In the present work, the non-linear vibrations and the corresponding dynamic fracture mechanics of cables of cable-stayed bridges are studied. The cables are among the most critical components in cable-stayed bridges and there are different damage sources such as corrosion, vibration, fatigue and fretting fatigue that can significantly affect them, thereby reducing the cable’s service life and even producing their failure. Cable-Parametric Resonance is the specific non-linear vibration studied in this research. This type of vibration occurs due to displacements presented at the cable supports. These displacements are induced by the wind and traffic loads acting on the pylon and deck of the bridge. Under certain conditions, unstable cable-vibration of significant amplitude can be registered. Therefore, numerical and experimental analyses are carried out in order to describe this phenomenon and to determine the corresponding instability conditions. Two non-linear models of cable-parametric resonance are studied to predict the cable response. In the simulation method, the non-linear components are treated as external forces acting on the linear systems, which are represented by Single Degree of Freedom systems and described by digital filters. A clear non-linear relationship between the excitation and the cable response is observed in the simulations and the experiments. The corresponding experimental analysis is based on a scaled model (1:200) of the Öresund bridge and a good agreement between the numerical and experimental results is found. After obtaining the relationship between the cable response and the excitation, the cable instability conditions are determined. This is done by finding the minimum displacement required at the cable supports in order to induce nonlinear cable vibration of considerable amplitude. The instability conditions are determined within a wide range of excitation frequencies and conveniently expressed in a simplified and practical way by a curve. The determination process is rather fast and offers the possibility to evaluate all bridge cable stays in a rather short time. Finally, the dynamic fracture mechanics of the cable is considered by studying the fracture toughness characteristics of the material under dynamic conditions. Finite Element simulations on a pre-cracked three-point bending specimen under impact loading are performed. The observed cable instability is equivalently considered as the associated response to impact load conditions, and a crack as a defect on the wires of a cable stay. The simulations are based on an experimental work by using the Split Hopkinson pressure bar (Jiang et al). The dynamic stress intensity factor KI(t) up to crack initiation is then obtained by different methods. The numerical estimations based on the specimen’s crack tip opening displacement (CTOD) and mid-span displacement were closest to the experimental results. It is observed that a better estimation of the dynamic stress intensity factor relies on a proper formulation of the specimen’s stiffness. / Lic March 2011

The ability to extract accurately the stress intensity factor and the T-Stress for fractured engineering materials is very significant in the decision-making process for in-service engineering components, mainly for their functionality and operating limit. The subject of computational fracture mechanics in engineering make this possible without resulting to expensive experimental processes. In this thesis, the Finite Block Method (FBM) has been developed for the meshless study of interface stationary crack under both static and dynamic loading in bi-materials. The finite block method based on the Lagrangian interpolation is introduced and the various mathematical constructs are examined. This includes the use of the mapping technique. In a one-dimensional and a two-dimensional case, numerical studies were performed in order to determine the interpolation error. The finite block method in both the Cartesian coordinate and the polar coordinate systems is developed to evaluate the stress intensity factors and the T-stress for interface cracks between bi-materials. Using the William's series for bi-material, an expression for approximating the stress and displacement at the interface crack tip is established. In order to capture accurately the stress intensity factors and the T-stress at the crack tip, the asymptotic expansions of the stress and displacement around the crack tip are introduced with a singular core technique. The accuracy and capability of the finite block method in evaluating interface cracks is demonstrated by several numerical assessments. In all cases, comparisons have been made with numerical solutions by using the boundary collocation method, the finite element method and the boundary element method, etc.

O trabalho apresenta uma metodologia para a simulação de abertura e fechamento de trinca, durante o processo de propagação, utilizando um programa comercial de elementos finitos. Este programa é utilizado para determinar os fatores de intensidade de tensão de abertura e fechamento de trinca. É apresentado o modelo de Newman que serve de embasamento para o desenvolvimento da metodologia de liberação de nós na carga mínima, utilizada no trabalho para a propagação da trinca. São avaliados quatro tipos de corpos de prova SE-(B) (corpo de prova de três pontos de apoio submetido a flexão), SE-(T)(corpo de prova com trinca lateral submetido a tração), M-(T) (corpo de prova com trinca central submetido a tração) de uma liga de alumínio Al 2024-T351 e um aço bifásico ( ferrita + martensita). Um corpo de prova do tipo C-(T) (corpo de prova compacto submetido a tração) de aço bifásico também foi avaliado. Os corpos de prova SE-(B), SE-(T) e M-(T) da liga de alumínio Al 2024-T351 foram submetidos a carregamentos de amplitude constante, com razões de carga R = 0 e R = 0,5. Os resultados das análises são comparados com resultados do código FASTRAN, principal código numérico utilizado para simular abertura e fechamento de trinca por plasticidade induzida, através de uma normalização dos fatores de intensidade de tensão máxima e de abertura da trinca. Os resultados numéricos com o corpo de prova C-(T) submetido a carregamento de amplitude constante, com razão de carga R = 0,1 foram comparados com resultados de ensaio, objetivando validar o fator de intensidade de fechamento de trinca obtido através da análise numérica. Essa comparação é feita através de normalização numérica e experimental do fator de intensidade de tensão de fechamento de trinca com o fator de intensidade de tensão máxima. A metodologia de simulação de propagação de trincas, já aplicada na industria aeronáutica, pode ser aplicada em outras áreas como, por exemplo, na indústria automotiva, uma vez que o consumidor está cada vez mais exigente e o desenvolvimento de novos critérios de projeto se faz necessário. / The work introduces a methodology to simulate fatigue crack opening and closing during crack propagation, using a commercial finite element code. This code is used to determine the crack opening and closure stress intensity factors. The Newman model is used as a baseline to develop the methodology. The nodes are released at the minimum load, during the crack propagation process. Four kinds of specimens SE-(T) ( Single Edge Tension), SE-(B) ( Single Edge Bending), M-(T) ( Middle Tension) of the an aluminum alloy Al–2024-T351 and a dual phase steel (ferrite + martensite) were evaluated. A compact tension specimen C-(T) of a dual phase steel was evaluated. The aluminum alloy specimens, SE -(T), SE-(B) and M-(T), were evaluated under constant amplitude loading with load ratios R = 0 and R = 0.5. The results of these analyses are compared with the results of FASTRAN, principal numerical code used to simulate crack opening and closing plasticity induced by, normalizing the opening stress intensity factor. The numerical results from a C-(T) specimen, under constant amplitude loading and a load ratio R = 0.1, were compared with results from a test performed in the laboratory. The numerical and experimental closure stress intensity factors are normalized with the maximum stress intensity factor. Crack closure simulations are currently used in the aircraft industry. They are now being incorporated in same automotive and other ground vehicle fatigue analysis procedures.

<p>A common technique to evaluate load paths in complex structures is to perform FE-calculations with relative large elements. This procedure gives no information regarding stress concentrations at e.g. holes or radius but this phenomenon can later on be investigated in details with local individual submodels. Displacements is taken from the global model and used to analyse stress concentrations and crack driving parameters in the submodel.</p><p>Today, the crack controlling stress intensity factors are in general cases obtained from handbook solutions of elementary cases. This method requires engineering judgements in a conservative manner and one way to improve the solution is to model the crack in its correct surroundings in a local three-dimensional submodel.</p><p>This master thesis is focused on the development of an automated support for analysing three-dimensional cracks in submodels. The results from a global Nastran model can be imported to Trinitas and used for a more accurate stress and fatigue life analysis in a local model. Here a three-dimensional crack tip subdomain can be generated inside an eight point brick volume. The crack tip subdomain is specially designed and adjusted for accurate determination of stress intensity factors along the crack front. For example, all points are adjusted with respect to the brick volume and the crack size, triangular wedge elements are applied around the crack tip, the midpoints for these elements are moved to quarter points and the crack front is curved. The crack tip subdomain is validated against several reference cases and shows sufficiently good results with respect to the stress intensity factor.</p><p>Finally, the automated crack tip subdomain generation is applied to a geometrically complex part of a main wing carry-through bulkhead of a fighter aircraft in order to show the applicability of the procedure in an industrial environment.</p>

During the past few years, in comparison to traditional riveted structures, integral metallic skin stringer structures have played more and more important roles in aircraft design due to the fact they are economical and also have the ability to reduce weight. Their wide application in aircraft, especially large integral structures is limited because of the fact that they have shortcomings in damage tolerance performance. Hence, calculating the crack growth lives and improving the damage tolerance performance of integral structures by selecting appropriate materials or choosing rational structures is a critical work. Therefore the purpose of this thesis is to find effective analysis methods of integral metallic skin-stringer panels for the use in engineering. Cont/d.

A common technique to evaluate load paths in complex structures is to perform FE-calculations with relative large elements. This procedure gives no information regarding stress concentrations at e.g. holes or radius but this phenomenon can later on be investigated in details with local individual submodels. Displacements is taken from the global model and used to analyse stress concentrations and crack driving parameters in the submodel. Today, the crack controlling stress intensity factors are in general cases obtained from handbook solutions of elementary cases. This method requires engineering judgements in a conservative manner and one way to improve the solution is to model the crack in its correct surroundings in a local three-dimensional submodel. This master thesis is focused on the development of an automated support for analysing three-dimensional cracks in submodels. The results from a global Nastran model can be imported to Trinitas and used for a more accurate stress and fatigue life analysis in a local model. Here a three-dimensional crack tip subdomain can be generated inside an eight point brick volume. The crack tip subdomain is specially designed and adjusted for accurate determination of stress intensity factors along the crack front. For example, all points are adjusted with respect to the brick volume and the crack size, triangular wedge elements are applied around the crack tip, the midpoints for these elements are moved to quarter points and the crack front is curved. The crack tip subdomain is validated against several reference cases and shows sufficiently good results with respect to the stress intensity factor. Finally, the automated crack tip subdomain generation is applied to a geometrically complex part of a main wing carry-through bulkhead of a fighter aircraft in order to show the applicability of the procedure in an industrial environment.

In today&#039 / s technology severe working conditions increase demands on structural materials. A class of materials which are developed to meet these increased demands is Functionally Graded Materials (FGMs). These are inhomogeneous structural materials which are able to withstand large temperature gradients and corrosive environment. Application areas of FGMs are in aerospace industry, nuclear reactors, chemical plants and turbine systems. FGMs have gradual compositional variation from metal to ceramic which give them mechanical strength, toughness and heat resistance. However under high temperature gradients, cracking problems may arise due to thermal stresses. In layered structures the final stage of failure may be delamination due to crack extension. The objective of this study is to model a particular type of crack problem in a layered structure consisting of a substrate, a bond coat and an orthotropic FGM coating. There is an internal crack in the orthotropic layer and it is perpendicular to material gradation of coating. The position of the crack inside the coating is kept as a variable. The steady-state temperature distribution between the substrate and the coating causes a buckled shape along crack face. The critical temperature change, temperature distribution, mixed mode stress intensity values and energy release rates are calculated by using Displacement Correlation Technique. Results of this study present the effects of geometric parameters such as crack length, crack position, etc as well as the effects of the type of gradation on buckling behavior and mixed mode stress intensity factors.

The objective of this study is to determine stress intensity factors (SIFs) for a crack in a radially graded FGM layer on a substrate. Functionally graded coating with an edge crack perpendicular to the interface and a homogeneous substrate are bonded together. In order to make the problem analytically tractable, geometry is modeled as an FGM strip attached to a homogeneous layer. Introducing the elastic foundation underneath the homogeneous layer, an FGM coating on a thin walled cylinder can be modeled. At first, governing equations are obtained from stress displacement and equilibrium equations. Then using an assumed form of solution in terms of Fourier Transforms for displacements and applying the boundary conditions, a singular integral equation is obtained for the mode-I problem. Solving this singular integral equation numerically, stress intensity factors are obtained as functions of crack length, strip thicknesses and inhomogeneity parameter.

In this study finite element modeling of three dimensional elliptic and semielliptic cracks in a hollow cylinder is considered. Three dimensional crack and cylinder are modeled by using finite element analysis program ANSYS. The main objectives of this study are as follows. First, Ansys Parametric Design Language (APDL) codes are developed to facilitate modeling of different types of cracks in cylinders. Second, by using these codes the effect of some parameters of the problem like crack location, cylinder&rsquo / s radius to thickness ratio (R/t), the crack geometry ratio (a/c) and crack minor axis to cylinder thickness ratio (a/t) on stress intensity factors for surface and internal cracks are examined. Mechanical and thermal loading cases are considered. Displacement Correlation Technique (DCT) is used to obtain Stress Intensity Factors.

This study considers a symmetrical finite strip with a length of 2L and a width of 2h containing two collinear edge cracks located at the center of the strip. Each edge crack has a width h&amp / #8211 / a. Two ends of the finite strip are bonded to two rigid plates through which uniformly distributed axial tensile loads of intensity p0 are applied. The finite strip is assumed to be made of a linearly elastic and isotropic material. For the solution of the finite strip problem, an infinite strip of width 2h containing two internal cracks of width b&amp / #8211 / a at y=0 and two rigid inclusions of width 2c at y=&plusmn / L is considered. When the width of rigid inclusions approach the width of the strip, the portion of the infinite strip between the inclusions becomes identical with the finite strip problem. When the outer edges of the internal cracks approach the edge of the strip, they become edge cracks (notches). Governing equations are solved by using Fourier transform technique and these equations are reduced to a system of three singular integral equations. By using Gauss-Lobatto and Gauss-Jacobi integration formulas, these three singular integral equations are converted to a system of linear algebraic equations which is solved numerically.