph. D.
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Deformations of Piezoceramic-Composite ActuatorsJilani, Adel Benhaj 06 January 2000 (has links)
In the past few years a new class of layered piezoceramic and piezoceramic-composite actuators, known as RAINBOW and GRAPHBOW, respectively, that are capable of achieving 100 times greater out-of-plane displacements than previously available has been developed. Prior to the development of RAINBOW and GRAPHBOW, large stacks of piezoelectric actuators, requiring complicated electronic drive circuits, were necessary to achieve the displacement now possible through the use of a single RAINBOW actuator. The major issues with both RAINBOW and GRAPHBOW are the prediction of their room-temperature shapes after processing, and their deformation response under application of electric field.
In this research, a methodology for predicting the manufactured shapes of rectangular and disk-style RAINBOW and GRAPHBOW is developed. All of the predictive analyses developed are based on finding approximate displacement responses that minimize the total potential energy of the devices through the use of variational methods and the Rayleigh-Ritz technique. These analyses are based on classical layered plate theory and assumed the various layers exhibited linear elastic, temperature-independent behavior. Geometric nonlinearities are important and are included in the strain-displacement relations. Stability of the predicted shapes is determined by examining the second variation of the total potential energy. These models are easily modified to account for the deformations induced by actuation of the piezoceramic.
The results indicate that for a given set of material properties, rectangular RAINBOW can have critical values of sidelength-to-thickness ratio (Lx/H or Ly/H) below which RAINBOW exhibits unique, or single-valued, spherical or domed shapes when cooled from the processing temperature to room temperature. For values of sidelength-to-thickness ratio greater than the critical value, RAINBOW exhibits multiple room-temperature shapes. Two of the shapes are stable and are, in general, near-cylindrical. The third shape is spherical and is unstable. Similarly, disk-style RAINBOW can have critical values of radius-to-thickness ratios (R/H) below which RAINBOW exhibits axisymmetric room-temperature shapes. For values of R/H greater than the critical value, disk-style RAINBOW exhibits two stable near-cylindrical shapes and one unstable axisymmetric shape. Moreover, it is found that for the set of material properties used in this study, the optimal reduced layer thickness would be at 55%, since the maximum change in curvature is achieved under the application of an electric field, while the relationship between the change in curvatures and the electric field is kept very close to being linear. In general, good agreement is found for comparisons between the predicted and manufactured shapes of RAINBOW. A multi-step thermoelastic analysis is developed to model the addition of the fiber-reinforced composite layer to RAINBOW to make GRAPHBOW. Results obtained for rectangular RAINBOW indicate that if the bifurcation temperature in the temperature-curvature relation is lower than the composite cure temperature, then a unique stable GRAPHBOW shape can be obtained. If the RAINBOW bifurcation temperature is above the composite cure temperature, multiple room-temperature GRAPHBOW shapes are obtained and saddle-node bifurcations can be encountered during the cooling to room temperature of [0°/RAINBOW], [RAINBOW/0o], and [0o2/RAINBOW]. Rectangular [RAINBOW/0o/90o] seems to be less likely to encounter saddle-node bifurcations. Furthermore, the unstable spherical RAINBOW configuration is converted to a stable near-cylindrical configuration. For the case considered of disk-style GRAPHBOW, three stable room-temperature shapes are obtained and the unstable axisymmetric RAINBOW configuration is also converted to a stable near-cylindrical configuration. For both rectangular and disk-style GRAPHBOW, the relationship between the major curvature and the electric field is shown to be very close to being linear. This characteristic would aid any dynamic analysis of RAINBOW or GRAPHBOW. / Ph. D.
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Multiphase Layout Optimization for Fiber Reinforced Composites applying a Damage FormulationKato, Junji, Ramm, Ekkehard 03 June 2009 (has links)
The present study addresses an optimization strategy for maximizing the structural ductility of Fiber Reinforced Concrete (FRC) with long textile fibers. Due to material brittleness of both concrete and fiber in addition to complex interfacial behavior between above constituents the structural response of FRC is highly nonlinear. Consideration of this material nonlinearity including interface is mandatory to deal with this kind of composite. In the present contribution three kinds of optimization strategies based on a damage formulation are described. The performance of the proposed method is demonstrated by a series of numerical examples; it is verified that the ductility can be substantially improved.
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The effect of additional surface coating on the performance of additively manufactured fiber reinforced composite moldGaram Kim (8997584) 23 June 2020 (has links)
A composite part manufacturing mold was considered one of the most
important factors that affected a successful composite part manufacturing process
for this research. A highly durable surface was required for the mold to prevent
surface damages and increase mold life. A high surface finish quality of the mold
improved the surface quality of the composite part and lowered the demolding force.
However, the surface of additively manufactured fiber reinforced composite molds
usually had lower durability and surface finish quality compared to traditional metal
molds. To solve these issues, the author applied an additional coating on top of the
additively manufactured fiber reinforced composite mold surface. A thermal
analysis of the additively manufactured fiber reinforced composite material and the
coating material were performed to select an applicable coating technique and
coating material. The thermoset polymer coating with ceramic particles that was
applied with a liquid spray coating technique was selected as a coating material.
Various surface property tests were performed to evaluate the coated surface
compared to the non-coated surface. The additively manufactured fiber reinforced
composite test specimen manufacturing process and the coating application process
were demonstrated in this study. The surface durability of the test specimens was
tested using a surface hardness test and an abrasion resistance test. The surface
performance of the test specimens was measured using a surface roughness test and
a demolding test. The sustainability of the coating material on the additively
manufactured fiber reinforced composite was tested using coefficient of thermal expansion (CTE) test, coating adhesion test, and mold life experiment. In the mold
life experiment, the non-coated and coated mold were used for multiple composite
part manufacturing processes to investigate how the coating affected the life of the
mold. The test results showed that the coated surface had a significantly improved
surface abrasion resistance and demolding performance. However, the coating did
not significantly improved surface hardness and roughness with the coating. The
adhesion strength of the coating was not degraded even there was a coefficient of
thermal expansion (CTE) mismatch between the additively manufactured fiber
reinforced composite and the coating material. The coated additively manufactured
fiber reinforced composite mold was able to be used for multiple autoclave
composite part manufacturing cycles. The coating covered most of the small voids
on the mold surface and provided a more homogeneous surface compared to the
non-coated mold, but the voids which could not be covered with the coating caused
a chipped coating issue. Once the chipped coating occurred, the size of chipped
coating got larger each time the tool was used for a composite part manufacturing
cycle. Although the additional coating provided some improvements for the surface
properties, the coating applied in this research could not be an ultimate solution to
meet all the surface property requirements for composite part manufacturing mold.
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<b>Applying the conservation of Gaussian curvature to predict the deformation of curved L-angle laminates</b>Vaughan Alexander Doty (19836300) 11 October 2024 (has links)
<p dir="ltr">In composites manufacturing, predicting the shape change in parts is vital for making sure part dimensions are properly compensated. Different factors in the manufacturing process, such as the temperature change throughout a thermoset cure cycle, can influence shape change. The compensation process becomes more difficult for geometries with double curvature, as interactions between the two radii of curvature can reduce the effectiveness of applying methodologies for single curvature geometries. Additionally, using finite element analysis (FEA) to predict shape change can be costly and time-consuming depending on part geometry.</p><p dir="ltr">This thesis studies an approach for predicting the shape change of a symmetric thermoset laminate with a double-curved L-angle section in its geometry. Specifically, the conservation of Gaussian curvature is applied to predict shape change. The geometry studied in this thesis can be broken down and analyzed as a segment of a torus, which is attached on one end by a cylinder and on the other end by a curved flange. Varying the length of the cylinder and flange sections, the effectiveness of Gauss’s theorem is determined for the different part geometries, with developed formulas compared against finite element simulations and experimental measurements.</p><p dir="ltr">By approximating torus segments with certain geometric criteria as cylinders, linear elasticity equations for a cylinder undergoing free thermal strain can be solved and the change in the larger arc length in the double-curved geometry is predicted after deformation. The integral form of Gauss’ theorem is then applied to determine the deformed angle of the larger arc, from which geometric relations can be applied to extract the deformed radius. Abaqus is used first to study the torus segment on its own, and then to see the effects of the cylinder and flange segments on the overall geometry. Experimental measurements are also used as a comparison.</p><p dir="ltr">Generally, the formula derived using Gauss’ theorem predicts shape change very well for the torus segment on its own. When cylinder and flange segments are included in the geometry, an empirical correction factor can be introduced to account for geometrically induced stiffening effects. Future developments and next steps in this research are discussed.</p>
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Studies on Glass Fiber-Reinforced Composites for CAE-Driven Design of Impact Safety CountermeasuresLakshmanan, P January 2014 (has links) (PDF)
Man-made materials such as fiber-reinforced composites (FRCs) can be tailored for optimum performance in product design applications in terms of strength and weight. The current work is aimed at studying the behaviors of composite laminates based on E-glass CSM (Chopped Strand Mat) or WRM (Woven Roving Mat) plies with a polyester resin for impact protection applications. Detailed mechanical characterization of CSM and WRM laminates till failure is carried out for tensile, compressive and shear loads by varying manufacturing process, number of plies, and laminate thickness. The effect of fiber volume fraction on mechanical properties is shown. The efficacy of CSM and WRM laminates as energy- absorbing countermeasures is studied by performing quasi-static and axial impact tests on cylindrical tubes made of the stated FRCs. In addition to load-displacement and specific energy absorption attributes, failure modes are of interest in such studies. The potential of FRC laminates for protection against projectile impact is investigated by performing low velocity impact perforation tests with a falling tup fitted with an indentor, and medium to high velocity projectile impact tests in a gas gun-based device. The valuable results generated are used for the validation of nonlinear finite element-based CAE (Computer-Aided Engineering) procedures including application of a multi-modal failure criterion for explicit dynamic analysis. The present study not only throws light on complex mechanical behavior of an important class of lightweight materials under static and dynamic loads, but also simulation tools for the design of impact safety countermeasures such as bullet-proof laminates and energy–absorbing components for automotive body structures.
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Resistência à flexão, sorção, solubilidade e estabilidade de cor de compósitos odontológicos reforçados por fibras / Flexural strength, water sorption, solubility and color stability of some fiber reinforced compositeMedeiros, Renata Souza 10 August 2012 (has links)
Os objetivos deste estudo foram: 1) avaliar a resistência à flexão em três pontos de um compósito para uso direto (Filtek Z350 XT, 3M ESPE) e um para uso indireto (Signum, Heraeus, Kulzer) reforçados por uma ou duas camadas de fibras de polietileno (Ribbond -THM, Ribbond®) ou de vidro (Interlig, Ângelus) tratados termicamente (170°C por 10 minutos), comparados com os grupos controle (não reforçados por fibras e/ou não tratados termicamente; 2) avaliar a sorção, a solubilidade e a estabilidade de cor dos compósitos reforçados, após armazenamento em água destilada à 37°C por 14 dias. A estabilidade de cor foi avaliada com auxílio de um espectrofotômetro de contato dental (Vita EasyShade, Vident, CA, USA). Para o ensaio de resistência à flexão, foram confeccionados espécimes retangulares com dimensões de 12 x 2 x 2mm (n=10), com os seguintes fatores de variação: a) compósito (para uso direto ou indireto); b) tipo e número de camadas de fibras (vidro ou polietileno/uma ou duas camadas); c) submetidos ou não a tratamento térmico. O tratamento térmico foi realizado 24 horas após fotoativação em estufa à temperatura de 170°C por 10 minutos. O ensaio foi realizado 24 horas após fotoativação ou tratamento térmico. Para avaliação de sorção/solubilidade e estabilidade de cor, foram confeccionados espécimes em forma de disco com dimensões de 15 x 2mm (n=5), em que foram analisados os seguinte fatores: a) compósito (para uso direto ou indireto); b) tipo de fibra (vidro ou polietileno); c) número de camadas de fibras (uma ou duas). Foi realizada análise dos parâmetros de cor antes e após imersão em água deionizada por 14 dias. Os resultados foram analisados por ANOVA e teste de contraste de Tukey, com nível de significância de 5% e revelaram que a fibra de vidro, quando utilizada em duas camadas, propiciou os maiores valores de resistência à flexão para os dois compósitos testados (165,4 MPa Z350XT e 208,7MPa Signum ). O tratamento térmico não apresentou significância estatística quanto à resistência à flexão do compósito direto. Para o compósito para uso indireto (Signum ) foi encontrada diferença estatisticamente significante para o fator tratamento térmico, que indicou valores de resistência à flexão inferiores para os grupos tratados termicamente. O compósito para uso direto apresentou valor de sorção superior (33,6/cm3) ao do compósito para uso indireto (19,1/cm3). Para solubilidade, foi encontrada interação para os fatores compósito e tipo de fibra, indicando maiores valores para o compósito para uso direto associado à fibra de vidro. A análise de alteração de cor demonstrou maior valor de E para a fibra de polietileno (E =1,5) quando comparado à fibra de vidro (E=1,0). Concluiu-se que: 1) a adição de fibras propicia aumento dos valores de resistência à flexão de compósitos para uso direto e indireto, o aumento da resistência foi observado quando do uso de duas camadas de fibras; 2) o tratamento térmico à 170°C por 10 minutos não indicou melhora nas propriedades mecânicas dos compósitos reforçados; 3) adicionar fibras aos compósitos não aumentou os valores de sorção/solubilidade quando imersos em água; 4) Imersão em água não produziu alterações de cor relevantes para os compósitos reforçados com fibras se comparados aos sem fibras. / The aims of this study were: 1) to evaluate the flexural strength of one composite for direct use (Filtek Z350 XT, 3M ESPE) and one for indirect use (Signum, Heraeus, Kulzer) as a function of the reinforcement by one or two layers of polyethylene (THM-Ribbond, Ribbond ®) or glass fibers (Interlig, Angelus) submitted to heat treatment (170°C for 10 minutes) compared with control groups (not reinforced by fibers and/or not heat-treated; 2) evaluate water sorption, solubility and color stability of the reinforced composites, after storage in distilled water at 37°C for 14 days. Color stability was evaluated using a spectrophotometer (Vita Easyshade, Vident, CA, USA). For three point flexural bending test, rectangular specimens were prepared with dimensions of 12 x 2 x 2 mm (n=10), according to the following variation factors: a) composite (for direct or indirect use); b) type of fibers and number of layers (glass or polyethylene/one or two layers; c) subjected or not to heat treatment. The heat treatment was performed 24 hours after curing, in a furnace, at 170 ° C for 10 minutes. Tests were performed 24 hours after curing or heat treatment. To evaluate the water sorption/solubility and color stability, disc-shaped specimens were prepared with dimensions of 15 x 2 mm (n=5) according to the following variation factors: a) composite (for direct or indirect uses); b) fiber type (glass or polyethylene); c) number of fiber layers (one or two). Color parameters were analyze before and after immersion in deionized water for 14 days. The results were analyzed by ANOVA and Tukeys test with significance level of 5%, and indicated that the glass fiber when used in two layers, showed the highest flexural strength for the two tested composites (165.4 MPa - Z350XT and 208.7 MPa - Signum ). The heat treatment did not significantly affect the flexural strength of the direct composite. For the composite for indirect use (Signum ), a statistical significance for the factor heat treatment was found, indicating lower values of flexural strength for heat-treated groups. The composite for direct use showed higher water sorption value (33.6 /cm3) when compared to the composite for indirect use (19.1 /cm3). For solubility, a significant interaction was found for composite and fiber type, indicating higher values for direct composite and glass fiber. Color stability analysis showed higher color difference value for polyethylene fiber (E =1.5) when compared to glass fiber (E=1.0). It was concluded that: a) adding fibers increased the flexural strength values of the composites for direct or indirect use, the increase in strength was more pronounced when using two fiber layers; 2) heat treatment at 170 ° C for 10 minutes showed no improvement of the mechanical properties of fiber reinforced composites; 3) adding fibers to the composite did not increase the sorption/solubility after water immersion, 4) Immersion in water did not change the color of the fiber reinforced composites when compared with those without fibers.
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Caracterização de materiais compostos por ultra-som. / Ultrasonic characterization of composite materials.Boeri, Daniel Verga 19 April 2006 (has links)
Este trabalho apresenta duas técnicas de ensaios não-destrutivos por ultra-som realizados em um tanque com água para determinar as constantes elásticas de materiais compostos de fibra de vidro/epóxi. A primeira técnica é a transmissão direta utilizando um par de transdutores. A segunda é a técnica de pulso-eco, utilizando um único transdutor. A água do tanque atua como um acoplante para transferir a energia mecânica do transdutor para a amostra. Como o transdutor não fica em contato direto com a amostra, pode-se garantir um acoplamento constante. O sistema de medição dota de um dispositivo que permite medir a velocidade da onda elástica sob diferentes ângulos de incidência, através da rotação manual da amostra. Devido ao fenômeno de conversão de modos com incidência oblíqua na interface amostra-água, ensaios por ultra-som em tanques com água fornecem as informações necessárias para o cálculo das constantes elásticas em amostras de materiais anisotrópicos, numa dada direção, a partir das medições das velocidades longitudinal e de cisalhamento. Numa dada direção de propagação em um meio anisotrópico, existem três ondas elásticas distintas: uma longitudinal e duas de cisalhamento. Se as constantes elásticas do material são conhecidas, é possível obter as três velocidades em uma dada direção bastando resolver a equação de Christoffel. Invertendo a equação de Christoffel, obtém-se as constantes elásticas a partir das velocidades medidas em uma dada direção. Os experimentos são realizados com amostras de fibra de vidro/epóxi unidirecionais e bidirecionais, utilizando transdutores com freqüências de 0,5 MHz, 1 MHz e 2,25 MHz. Os resultados experimentais obtidos utilizando ambas as técnicas são comparados com um modelo denominado Regra das Misturas" e com resultados da literatura. / In this work, two ultrasonic non destructive techniques were implemented in a water tank and used to determine the elastic constants of glass-epoxy composites samples. The first is the through-transmission technique implemented with a pair of ultrasonic transducers. The second is the back-reflection technique that uses a single transducer in pulse-eco mode. The water acts as a couplant and transfers the mechanical energy from the transducer to the sample. As the transducer is not in direct contact with the sample, we can guarantee a good coupling with the immersion technique. With the system device, it is possible to measure the velocities of the elastic waves in different angles by manually rotating the sample. Due to wave mode conversion phenomenon at the sample-water interface with oblique incidence, ultrasonic immersion testing provides information to calculate the elastic constants of the specimen by measuring longitudinal and shear wave speeds. There are three different modes of waves, one longitudinal and two shear waves, for any given direction of propagation in an anisotropic medium. If the elastic constants of a medium are known, it is possible to obtain the three wave speeds in particular propagations directions by solving the Christoffel equation. Inverting the Christoffel equation, it is possible to obtain the elastic constants from the measured wave speed in several specific directions of the anisotropic material. Measurements were carried out on unidirectional and bidirectional glass-epoxy composite samples, using transducers with central frequency of 0.5 MHz, 1 MHz, and 2.25 MHz. The experimental results obtained with both techniques are compared with a model denominated Rule of Mixture" estimation and with the literature.
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Caracterização de materiais compostos por ultra-som. / Ultrasonic characterization of composite materials.Daniel Verga Boeri 19 April 2006 (has links)
Este trabalho apresenta duas técnicas de ensaios não-destrutivos por ultra-som realizados em um tanque com água para determinar as constantes elásticas de materiais compostos de fibra de vidro/epóxi. A primeira técnica é a transmissão direta utilizando um par de transdutores. A segunda é a técnica de pulso-eco, utilizando um único transdutor. A água do tanque atua como um acoplante para transferir a energia mecânica do transdutor para a amostra. Como o transdutor não fica em contato direto com a amostra, pode-se garantir um acoplamento constante. O sistema de medição dota de um dispositivo que permite medir a velocidade da onda elástica sob diferentes ângulos de incidência, através da rotação manual da amostra. Devido ao fenômeno de conversão de modos com incidência oblíqua na interface amostra-água, ensaios por ultra-som em tanques com água fornecem as informações necessárias para o cálculo das constantes elásticas em amostras de materiais anisotrópicos, numa dada direção, a partir das medições das velocidades longitudinal e de cisalhamento. Numa dada direção de propagação em um meio anisotrópico, existem três ondas elásticas distintas: uma longitudinal e duas de cisalhamento. Se as constantes elásticas do material são conhecidas, é possível obter as três velocidades em uma dada direção bastando resolver a equação de Christoffel. Invertendo a equação de Christoffel, obtém-se as constantes elásticas a partir das velocidades medidas em uma dada direção. Os experimentos são realizados com amostras de fibra de vidro/epóxi unidirecionais e bidirecionais, utilizando transdutores com freqüências de 0,5 MHz, 1 MHz e 2,25 MHz. Os resultados experimentais obtidos utilizando ambas as técnicas são comparados com um modelo denominado Regra das Misturas e com resultados da literatura. / In this work, two ultrasonic non destructive techniques were implemented in a water tank and used to determine the elastic constants of glass-epoxy composites samples. The first is the through-transmission technique implemented with a pair of ultrasonic transducers. The second is the back-reflection technique that uses a single transducer in pulse-eco mode. The water acts as a couplant and transfers the mechanical energy from the transducer to the sample. As the transducer is not in direct contact with the sample, we can guarantee a good coupling with the immersion technique. With the system device, it is possible to measure the velocities of the elastic waves in different angles by manually rotating the sample. Due to wave mode conversion phenomenon at the sample-water interface with oblique incidence, ultrasonic immersion testing provides information to calculate the elastic constants of the specimen by measuring longitudinal and shear wave speeds. There are three different modes of waves, one longitudinal and two shear waves, for any given direction of propagation in an anisotropic medium. If the elastic constants of a medium are known, it is possible to obtain the three wave speeds in particular propagations directions by solving the Christoffel equation. Inverting the Christoffel equation, it is possible to obtain the elastic constants from the measured wave speed in several specific directions of the anisotropic material. Measurements were carried out on unidirectional and bidirectional glass-epoxy composite samples, using transducers with central frequency of 0.5 MHz, 1 MHz, and 2.25 MHz. The experimental results obtained with both techniques are compared with a model denominated Rule of Mixture estimation and with the literature.
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