Diplomová práce popisuje metodiku výpočtů částí náchylných k rozvoji mnoho-ohniskového únavového poškození (WFD). Nejdříve se práce zabývá rozborem předpisů letové způsobilosti souvisejících s WFD pro letadla certifikovaných podle FAR 23 v kategorii commuter. Následuje popis metodiky únavového výpočtu a predikce šíření trhliny. Dále jsou popsány řešení pro výpočet faktoru intenzity napětí pro základné konfigurace trhliny, tam kde to bylo možné v uzavřeném tvaru, jinak ve formě tabulky. Hlavní částí práce je návrh algoritmu AIMA schopného provést kompletní analýzu části náchylné k rozvoji únavového poškození na více místech (MSD). Model se validoval únavovou zkouškou vzorku přeplátovaného spoje dolního panelu křídla. Následně byla analyzována reálná konstrukce spoje dolních panelů křídla letounu L 410 NG.

In the past, the disagreement of near-threshold fatigue-crack growth (FCG) rate data generated from constant Kmax tests, high load ratio (minimum to maximum load) constant R tests, and ΔKeff based data was a mysterious issue. Because of the disagreement, a variety of test or analysis methods were created to correlate FCG rate data. It was suspected that the ASTM threshold test method using load reduction was inducing remote crack closure due to plastically deformed material, which caused elevated thresholds and slower rates than steady-state behavior. The first goal of this study was the development of a test method to eliminate remote closure during threshold testing. In order to avoid/minimize remote closure effect, compression-precracking methods were used to initiate a crack from a starter notch on compact specimens. Two materials with different fatigue crack surface profiles (flat or very rough) were tested and the results generated from the conventional ASTM precracking method and the compression-precracking test method were compared. In order to understand the disagreement of near-threshold data, crack-opening load measurements were performed from locally (near crack tip) installed strain gages instead of the remote gage (i.e., back face gage). Some careful specimen preparations were performed to avoid out-of-plane bending, to maintain straight crack fronts, and to ensure testing system linearity. It was known that remote gages, such as crack-mouth- opening-displacement-gages were insensitive to measuring load-strain records near threshold. By using local gages, the crack closure effects were clearly observed even in high load ratio (R) tests, like or higher than R = 0.7, and constant Kmax tests, which were believed to be crack closure free. By measuring load-reduced-strain records from local gages, crack-opening loads were able to correlate FCG rate data and showed that ΔKeff-rate data was unique for a wide variety of materials. By comparing (ΔKeff)th values, it may provide reasonable guidance for the material resistance against FCG. Because of “high R crack closure”, some theories considered in the past may need to be reconsidered. First, constant Kmax tests are not entirely crack-closure free. Second, there is no critical load ratio, Rc, to indicate the transition from crack-closure affected to crack-closure free data, and Kmax effects that appear in ΔKth-Kmax relations. Research has shown that the three dominate crack-closure mechanisms (plasticity-, roughness- and debris-induced crack closure) FCG rate behavior in the threshold regime from low to high load ratios.

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The structural optimization of a cantilever aircraft wing with curvilinear spars and ribs and stiffeners is described. The design concept of reinforcing the wing structure using curvilinear stiffening members has been explored due to the development of novel manufacturing technologies like electron-beam-free-form-fabrication (EBF3). For the optimization of a complex wing, a common strategy is to divide the optimization procedure into two subsystems: the global wing optimization which optimizes the geometry of spars, ribs and wing skins; and the local panel optimization which optimizes the design variables of local panels bordered by spars and ribs. The stiffeners are placed on the local panels to increase the stiffness and buckling resistance. The panel thickness, size and shape of stiffeners are optimized to minimize the structural weight. The geometry of spars and ribs greatly influences the design of stiffened panels. During the local panel optimization, the stress information is taken from the global model as a displacement boundary condition on the panel edges using the so-called "Global-Local Approach". The aircraft design is characterized by multiple disciplines: structures, aeroelasticity and buckling. Particle swarm optimization is used in the integration of global/local optimization to optimize the SpaRibs. The interaction between the global wing optimization and the local panel optimization is usually computationally expensive. A parallel computing technology has been developed in Python programming to reduce the CPU time. The license cycle-check method and memory self-adjustment method are two approaches that have been applied in the parallel framework in order to optimize the use of the resources by reducing the license and memory limitations and making the code robust. The integrated global-local optimization approach has been applied to subsonic NASA common research model (CRM) wing, which proves the methodology's application scaling with medium fidelity FEM analysis. Both the global wing design variables and local panel design variables are optimized to minimize the wing weight at an acceptable computational cost. The structural weight of the wing has been, therefore, reduced by 40% and the parallel implementation allowed a reduction in the CPU time by 89%. The aforementioned Global-Local Approach is investigated and applied to a composite panel with crack at its center. Because of composite laminates' heterogeneity, an accurate analysis of these requires very high time and storage space. In the presence of structural discontinuities like cracks, delaminations, cutouts etc., the computational complexity increases significantly. A possible alternative to reduce the computational complexity is the global-local analysis which involves an approximate analysis of the whole structure followed by a detailed analysis of a significantly smaller region of interest. We investigate here the performance of the global-local scheme based on the finite element method by comparing it to the traditional finite element method. To do so, we conduct a 2D structural analysis of a composite square plate, with a thin rectangular notch at its center, subjected to a uniform transverse pressure, using the commercial software ABAQUS. We show that the presence of the thin notch affects only the local response of the structure and that the size of the affected area depends on the notch length. We investigate also the effect of the notch shape on the response of the structure. Stiffeners attached to composite panels may significantly increase the overall buckling load of the resultant stiffened structure. Buckling analysis of a composite panel with attached longitudinal stiffeners under compressive loads is performed using Ritz method with trigonometric functions. Results are then compared to those from ABAQUS FEA for different shell elements. The case of composite panel with one, two, and three stiffeners is investigated. The effect of the distance between the stiffeners on the buckling load is also studied. The variation of the buckling load and buckling modes with the stiffeners' height is investigated. It is shown that there is an optimum value of stiffeners' height beyond which the structural response of the stiffened panel is not improved and the buckling load does not increase. Furthermore, there exist different critical values of stiffener's height at which the buckling mode of the structure changes. Next, buckling analysis of a composite panel with two straight stiffeners and a crack at the center is performed. Finally, buckling analysis of a composite panel with curvilinear stiffeners and a crack at the center is also conducted. ABAQUS is used for these two examples and results show that panels with a larger crack have a reduced buckling load. It is shown also that the buckling load decreases slightly when using higher order 2D shell FEM elements. A damage tolerance framework, EBF3PanelOpt, has been developed to design and analyze curvilinearly stiffened panels. The framework is written with the scripting language PYTHON and it interacts with the commercial software MSC. Patran (for geometry and mesh creation), MSC. Nastran (for finite element analysis), and MSC. Marc (for damage tolerance analysis). The crack location is set to the location of the maximum value of the major principal stress while its orientation is set normal to the major principal axis direction. The effective stress intensity factor is calculated using the Virtual Crack Closure Technique and compared to the fracture toughness of the material in order to decide whether the crack will expand or not. The ratio of these two quantities is used as a constraint, along with the buckling factor, Kreisselmeier and Steinhauser criteria, and crippling factor. The EBF3PanelOpt framework is integrated within a two-step Particle Swarm Optimization in order to minimize the weight of the panel while satisfying the aforementioned constraints and using all the shape and thickness parameters as design variables. The result of the PSO is used then as an initial guess for the Gradient Based Optimization using only the thickness parameters as design variables. The GBO is applied using the commercial software VisualDOC. / Ph. D.

Disertační práce se věnuje problematice obecných koncentrátorů napětí v anisotropních prostředích. Zejména se jedná o problém trhlin končících na rozhraní dvou různých materiálů, či problém obecného více-materiálového klínu. Cílem práce je vytvořit komplexní nástroj pro posuzování obecných koncetrátorů napětí tj, popis pole napětí v jeho okolí, zahrnutí případného vlivu přemostění trhliny do výsledného pole napětí a definici lomových kritérií pro obecný koncentrátor v anisotropním prostředí. U popisu pole napětí je využit tzv. Lechnického-Strohův formalismus a technika spojitě rozložených dislokací využívající teorii komplexních potenciálů. V práci je rovněž široce uplatněn tzv. dvoustavový "psí"-integrál (pro výpočet různých součinitelů asymptotického rozvoje pro napětí), založený na Bettiho recipročním teorému v kombinaci s metodou konečných prvků. Pro formulaci lomových kritérií je použita teorie tzv. „konečné lomové mechaniky“ a teorie sdružených asymptotických rozvojů. Studován je především vztah mezi ohybem trhliny podél rozhraní a její případnou pentrací do základního materiálu. Veškeré potřebné výpočty jsou prováděny v matematických softwarech MAPLE 10.0, MATLAB 7.1 a konečnoprvkovém systému ANSYS 10.0.

O trabalho trata da utilização de formulações não-convencionais de elementos finitos na obtenção de fatores de intensidade de tensão associados a múltiplas fissuras distribuídas num domínio bidimensional. A formulação do problema de múltiplas fissuras baseia-se numa abordagem de sobreposição proposta pelo Método da Partição (\"Splitting Method\"). Segundo essa abordagem a solução do problema pode ser encontrada a partir da sobreposição de três subproblemas combinados de tal forma que o fluxo de tensão resultante nas faces das fissuras seja nulo. O uso do Método dos Elementos Finitos (MEF) em sua forma convencional pode requerer um refinamento excessivo da rede nesse tipo de problema, aumentando o custo computacional da análise. Objetivando reduzir este custo, empregam-se duas formulações não-convencionais, de forma independente, num dos subproblemas, dito local: a formulação híbrido-Trefftz de tensão e o Método dos Elementos Finitos Generalizados (MEFG). Na formulação híbrido-Trefftz é adotado o recurso do enriquecimento seletivo mediante o refrno- p na aproximação dos campos de deslocamento no contorno do elemento. Já com relação ao MEFG, empregam-se funções polinomiais e a solução analítica da mecânica da fratura como funções enriquecedoras. Exemplos de simulação numérica são apresentados no sentido de comprovar que a utilização dessas formulações não-convencionais juntamente com o Método da Partição viabiliza a obtenção de resultados com boa aproximação com recurso a redes pouco refinadas, reduzindo significativamente o custo computacional de toda a análise. / This paper treats with the use of non-conventional finite element formulations to obtain the stress intensity factor of multiple cracks located in a two-dimensional domain. The formulation of the multiple cracks problem is based on an overlapping approach suggested by the Splitting Method. Accordingly, the solution of the problem can be achieved by dividing the problem in three steps, combined so that the resulting stress flux is zero on the cracks face. The use of the Finite Element Method (FEM) in its conventional formulation requires a mesh refinement in this kind of problem, then increasing the computational cost. Aiming to reduce this cost, two non-conventional formulations are used independently to solve the local problem: the Hybrid-Trefftz stress formulation and the Generalized Finite Elements Method (GFEM). The Hybrid-Trefftz formulation is applied with selective enrichment using p-refinement in the displacements field on the element boundaries. The GFEM employs polynomial functions and analytical solutions of the fracture mechanics as enrichment functions. Examples of numerical simulations are presented in order to show that non- conventional formulations and the Splitting Method can provide accurate results with coarse mesh, thus reducing the computational cost.

O Jateamento com granalha (shot peening, em inglês) é um processo de fabricação amplamente utilizado em indústrias mecânicas, automotivas, navais, aeronáuticas e outras indústrias metalúrgicas. O objetivo principal é induzir tensões residuais de compressão para melhorar a vida à fadiga das peças e estruturas. A modelagem e simulação do processo são muito difíceis, pois envolvem a consideração de muitos e complexos aspectos. Este trabalho propõe um método de modelagem tridimensional utilizando o método dos elementos finitos para a simulação numérica desse processo assim como a sua influência na propagação de trinca, considerando efeitos pouco estudados, como o amolecimento do material devido ao aumento da temperatura na peça durante os impactos, ao comportamento elasto-plástico das granalhas e a rugosidade da peça tratada nos parâmetros da trinca. A modelagem proposta para simular o processo de jateamento com granalhas inclui: (i) análise dinâmica explícita, (ii) modelagem tridimensional, (iii) cálculo da velocidade real das granalhas, (iv) modelo de contato com coeficientes de atrito estático e dinâmico entre as áreas em contato, (v) o modelo constitutivo de Johnson-Cook para o comportamento do material alvo, (vi) um comportamento elasto-plástico multilinear para as granalhas, (vii) a consideração da cobertura real de uma área dada da superfície jateada, (viii) a consideração do aumento da temperatura no material durante o processo e (ix) o relaxamento de tensões residuais devido a este aumento de temperatura. As simulações numérico-computacionais para investigar a influência do processo em fenômenos, tais como fadiga e propagação de trinca, necessitou uma nova abordagem para a incorporação das tensões residuais num modelo de elementos finitos. Além disso, foram realizados vários ensaios quase-estáticos e dinâmicos para a determinação dos parâmetros do modelo constitutivo de Johnson-Cook para o aço AISI 5160. Para a avaliação das metodologias propostas, as tensões residuais foram introduzidas e avaliadas em uma mola parabólica automotiva, sendo que as tensões residuais foram avaliadas através da técnica de difração de raios-X, a intensidade e a cobertura do processo de jateamento com granalha na mola foram avaliadas com Lupa e rugosímetro. Também, dados experimentais de ensaios de fadiga relatados na literatura, realizados em corpos de prova tipo CT foram utilizados. A modelagem numérica do processo de jateamento com granalha desenvolvida neste trabalho consegue prever com sucesso os perfis das tensões residuais, com valores bem próximos aos obtidos experimentalmente. A investigação numérica do efeito do processo na vida à fadiga e fratura das peças comprovou a sua influência nos parâmetros de propagação de trinca nas regiões afetadas pelo processo, ocasionando um amplo aumento da vida à fadiga, e confirmou o relaxamento das tensões residuais devido aos ciclos de carregamento conforme as observações experimentais na literatura. / Shot peening is a manufacturing process widely used in the mechanical, automotive, marine, aeronautical and other metallurgical industries. The main purpose is to induce residual compression stresses to improve fatigue life. The modeling and simulation of the process are very difficult as they involve the consideration of many and complex aspects. This work proposes a three-dimensional modelling method using the finite element method for the numerical simulation of this process as well as its influence on crack propagation, considering little studied effects such as softening of the material due to the increase in temperature in the part during impacts , the elastic-plastic behavior of the shot and the roughness of the treated part in the crack parameters. The proposed modelling approach to simulate the shot peening process includes: (i) explicit dynamic analysis, (ii) three-dimensional modeling, (iii) calculation of the real velocity of the shot, (iv) contact model with static and dynamic friction coefficients between the contact areas, (v) the Johnson-Cook constitutive model for target material behavior, (vi) a multilinear elasto-plastic behavior for the shot, (vii) consideration of real coverage in a given area of the peened surface, (viii) consideration of temperature increase in the material during the process and (ix) relaxation of residual stresses due to this rise in temperature. Numerical-computational simulations to investigate the influence of the shot peening process on phenomena, such as fatigue and crack propagation, required a new approach for the incorporation of residual stress in a finite element model. In addition, several quasi-static and dynamic tests were carried out to determine the parameters of the constitutive Johnson-Cook model for AISI 5160 steel. To assess the proposed methodologies, the residual stresses were introduced and evaluated in an automotive parabolic spring, with the residual stresses being evaluated by the X-ray diffraction technique, the intensity and coverage of the shot peening process for the spring were evaluated with magnifying glass and roughness gauge. Also, fatigue tests available in the literature, carried out on types of CT specimens, were used. The numerical modeling of the shot peening process developed in this work can successfully predict the residual stress profiles, with values close to those obtained experimentally. The numerical investigation of the effect of the process in the fatigue life and fracture of the pieces proved its influence in the parameters of crack propagation in the regions affected by the process, causing a wide increase of the fatigue life, and confirmed the relaxation of the residual stresses due to the cycles loading according to experimental observations in the literature.

The modified mapping-collocation (MMC) method is applied to analyze a circumferential crack in an isotropic curved beam. Based on the method a MATLAB code was developed to obtain the stress field. Incorporating the stress correlation technique, the opening and sliding fracture mode stress intensity factors (SIF)s of the crack for the beam under pure bending moment load case are calculated. The MMC method aims to solve two-dimensional problems of linear elastic fracture mechanics (LEFM) by combining the power of analytic tools of complex analysis (Muskhelishvili formulation, conformal mapping, and extension arguments) with simplicity of applying the boundary collocation method as a numerical solution approach. Qualitatively, a good agreement between the computed stress contours and the fringe shapes obtained from the photoelastic experiment on a plexiglass specimen is observed. Quantitatively, the results are compared with that of ANSYS finite element analysis software. The effect of crack size, crack position and beam thickness variation on SIF values and mode mixity is investigated.

Probabilistic assessment and life cycle management of engineering components and systems in a nuclear power plant is intended to ensure safe and efficient operation of energy generation over its entire life. The CANDU reactor core consists of 380-480 pressure tubes, which are like miniature pressure vessels that contain natural uranium fuel. Pressure tubes operate under severe temperature and radiation conditions, which result in degradation with ageing. Presence of flaws in a pressure tube makes it vulnerable to delayed hydride cracking (DHC), which may lead to rupture or break-before-leak situation. Therefore, assessment of flaws in the pressure tubes is considered an integral part of a reactor core assessment program. The main objective of the thesis is to develop advanced probabilistic and mechanical stress field models for the assessment of flaws. The flaw assessment models used by the industries are based on deterministic upper/lower bound values for the variables and they ignore uncertainties associated with system parameters. In this thesis, explicit limit state equations are formulated and first order reliability method is employed for reliability computation, which is more efficient than simulation-based methods. A semi-probabilistic approach is adopted to develop an assessment model, which consists of a mechanics-based condition (or equation) involving partial factors that are calibrated to a specified reliability level. This approach is applied to develop models for DHC initiation and leak-before-break assessments. A novel feature of the proposed method is that it bridges the gap between a simple deterministic analysis and complex simulations, and it is amenable to practical applications. The nuclear power plant systems are not easily accessible for inspection and data collection due to exposure to high radiation. For this reason, small samples of pressure tubes are inspected at periodic intervals and small sample of data so collected are used as input to probabilistic analysis. The pressure tube flaw assessment is therefore confounded by large sampling uncertainties. Therefore, determination of adequate sample size is an important issue. In this thesis, a risk informed approach is proposed to define sample size requirement for flaw assessment. Notch-tip stress field is a key factor in any flaw assessment model. Traditionally, linear elastic fracture mechanics (LEFM) and its extension, serves the basis for determination of notch-tip stress field for elastic and elastic-perfectly-plastic material, respectively. However, the LEFM solution is based on small deformation theory and fixed crack geometry, which leads to singular stress and strain field at the crack-tip. The thesis presents new models for notch and crack induced stress fields based on the deformed geometry. In contrast with the classical solution based on small deformation theory, the proposed model uses the Cauchy's stress definition and boundary conditions which are coupled with the deformed geometry. This formulation also incorporates the rotation near the crack-tip, which leads to blunting and displacement of the crack-tip. The solution obtained based on the final deformed configuration yields a non-singular stress field at the crack-tip and a non-linear variation of stress concentration factor for both elastic and elastic-perfectly-plastic material. The proposed stress field formulation approach is applied to formulate an analytical model for estimating the threshold stress intensity factor (KIH) for DHC initiation. The analytical approach provides a relationship between KIH and temperature that is consistent with experimental results.

Probabilistic assessment and life cycle management of engineering components and systems in a nuclear power plant is intended to ensure safe and efficient operation of energy generation over its entire life. The CANDU reactor core consists of 380-480 pressure tubes, which are like miniature pressure vessels that contain natural uranium fuel. Pressure tubes operate under severe temperature and radiation conditions, which result in degradation with ageing. Presence of flaws in a pressure tube makes it vulnerable to delayed hydride cracking (DHC), which may lead to rupture or break-before-leak situation. Therefore, assessment of flaws in the pressure tubes is considered an integral part of a reactor core assessment program. The main objective of the thesis is to develop advanced probabilistic and mechanical stress field models for the assessment of flaws. The flaw assessment models used by the industries are based on deterministic upper/lower bound values for the variables and they ignore uncertainties associated with system parameters. In this thesis, explicit limit state equations are formulated and first order reliability method is employed for reliability computation, which is more efficient than simulation-based methods. A semi-probabilistic approach is adopted to develop an assessment model, which consists of a mechanics-based condition (or equation) involving partial factors that are calibrated to a specified reliability level. This approach is applied to develop models for DHC initiation and leak-before-break assessments. A novel feature of the proposed method is that it bridges the gap between a simple deterministic analysis and complex simulations, and it is amenable to practical applications. The nuclear power plant systems are not easily accessible for inspection and data collection due to exposure to high radiation. For this reason, small samples of pressure tubes are inspected at periodic intervals and small sample of data so collected are used as input to probabilistic analysis. The pressure tube flaw assessment is therefore confounded by large sampling uncertainties. Therefore, determination of adequate sample size is an important issue. In this thesis, a risk informed approach is proposed to define sample size requirement for flaw assessment. Notch-tip stress field is a key factor in any flaw assessment model. Traditionally, linear elastic fracture mechanics (LEFM) and its extension, serves the basis for determination of notch-tip stress field for elastic and elastic-perfectly-plastic material, respectively. However, the LEFM solution is based on small deformation theory and fixed crack geometry, which leads to singular stress and strain field at the crack-tip. The thesis presents new models for notch and crack induced stress fields based on the deformed geometry. In contrast with the classical solution based on small deformation theory, the proposed model uses the Cauchy's stress definition and boundary conditions which are coupled with the deformed geometry. This formulation also incorporates the rotation near the crack-tip, which leads to blunting and displacement of the crack-tip. The solution obtained based on the final deformed configuration yields a non-singular stress field at the crack-tip and a non-linear variation of stress concentration factor for both elastic and elastic-perfectly-plastic material. The proposed stress field formulation approach is applied to formulate an analytical model for estimating the threshold stress intensity factor (KIH) for DHC initiation. The analytical approach provides a relationship between KIH and temperature that is consistent with experimental results.