Crack propagation in structures when subjected to fatigue loading, follows three different phases namely - short crack growth, stable crack growth and unstable crack growth. Accurate fatigue life prediction demands the consideration of every crack propagation phase rather than only the stable crack growth stage. Further, the use of existing crack growth laws in structures with small cracks under-predicts the growth rate compared to experimentally observed ones, thereby leading to an unsafe design and keeping the structure in a potentially dangerous state. In the present work, an attempt is made to establish fatigue crack propagation laws for plain concrete, reinforced concrete and concrete-concrete jointed interfaces from first principles using the concepts of dimensional analysis and self-similarity. Different crack growth laws are proposed to understand the behavior in each of the three regimes of the fatigue crack growth curve. Important crack growth characterizing material and geometrical parameters for each zone are included in the proposed analytical models. In real life applications to structures, the amplitude of cyclic loading rarely remains constant and is subjected to a wide spectrum of load amplitudes. Furthermore, the crack growth behavior changes in the presence of high amplitude load spikes within a constant amplitude history and this is incorporated in the model formulation. Using scaling laws, an improved understanding of the scaling behavior on different parameters is achieved. The models describing different regimes of crack propagation are finally unified to obtain the entire crack growth curve and compute the total fatigue life. In addition, crack growth analysis is performed for a reinforced concrete member by modifying the model derived for plain concrete in the Paris regime. Energy dissipation occurring due to shake-down phenomenon in steel reinforcement is addressed. The bond-slip mechanism which is of serious concern in reinforced concrete members is included in the study and a method is proposed for the prediction of residual moment carrying capacity as a function of relative crack depth. The application of the proposed analytical model in the computation of fatigue crack growth is demonstrated on three practical problems – beam in flexure, concrete arch bridge and a patch repaired beam. Through a sensitivity study, the influence of different parameters on the crack growth behavior is highlighted.

Rock slope failures leading to rock falls and rock slides are caused by a multitude of factors, including seismic activity, weathering, frost wedging, groundwater and thermal stressing. Although these causes are generally attributed as separate causes, some of them will often act together to cause rock slope failures. In this work, two of the above factors, seepage of water through cracks and crack propagation due to the after effects of blasting are considered. Their combined impact on the development of rock falls and rock slides is modeled on ANSYS workbench using the Bingham Canyon mine slope failure of 2013 as a case study. Crack path modeling and slope stability analysis are used to show how a combination of crack propagation and seepage of water can lead to weakening of rock slopes and ultimate failure. Based on the work presented here, a simple approach for modeling the development of rock falls and rock slides due to crack propagation and seepage forces is proposed. It is shown how the information from remote sensing images can be used to develop crack propagation paths. The complete scope of this method involves demonstrating the combination of basic remote sensing techniques combined with numerical modeling on ANSYS workbench.

It is reasonable to assume that an aircraft might experience some in-flight discrete source damage caused by various incidents. It is, thus, necessary to evaluate the impact of such damage on the performance of the aircraft. This study is focused on evaluating the effect of a simple discrete damage in an aircraft wing on its static and dynamic response. The damaged wing is modeled by a thin-walled beam with a longitudinal crack the response of which can be obtained analytically. As uncertainties are present in the location and size of the crack as well as in the applied loads, their effects are incorporated into the framework consisting of structural response, crack propagation and aeroelasticity. The first objective of this study is to examine the effect of damage represented by a crack on the wing flexibility that influences its deformation and aero-elastic divergence characteristics. To study this, the thin-walled beam is modeled by Benscoter thin-walled beam theory combined with Gunnlaugsson and Pedersen compatibility conditions to accurately account for the discontinuity at the interface of the cracked and uncracked beam segments. Instead of conducting a detailed finite element analysis, the solution is obtained in an exact sense for general distributed loads representing the wind pressure effects. This analytical approach is shown to provide very accurate values for the global beam response compared with the detailed finite element shell analysis. This analytical solution is, then, used to study the beam response probabilistically. The crack location and size are assumed to be uncertain and are, thus, characterized by random variable. For a specified limit state, the probability of failure can be conveniently calculated by the first order second moment analysis using the safety index approach. The same analytical solution is also used to study the aero-elastic divergence characteristics of a wing, the inner structure of which is represented by a thin-walled beam with a crack of uncertain size and position along the beam. The second objective of this study is to examine the time growth of a crack under dynamic gust type of loading to which a wing is likely to be exposed during flight. Damage propagating during operation further deteriorates the safety of the aircraft and it is necessary to study its time growth so that its impact on the performance can be evaluated before it reaches its unstable state. The proposed framework for the crack growth analysis is based on classical fracture mechanics where the remaining flight time is obtained by Monte Carlo simulation in which various uncertainties are taken into account. To obtain equivalent cyclic loading required for crack growth analysis, random vibration analysis of the thin-walled beam is conducted for stochastic wind load defined by a gust load spectral density function. The probability of failure represented by the crack size approaching the critical crack size within the flight duration or the remaining flight time before a crack reaches its limiting value are obtained. This study with a simple representation of a wing and damage is anticipated to provide initial guidance for future studies to examine the impact of discrete source damage on the in-flight performance of the aircrafts, with the ultimate goal of minimizing the adverse effect and enhancing the safety of aircrafts experiencing damage. / Ph. D.

Elastic-plastic finite element analyses were performed to predict the crack opening level profiles in semi-elliptical surface cracks. A script was written to use the commercial finite element code ANSYS to predict opening levels in cracked geometries. The functionality of the scripts was verified by comparing predicted opening levels in two and three-dimensional center-cracked geometries to experimental results. In addition, a parameter study was performed in which various aspects of the modeling routine were modified. This included a mesh refinement study as well as a study into the effect of a strain hardening material. The main focus of the current research, however, is to compare finite element predicted opening levels with published opening levels determined experimentally. Due to the complexities and long run-times involved with these models, no attempt was made at growing the cracks from initial length to final length. Instead, discrete crack lengths at which experimental opening levels were published were instead used. Also, no attempt was made to predict the crack aspect ratio evolution. The finite element predicted opening levels were in all cases significantly lower than those reported experimentally, however, similar trends in both crack opening level profile along the crack front, and opening level variations with crack growth were shown.

No description available.

A computer-based parametric study of the effect of reinforcement architectures on fracture response of aluminum compact-tension (CT) specimens was performed using the finite element code ABAQUS. A three-dimensional crack propagation procedure based on the crack tip opening angle (CTOA) was developed using Python. Eleven different reinforcement architectures consisting of rectangular and triangular cross-section reinforcements were evaluated. Reinforced specimens produced between 13 and 28 percent higher fracture load than achieved with the non-reinforced case. Reinforcements with blunt leading edges (rectangular reinforcements) exhibited superior performance relative to the triangular reinforcements with sharp leading edges. Relative to the rectangular reinforcements, the most important architectural feature was reinforcement thickness. At failure, the reinforcements carried between 58 and 85 percent of the load applied to the specimen, suggesting that there is considerable load transfer between the base material and the reinforcement. The amount of load transfer is linked to strains experienced by the reinforcement ahead of the crack tip. / Master of Science

Structural concrete is the most widely used material in the construction of bridges, pave-ments, runways, dams and other infrastructures which are subjected to uctuating loads during its service period. Concrete contains internal aws in the form of micro-cracks as an inherent property. When subjected to fatigue loading, distributed micro-cracks are formed at the sites of pre-existing aws, which subsequently, localize to form a major crack and propagates. The crack growth curve of a structural component when subjected to fatigue loading depicts a sigmoidal pattern. This curve is divided into three distinct regions namely sub-threshold crack propagation (short crack), stable crack propagation (long crack) and unstable crack propagation depending on the crack propagation rate. Most of the fatigue life is spent in the sub-critical stage (small crack) before the for-mation of long cracks. Hence, from the view of estimating the fatigue life, the crack initiation and early crack propagation (short crack stage) phase are the most important and correct concepts need to be developed. Hence, in this work, the behavior of propa-gation and non-propagationof short cracks in concrete when subjected to fatigue loading is addressed. Small non-propagating cracks are usually found at notch roots when the nominal stress range is below certain limits that depend on the notch sensitivity. Analysis is performed on geometrically similar three-point bend beams of three di erent sizes and subjected to fatigue loading in order to determine the important factors that a ect the notch sensitivity and to determine the minimum stress range required for the initiation and propagation of short cracks. A criterion for crack initiation and propagation is proposed based on linear elastic fracture mechanics. Using this criterion, the maximum length of non-propagating crack that can be formed from fatigue loading alone and the minimum stress range required to propagate a crack without arrest are computed. It is observed that the notch sensitivity increases with increase in beam size, decrease in notch-tip aspect ratio and increase in the fatigue limit of the material. Since the probability of formation of a non-propagating crack at a notch tip decreases with increase in notch sensitivity, and since it is desirable not to have a non-propagating crack in experimental investigations, it is essential to design a specimen with higher notch sensitivity. A crack spends a considerable amount of time in the short crack regime. The short cracks are found to propagate at higher rates than the long cracks at the same nominal stress intensity factor which is known as the short crack anomaly. It is important to consider this anomaly in the prediction of the residual life of damaged concrete structures. Hence, in the present work, an analytical model is developed using the principles of dimensional analysis and self-similarity in order to estimate the rate of short crack growth in concrete. The important parameters such as load range, threshold value of stress intensity factor range, modulus of elasticity, tensile strength, fracture energy, stress ratio, crack size and the maximum aggregate size are considered in the development of the short crack growth model. The model is calibrated and validated using the experimental results that are available in the literature. A probabilistic analysis is carried out to determine the sensitivity of each of the di erent parameters that has been considered on the crack growth rate using the coe cient of variation method. It is found that the crack length is the most sensitive parameter to short crack growth rate followed by the load range. A term called `characteristic fatigue life of short crack' is de ned as the number of fatigue cycles that can be applied such that not more than ve percent of the short cracks is expected to proceed to the long crack regime. Furthermore, the fatigue life of a crack spent in the short crack regime is determined through a reliability based study using the Monte Carlo technique. It is found that the smaller sized specimens have larger fatigue life in the short crack regime than the larger specimens.

Les techniques de mesure de champs, et en particulier celles basées sur la Corrélation d’Images Numériques (CIN), sont matures et reconnues pour la détermination de déplacements d’objets quelconques, en deux ou trois dimensions. Ces travaux ont pour objet le développement d’essais et de techniques d’identification associées, en s’appuyant sur les méthodes de mesure par CIN, pour permettre l’évaluation des caractéristiques mécaniques d’un liner en titane T35, développé pour des applications spatiales. Des essais de traction uniaxiale sont tout d'abord utilisés pour déterminer le comportement élastoplastique du T35. Plusieurs méthodes d'identification sont comparées. En particulier, il est proposé d'étendre la corrélation d'image dite "intégrée" aux cas élastoplatiques. Cette méthode permet d'évaluer à la fois les déplacements du solide observé et les paramètres mécaniques des matériaux le constituant. Elle est comparée à une méthode de recalage de référence. L'étude se porte ensuite sur l'analyse de l'amorçage des fissures dans le liner. Les chargements cycliques du réservoir imposent à la tôle une déformation biaxiale cyclique en traction-compression de quelques pourcents, qui a été reproduite expérimentalement dans une machine multiaxiale. Cette partie a notamment nécessité le développement d’un essai triaxial à rapport de charge négatif sur tôle mince. Une estimation de la limite d'amorçage a été obtenue pour les niveaux de déformation visés. Enfin, la fissuration du liner a été étudiée par des techniques d'analyse dédiées. Certaines de ces techniques sont comparées quantitativement, afin d'étudier leurs capacités et limitations respectives. Des lois de propagation de type Paris ont été identifiées directement à partir d'images du voisinage de la fissure. / Field measurement techniques, and more particularly those based on Digital Image Correlation (DIC), are mature techniques for the determination of displacements of two or three-dimensional objects. The goal of this work is to develop test and associated identification DIC-based techniques to identify the mechanical behavior of a commercially-pure titanium liner, conceived for spatial applications. Uniaxial tensile teste are first used to identify the elasto-plastic behavior of this material. Several identification methods are compared. It is especially proposed to extend said "integrated" Digital Image Correlation to elasto-plastic cases. This methods allows to identify directly the displacement of the observed solid and the mechanical parameters of the constituting material. It is compared to a reference updating method. The crack initiation is then studied in this material. Some zones of the liner will be submitted to a plastic cyclic deformation, that has to be reproduced experimentally. A dedicated test has been conceived, allowing to apply a negative load ratio to the thin sheet. An estimation of the initiation limit has been obtained for this material. Finally, the crack propagation in the liner has been studied, using dedicated techniques. Some of these have been quantitatively compared, to study their respective capabilities. Paris' propagation laws have been identified directly from a set of raw images of the crack tip vicinity.

Foram estudadas as propriedades de fadiga em dois grupos de soldas de alta resistência e baixa liga com diferentes composições microestruturais. As soldas do grupo A apresentaram microestruturas compostas de ferrita acicular, ferrita alotriomórfica e ferrita de Widmanstätten, com limite de escoamento de aproximadamente 460 MPa, enquanto que as soldas do grupo B apresentaram microestruturas compostas de martensita de baixo carbono, bainita e ferrita acicular, com limite de escoamento de aproximadamente 850 MPa. A partir do ensaio de trincas longas, foi obtida a taxa de crescimento por ciclos de carregamento, da/dN, de da/dN=1,18·10-12·DeltaK2,91 e da/dN=1,34·10-11·DeltaK2,64, respectivamente para as soldas dos grupos A e B. Como pode ser observado a partir destas equações, a taxa de crescimento foi mais alta para o grupo B. Da análise do fechamento da trinca pode ser concluído que o principal fator determinante de uma menor taxa de propagação para as soldas do grupo A foi a plasticidade desenvolvida pela estrutura. Dos ensaios de trincas curtas foi observado que no caso das soldas do grupo A, uma vez nucleada a trinca, esta se propagava até o colapso do corpo de prova. Para as soldas do grupo B foi observado que não bastava a existência de uma trinca para que esta se propagasse até a fratura total do corpo de prova e que o fator controlador foi a granulomentria associada a uma determinada composição microestrutural. / The fatigue properties of two groups of high strength low alloy steel weld metals with different microstructural composition were studied. Weld metals from group A presented microstructures composed of acicular ferrite, Widmanstätten ferrite and allotriomorphic ferrite, with yield strength of 460 MPa. Weld metals from group B exhibited a microstructural composition of low carbon martensite, bainite and acicular ferrite, with a yield strength of 850 MPa. The fatigue crack growth per cycle of loading, da/dN, for weld metals from groups A and B is obtained from the relationships, da/dN=1,18·10-12·DeltaK2,91 and da/dN=1,34·10-11·DeltaK2,64, respectively. As can be seen from these equations, the crack growth rate was higher for group B. From the crack growth closure analysis, it may be concluded that the lower crack growth rate obtained for weld metals from group A was mainly due to the higher crack tip plasticity developed in this type of microstructure. From the short crack fatigue tests, it was observed for weld metals from group A, that once a crack was nucleated, it propagated until the testpiece plastic collapsed. For weld metals from group B, it was observed that the existence of a crack was not sufficient to cause the complete testpiece failure, and the association of the grain size with the local microstructure was the main factor controlling the failure process.

[pt] Apesar da extensa aplicabilidade do Método de Elementos Finitos na representação e solução de problemas dos mais diversos campos da Engenharia, há ainda classes de problemas em que o seu uso encontra severas dificuldades. Uma delas está relacionada com a simulação da evolução temporal da geometria ou de condições de contorno móveis na Mecânica Computacional. Exemplos típicos destes problemas envolvem grandes deformações, propagação de trincas na mecânica da fratura, escoamentos bi-fásicos , transferência de calor em meios com mudança de fase , entre outros. Nestes casos, a tarefa do acompanhamento das modificações de geometria, dos deslocamentos nas interfaces e das descontinuidades a serem representadas pela malha de elementos finitos implica em modificações da discretização a cada passo da análise, o que requer o emprego de sofisticados procedimentos de adaptação ou de reconstrução da malha. Para atender a estas situações, duas classes de novas estratégias foram recentemente propostas na literatura: i) Métodos sem Malha, em que a discretização é estabelecida a partir de um conjunto de nós distribuídos sobre o domínio, dispensando o uso da entidade elemento e, ii) Método de Elementos Finitos Generalizados (MEFG), em que a capacidade de representação da base de funções de forma tradicionais do MEF é estendida utilizando-se funções específicas ao problema em analise. Neste trabalho investigam-se as características destas duas classes de métodos e, suas vantagens e limitações na aplicação à análise de problemas da mecânica da fratura computacional. Da comparação do desempenho destas técnicas na solução de problemas envolvendo descontinuidades localizadas demonstra-se que o MEFG é numericamente superior aos demais, em aplicações com a análise da propagação de trincas no contexto da Mecânica da Fratura Linear Elástica (MFLE). Por este método, o campo de deslocamentos representados no MEF tradicional por funções lagrangianas é adicionado (enriquecido) localmente por funções que representam as características de descontinuidade (trinca) presentes no contínuo de forma implícita e independente da malha. A nova base de funções incorpora também termos que representam a solução da mecânica da fratura linear elástica para os deslocamentos na vizinhança da ponta-de- trinca, mantendo as características de partição da unidade próprias do MEF. A formulação foi implementada em um programa para a análise de problemas planos juntamente com uma nova estratégia de integração numérica das equações de equilíbrio que permite eliminar o emprego de eventuais modificações da malha . Este procedimento de integração emprega uma composição das quadraturas de Gauss-Lobato e Gauss-Radau, capacitando o método à uma analise robusta sem o uso de quaisquer procedimentos de reconstrução de malha. Testes numéricos com modelos do MEFG são apresentados e discutidos , verificando-se uma boa correlação da solução numérica obtida com resultados experimentais ou outras soluções clássicas da MFLE. / [en] The Finite Element Method is certainly the most generally used technique for the solution of Engineering problems. However, there are some classes of problems in which the method is still not straightly applicable. One of those is related to the simulation of problems with moveable geometry and/or boundary conditions, in the field of Computation Mechanics. Typical examples are found in fields such : large deformations, crack propagation, two- phase flow, heat transfer with phase change, and so on. In these cases, because displacements at the interfaces and the geometry are to be followed throughout the solution, a regular finite element procedure becomes too cumbersome to represent, requiring the use of sophisticated procedures for adaptation and mesh reconstruction. To overcome these difficulties, two classes of new numerical procedures have been recently proposed: i) Meshless Methods (MM), where the state-variables are interpolated by a set of node values, within the problem domain, without using element boundaries and, ii) Generalized Finite Elements Method (GFEM), where the interpolation function basis is expanded in order to accommodate specific interpolation functions, adjusted to the problem in consideration. In this work the characteristics of these two procedures were evaluated considering their applications to numerical problem solutions, in the field of fracture mechanics. It is demonstrated that the GFEM results in a better numerical procedure considering applications to the crack propagation problem, in the context of linear fracture mechanics. In this method, the displacement fields provided by standard FEM are locally enriched by specific functions which represent, implicitly and independently of the mesh, the requirements for displacement discontinuities. The new function basis also incorporates a solution for the displacements in the neighborhood of the crack tip, obtained from linear fracture mechanics solution. The formulation has been implemented for the analysis of plane problems using a new numerical integration strategy, for numerical evaluation of the equilibrium equations. This integration procedure uses a composition of Gauss-Lobato e Gauss-Radau quadratures, assuring the method numerical robustness, with no requirements for mesh reconstruction. Numerical test solutions with GFEM models are compared to experimental and other classic solutions to demonstrate the method applicability to the analysis of linear fracture mechanics problems.