An axisymmetric finite cylinder with rigid ends and a circumferential edge crack is considered in this study. The finite cylinder is under the action of uniformly distributed loads at two rigid ends. Material of the finite cylinder is assumed to be linearly elastic and isotropic. This finite cylinder problem is solved by considering an infinite cylinder containing an internal ring-shaped crack located at z=0 plane and two penny-shaped rigid inclusions located at z=&plusmn / L planes. General expressions of the infinite cylinder problem are obtained by solving Navier equations with Fourier and Hankel transforms. This infinite cylinder problem is then converted to the target problem by letting the radius of the rigid inclusions approach the radius of the cylinder and letting the outer edge of the crack approach the surface of the cylinder. Consequently, these rigid inclusions form the rigid ends and internal crack form the circumferential edge crack resulting in the problem of a finite cylinder with rigid ends having an edge crack. The problem is reduced to a set of three singular integral equations. These singular integral equations are converted to a system of linear algebraic equations with the aid of Gauss-Lobatto and Gauss-Jacobi integration formulas and are solved numerically.

Nucleation of dislocation loop at the crack tip in a material subjected to uniaxial loading is investigated. Analytical expression for the total energy of rectangular dislocation loop at the crack tip is found. Depencence of the nucleation energy barrier on dislocation loop shape and stress intensity factor at the crack tip is determined. It is established that the energetic barrier for nucleation of dislocation loop strongly depends on the stress intensity factor. Nucleation of dislocation loop is very sensitive to stress field modifiers (forest dislocations, precipitates, clusters of point defects, etc.) in the crack tip vicinity.

In the present work, an investigation of the fatigue life benefits emerging from fillet weld geometries optimization has been carried out. At first, an introduction to ageing mechanisms, corrosion and especially fatigue, acting on operating marine structures has been made. Residual stresses at weld toes, stress modes, and types, geometrical factors (weld angle, toe radius, leg length), welding techniques selected, post-welding treatment and plate‟s material are some of the principal factors affecting the fatigue life of a fillet weld joint. Especially, the accuracy of various approaches in fatigue life estimation of specific geometries under pre-set types and levels of stress is studied. It is evident so far that even the notch stress concept is the most accurate method based on S-N curves, the Fracture Mechanics approach can offer more accurate solutions of a crack development through the material. Towards this, a literature review on crack evolution aspects in welded and non-welded plates under bending and tension was performed; substantial parameters were determined and finally implemented in the LEFM model which was used for the simulation purposes of Chapter 6. As far as the crack aspect ratio evolution is concerned, an extensive reference is available in literature since many researchers have investigated its contribution to the determination of geometrical paths, commonly known as “Preferred Propagation Paths”. Their significance is related with our ability to determine accurate SIF solutions leading to precise fatigue life estimations. A typical fillet weld joint 2-D model has been developed in CAE Abaqus software and a Finite Element Analysis of subject T-profile has been carried out. Through this analysis, the fillet weld angle, the weld leg length, the weld toe curvature radio ρ and the carrying load plate thickness are examined for their impacts on the maximum surface stress. Finally, a number of stress mitigating measures are proposed and their effects are analyzed. Undoubtedly, the notch stress concept today is gradually gaining more and more acceptance among other fatigue analysis practices, hence the need for an estimation of the actual surface stresses along fillet weld toes, has become imperative. Towards this, different 2-D geometries are tested against stress concentration factors developed at weld toes, which are calculated on the basis of maximum in-plane principal stresses over nominal stresses in mode I pure bending and pure tension respectively. Moreover, validation with corresponding results from literature is provided. Finally, three different concepts for reducing the maximum surface stresses are presented. The first one proposes grinding of the weld toe area and formulation of an artificial U-notch or a part- circular profile. The second one applies to non-penetrating welds and assumes the existence of a root gap of a specific geometry which is related to the fatigue life and stress concentration factor of the fillet weld joint. Last but not least, the relatively recent concept of the variable radius notch is discussed, even though it is applicable mostly to notched bodies, not weld joints. Afterwards, a Linear Elastic Fracture Mechanics analysis of reference 2D fillet weld model is demonstrated. A number of geometrical parameters considered at previous stage for their impact on surface Stress Concentration levels at the weld toe region, have been correlated to fatigue life benefits in terms of increased number of stress cycles till failure. An extensive analysis of 9 different T-butt weld joint geometries has been provided in order to investigate how positively a possible SCF reduction can affect the fatigue life of a weld joint. Essential geometric variations (weld angle, length, toe radius, root slot) were considered in the 2D model. All calculated benefits both in pure bending and pure tension cases have been reported accordingly. Based on a linear interpolation of the points scatter (SCF, N-cycles) both in banding and tension, it was observed that a surface stress mitigation of 1% could lead to 1,33 up to 2,5% fatigue life benefit in the range of SCF=2 – 2,5. It is evident so far that the geometrical optimization of a weld joint in respect of notch stress mitigation can be a powerful tool both in shipbuilding and maintenance practice in the future. However, technically wise their application may incur high initial costs of improved tools of welding and post welding treatment and robots even though it would consist a cost effective solution in a medium/long term basis. Finally, the above process is followed by a reliability analysis of the most critical geometrical parameters affecting the fatigue life of a fillet weld joint. Reliability assessment results concerning medium, high and low cycle fatigue are provided and a comparative analysis of each factor‟s impact on fatigue life has been carried out.

The panel is symmetrical about both x- and y- axes. The central strip (strip1) of width 2h1 contains a central transverse crack of width 2a on x-axis. The two strips (strip2) contain transverse cracks of width c-b also on x-axis. The panel is subjected to axial loads with uniform intensities p1 and p2 in strip1 and strip2 , respectively at . Materials of all strips are assumed to be linearly elastic and isotropic. Due to double symmetry, only one quarter of the problem and will be considered. The solutions are obtained by using Fourier transforms both in x and y-directions. Summing several solutions is due to the necessity for sufficient number of unknowns in general expressions in order to be able to satisfy all boundary conditions of the problem. The conditions at the edges of the strips and at the interfaces are satisfied and the general expressions for a three layer panel become expressions for the panel with free edges. Use of remaining boundary conditions leads the formulation to a system of two singular integral equations. These equations are converted to a system of linear algebraic equations which is solved numerically

In this study, a long annulus bonded to a rigid cylinder containing an axisymmetric circumferential crack of width (d-c) at the midplane is considered. The material of the annulus is assumed to be linearly elastic and isotropic. The external surface of the annulus is free of stress. Surfaces of the crack are subject to distributed compressive loads. The Fourier and Hankel transform techniques are used to solve the governing equations which are reduced to a singular integral equation for crack surface displacement derivative. This integral equation is converted to a system of linear algebraic equations which are solved numerically by using Gauss-Lobatto and Gauss-Jacobi quadrature formulas. Then, the stress intensity factors at the edges of the crack are calculated. Results are presented in graphical form.

No description available.

Modern engineering analysis requires accurate, reliable and efficient evaluation of outputs of interest. These outputs are functions of "input" parameter that serve to describe a particular configuration of the system, typical input geometry, material properties, or boundary conditions and loads. In many cases, the input-output relationship is a functional of the field variable - which is the solution to an input-parametrized partial differential equations (PDE). The reduced-basis approximation, adopting off-line/on-line computational procedures, allows us to compute accurate and reliable functional outputs of PDEs with rigorous error estimations. The operation count for the on-line stage depends only on a small number N and the parametric complexity of the problem, which make the reduced-basis approximation especially suitable for complex analysis such as optimizations and designs. In this work we focus on the development of finite-element and reduced-basis methodology for the accurate, fast, and reliable prediction of the stress intensity factors or strain-energy release rate of a mode-I linear elastic fracture problem. With the use of off-line/on-line computational strategy, the stress intensity factor for a particular problem can be obtained in miliseconds. The method opens a new promising prospect: not only are the numerical results obtained only in miliseconds with great savings in computational time; the results are also reliable - thanks to the rigorous and sharp a posteriori error bounds. The practical uses of our prediction are presented through several example problems. / Singapore-MIT Alliance (SMA)

This project aims to characterise the fatigue behaviour of a crack propagating in a residual stress field changing from tension to compression in the welded zone of a ferritic pressure vessel steel. The fatigue tests were carried out keeping the applied stress intensity factor range constant to determine the role of residual stresses on fatigue crack growth. The residual stresses prior to crack growth were evaluated by X-ray diffraction. The weight function method was used to infer the expected influence of the residual stress on the crack tip in terms of the residual stress intensity factor. Two metrics were used to quantify the crack driving force local to the fatigue crack. Firstly the stress intensity amplitude expressed in terms of the change in the J-integral between maximum and minimum load and secondly the change in the crack opening displacement COD to estimate closure stress intensity factor. The displacement fields local to a fatigue crack were obtained by Digital Image Correlation (DIC) and then analysed by JMAN, an in-house developed algorithm to extract the J-integral based on finite element method and implemented using MATLAB. The difference between the applied stress intensity factor range and the effective crack driving force at the crack tip was determined in order to understand the interaction between the prior residual stresses and crack closure phenomena. Three different R-ratios were evaluated during the experiment (R=0.1, R=0.3 and R=0.5) in order to quantify the effect of residual stress on crack tip stress intensity and crack opening displacement. R-ratio plays a very important role on the fatigue crack growth rate (FCGR): as R increases, FCGR also increases. The COD was assessed by means of the displacements obtained by DIC local to the crack faces. The COD method turned out to be more insightful than the JMAN method for characterising the crack propagation, this is due to the presence of plasticity in the ligament which breaks the non-linear elastic conditions, causing the path-dependence on the J-integral. The FCGR is influenced to a greater degree by the R-ratio and to a lesser degree by the residual stress effect. There is a direct relationship between R and FCGR: as R increases, FCGR also increases, irrespective of the presence of tensile or compressive residual stresses, with the crack closure showing more tendency to occur at low R (i.e. R=0.1) than at high R (i.e. R=0.5). The relationship between R and the residual stress effects on FCGR is inversely proportional: as R increases, the effect of RS decreases.

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.

This diploma thesis deals with influence of a notch on stress-strain states at the front of cracks by shear modes. Starting with fracture mechanics and its division, followed by stress intensity factor and calculate its by finite element method. Calculation is solved for two types of notches, U-notched and V-notched, both notches were modeled parametrically so their geometry was changeable and stress intensity factor were calculated for all configurations. Subsequently was solved next calculation of stress intensity factor but for shaft without notch. Finally, was evaluated influence of notch on stress intensity factor. Software for finite element method has been used ANSYS. Others calculation was provided in software MATLAB