[pt] O desenvolvimento de um modelo fotoelástico com módulo de elasticidade variável, é objeto deste trabalho. O material utilizado foi obtido a partir da resina epoxi (Cy-205-CIBA) com a combinação dos endurecedores anidrido ftálico e anidrido maleico. Obtidas as curvas de nível do módulo de elasticidade, temperatura crítica e coeficiente de dilatalção térmico para materiais com diferentes partes em peso dos enducedores, pode-se escolher por supersição dessas curvas materiais com mesma temperatura crítica e expansão térmica a essa temperatura. Feita a colagem dos materiais, foi analisado o efeito das tensões térmicas durante o aquecimento até alcançarem a temperatura de congelamento(crítica) e discutidos os resultados. Este trabalho destina-se a fotoelasticidade tridimensional para a análise e congelamento de tensões em materiais diferentes módulos de elasticidade, minimizando-se os efeitos causados por diferentes nos coeficientes de dilatação térmico. / [en] The present work deals with the development of the photoelastic model with variable modulus of elasticity.The experiment materials was prepared from an epoxi resin (CY-2050) with the hardener phatalic anhydride and maleic anhydride. The nomagrames of the modulus of elasticity, critical temperature and thermel expansion coefficient were obtained for these curves were selected materials with the same critical temperature and correspoding thermal expansion coefficient. These materials were bound together and the effects of thermal stresses was analised during the heating till they reach the freezing temperature and the results are subsequently discussed. This work is intended for three-dimensional experiments with analyses and frozen stress in photoelastic material with different modulus of elasticity to minimaze the different thermal expansion effects.

The stresses and deformations in cross-ply composite tubes subjected in circumferential temperature gradients are studied. The motivation behind the study is the anticipated use of composite tubes in space structures where the tube is exposed to the heat of the sun on one side and the cryogenic temperatures of space on the other. Experiments were performed to measure the functional form of the temperature gradient and the displacements. It was found that the form of the temperature gradient, T(Ɵ), can accurately be represented by T(Ɵ) = A + BcosƟ¸ and that the displacement of the tube is parabolic in the axial coordinate. Two types of analytical solutions were developed: an exact elasticity U solution and an approximate solution. The approximate solution includes a linear variation of the material properties with temperature and uses the principle of complementary virtual work in conjunction with a Ritz approximation on the stress field. The elasticity solution predicts that high tensile stresses could crack the matrix. The effect of including temperature-dependent material properties is to reduce the circumferential dependency of the stresses. / Master of Science

The objective of this study was to investigate, both experimentally and analytically, the stresses and deformations in angle-ply composite tubes subjected to axisymmetric thermal loading. For the theoretical portion, a generalized plane strain elasticity analysis was developed. The analysis included mechanical and thermal loading and temperature-dependent material properties. Using the elasticity analysis and a temperature range of 116 K to 450 K, stress levels were found to be high for the specific designs considered, compared to material failure levels. In addition, the use of temperature-dependent material properties was found to have a significant effect on the predicted stresses and deformations. The elasticity analysis was also used to study the effect of including a thin metallic coating on a graphite-epoxy tube. The stresses in the coatings were found to be quite high, exceeding the yield stress of aluminum. An important finding in the analytical studies was the fact that even tubes with a balanced-symmetric lamination sequence exhibited shear deformation or twist. The radial location of an off-axis ply was found to influence its effect on the overall torsional tube response. For the experimental portion, an apparatus was developed to measure torsional and axial response in the temperature range of 140 K to 360 K. Eighteen specimens were tested, combining three material systems, eight lamination sequences, and three off-axis ply orientation angles. For the twist response, agreement between analysis and experiment was found to be good. The axial response of the tubes tested was found to be greater than predicted by a factor of three. As a result of the study, it is recommended that the thermally-induced axial deformations be investigated further, both experimentally and analytically. / Master of Science

The temperature and thermal stress distributions in a semi-transparent solid of flat plate geometry exposed to a collimated radiative source for various angles of incidence is investigated. This plate is convectively insulated on the surface where the radiation is incident while the rear surface is convectively cooled. Tile effective internal heat generation term is rederived so as to take into account the internal specular reflections (diffuse reflections were not considered) in the plate when the source is present. The newly-derived effective internal heat generation term allows for variations in the angle of incidence of the collimated source. This one-dimensional analysis investigates the importance of the incoming radiation wavelength, and the angle of incidence, on the behavior of the temperature and stress distributions. The nature of the concavity of the temperature distribution in relation to the stress distribution is also studied. The heating of the plate by a single pulsed source (laser) for a duration of 0.001 seconds followed by the subsequent cooling of the plate is examined by numerical example using Corning Glass Works #7940 Fused Silica glass as the semitransparent material. / Master of Science

Vibrations of nuclei in crystals govern various properties such as thermal expansion, phase transitions, and elasticity, and the quasiharmonic approximation (QHA) is the simplest nontrivial approximation which includes the effects of vibrational anharmonicity into temperature dependent observables. Nonetheless, the QHA is often implemented with additional approximations due to the complexity of computing phonons under arbitrary strains, and the generalized QHA, which employs constant stress boundary conditions, has not been completely developed. Here we formulate the generalized QHA, providing a practical algorithm for computing the strain and other observables as a function of temperature and true stress. We circumvent the complexity of computing phonons under arbitrary strains by employing irreducible second order displacement derivatives of the Born-Oppenheimer potential and their strain dependence, which are efficiently and precisely computed using the lone irreducible derivative approach. We formulate two complementary strain parametrizations: a discretized strain grid interpolation and a Taylor series expansion in symmetrized strain. We illustrate the quasiharmonic approximation by evaluating the temperature and pressure dependence of select elastic constants and the thermal expansion in thoria (ThO₂) using density functional theory with three exchange-correlation functionals. The convergence of the two complementary strain parametrizations is evaluated for the computed thermal expansion. The temperature dependent lattice parameter and thermal expansion computed within the QHA is compared with experimental measurements. The QHA results are compared to measurements of the elastic constant tensor using time domain Brillouin scattering and inelastic neutron scattering. We then demonstrate the generalized quasiharmonic approximation in a non-cubic material, ferroelectric lead titanate, computing the temperature and stress dependence of the full elastic constant tensor. The irreducible derivative approach is employed for computing strain dependent phonons using finite difference, explicitly including dipole-quadrupole contributions. We use density functional theory, computing all independent elastic constants and piezoelectric strain coefficients at finite temperature and stress. There is good agreement between the quasiharmonic approximation and the experimentally measured lattice parameters close to 0 K. The quasiharmonic approximation overestimates the measured temperature dependence of the lattice parameters and elastic constant tensor, demonstrating that a higher level of strain dependent anharmonic vibrational theory is needed. The next material we study is zirconium nitride, employing the quasiharmonic approximation with the irreducible derivative approach to compute the phonons and thermal expansion. Density functional theory is used with two exchange-correlation functionals. We investigate the difference between the measured and computed optical phonon branches, showing that volume effects, two-phonon scattering, and nitrogen vacancies do not explain the discrepancy between the measurement and computation. The temperature dependent lattice parameter is computed within the QHA, where the thermal expansion is overestimated as compared with existing experimental measurements.

The characteristics of thermally-induced transverse cracks in T300/5208 graphite-epoxy cross-ply and quasi-isotropic laminates were investigated both experimentally and analytically. The formation of transverse cracks and the subsequent crack spacing present during cooldown to -250°F (116K) and thermal cycling between 250 and -250°F (116 and 394K) was investigated. The state of stress in the vicinity of a transverse crack and the influence of transverse cracking on the laminate coefficient of thermal expansion (CTE) was predicted using a generalized plane-strain finite element analysis and a modified shear-lag analysis. It is shown that a majority of the cross-ply laminates experienced transverse cracking during the initial cool-down to -250°F whereas the quasi-isotropic laminates remained uncracked. All cross-ply laminates and the [0/±45/90]_s quasi-isotropic laminate exhibited transverse cracking following 20 thermal cycles. The uniformity of crack spacing increased with an increasing number of thermal cycles. The cross-ply laminates exhibited a rather sharp drop in CTE at crack densities less than 50 cracks/in. (19.7 cracks/cm) whereas the quasi-isotropic laminates exhibited a smaller decrease in CTE. The in situ transverse strength of the 90° layers was more than 1.9 times greater than the transverse strength of the unidirectional 90° material for all laminates investigated. / M.S.

No description available.

A soldagem é o processo de união mais utilizado na fabricação de equipamentos pela indústria mecânica. Devido à introdução de calor durante o processo de soldagem, dependente do posicionamento da tocha e consequentemente do tempo, dilatações e contrações não uniformes produzem tensões térmicas no componente em questão, as quais permanecem como residuais ao final do processo, ao se atingir o equilíbrio térmico. O entendimento da formação e comportamento destas tensões se torna importante, pois na presença de carregamentos externos, a integridade estrutural do elemento mecânico pode ser comprometida. Portanto, este estudo visa analisar o comportamento destas tensões térmicas, avaliando ao final a magnitude e distribuição das tensões residuais, tendo como ferramenta o método dos elementos finitos. Inicialmente são apresentados os principais processos de soldagem envolvendo a fusão de materiais por meio de arco elétrico, sendo possível com base em uma explicação teórica, observar e entender a formação das tensões oriundas destes processos. Na sequência uma revisão bibliográfica contendo as principais técnicas para modelamento deste problema pelo método dos elementos finitos é apresentada, navegando por conceitos da análise térmica, que envolve o estudo das temperaturas e mecânica, a qual avalia as tensões formadas. Com toda parte teórica consolidada, um caso exemplo é analisado, simulando desta maneira um processo GTAW pelo programa computacional ANSYS, e comparando os resultados numéricos com os dados experimentais e numéricos obtidos na literatura. Ao final da simulação conclui-se que o modelo analisado reproduz fielmente a distribuição de temperaturas durante o processo e também estima corretamente as tensões residuais na chapa soldada, mostrando que a simulação de processos de soldagem utilizando o método dos elementos finitos se apresenta como uma ferramenta alternativa a indústria no aprimoramento de processos existentes ou desenvolvimento de novos. / Welding is the most used joining process in equipment manufacture by mechanical industry. Due to heat application during welding, varying with torch position and therefore by time, non-uniform expansion and contraction produces thermal stresses, which remains as residual when the component reaches thermal equilibrium. Formation and behavior of these stresses understanding becomes important since on external forces presence the mechanical piece may have it structural integrity compromised. This study aims to analyze thermal stress behavior due to welding evaluating residual stress magnitude and distribution at the process end by the finite element method. First of all fusion welding process by an electric arc are presented and a theoretical explanation about thermal stresses formation during welding is shared. Next is shown a bibliographic research with main techniques to model these problems using the finite element method, including thermal analysis, which involves temperature distribution study, and structural analysis that evaluate resulting stresses. With all theoretical background consolidated an example case of a GTAW process is studied utilizing ANSYS software, comparing numerical results with experimental and numerical data obtained in literature. It is possible to conclude that analyzed model accurately reproduces temperature distribution and also residual stress in the welded specimen proving that a welding process simulation via finite element method is an alternative tool for industry purposes on improving existing process and developing new ones.

No description available.

The main objective of this study is to examine the three-dimensional surface crack problems in orthotropic materials subjected to mechanical or thermal loading. The cracks are modeled and embedded in the orthotropic material by considering semielliptical crack front geometry. In the model special elements are embedded in the crack front region, in this way it is possible to include crack tip singular fields along the crack front. Three-dimensional finite element analyses are conducted to obtain mode I stress intensity factors. The stress intensity factor is calculated by using the displacement correlation technique. In the analysis, collapsed 20-node iso-parametric elements are utilized to simulate strain singularity around the semi-elliptical crack front. The surface crack problem is analyzed under both mechanical and thermal stresses. In the case of mechanical loading, uniform tension and fixed grip tension loading cases are applied on the model. In thermal analysis, thermal boundary conditions are defined. Comparisons of the results generated to those available in the literature verify the developed techniques.