É conhecida ao longo da história da humanidade a grande quantidade de acidentes vinculados à ação de cargas cíclicas. Há mais de 100 anos, metodologias levam em conta o fenômeno de fadiga em projetos de novos componentes. As metodologias existentes para avaliar a vida em fadiga são empíricas e têm sido aplicadas com sucesso na determinação da vida do componente em fadiga quando o mesmo é submetido a carregamento uniaxial ou a carregamento multiaxial proporcional. Mas a evidencia experimental tem mostrado que quando a solicitação é multiaxial e não proporcional, as leis antes mencionadas deixam de ser adequadas. Dessa forma os critérios clássicos utilizados não preveem corretamente a vida do componente. Neste contexto o presente trabalho avalia algumas das metodologias de fadiga multiaxial não proporcionais disponíveis na bibliografia especializada. Os resultados obtidos com estes métodos são comparados entre sim e com os resultados obtidos utilizando a metodologia de fadiga multiaxial proporcional. Para comparar as metodologias citadas é apresentado um exemplo de solicitação simples, e também a análise do componente de uma máquina agrícola solicitada por um histórico de tensões típicas, obtida a partir do teste da máquina em campo. Finalmente são apresentadas as conclusões sobre as metodologias utilizadas e sobre a importância de levar em conta a não proporcionalidade de um estado de tensões multiaxial oscilantes. / It is known throughout human history the large amount of accidents linked to action of cyclic loading. For over 100 years, methodologies take into account the fatigue phenomenon of new components projects. Existing methodologies for assessing the fatigue life are empirical and have been successfully applied in the determination of fatigue life of the component when it is subjected to uniaxial loading or proportional multiaxial loading. But the experimental evidence has shown that when the request is multiaxial and not proportional, the laws mentioned above are no longer adequate. Thus the classical criteria used not correctly predict component life. In this context, this paper analyzes some of the methodologies of multiaxial fatigue non proportionate available in the relevant literature. The results obtained with these methods are compared with the results so obtained and using the proportional multiaxial fatigue methodology. To compare the methods mentioned is an example of simple request, and also the analysis component of an agricultural machine requested by a history of typical strains, obtained from the machine field testing on a test track. Finally conclusions on the methodologies used and the importance of taking into account the non-proportionality of a state of oscillating multiaxial stresses are presented.

É conhecida ao longo da história da humanidade a grande quantidade de acidentes vinculados à ação de cargas cíclicas. Há mais de 100 anos, metodologias levam em conta o fenômeno de fadiga em projetos de novos componentes. As metodologias existentes para avaliar a vida em fadiga são empíricas e têm sido aplicadas com sucesso na determinação da vida do componente em fadiga quando o mesmo é submetido a carregamento uniaxial ou a carregamento multiaxial proporcional. Mas a evidencia experimental tem mostrado que quando a solicitação é multiaxial e não proporcional, as leis antes mencionadas deixam de ser adequadas. Dessa forma os critérios clássicos utilizados não preveem corretamente a vida do componente. Neste contexto o presente trabalho avalia algumas das metodologias de fadiga multiaxial não proporcionais disponíveis na bibliografia especializada. Os resultados obtidos com estes métodos são comparados entre sim e com os resultados obtidos utilizando a metodologia de fadiga multiaxial proporcional. Para comparar as metodologias citadas é apresentado um exemplo de solicitação simples, e também a análise do componente de uma máquina agrícola solicitada por um histórico de tensões típicas, obtida a partir do teste da máquina em campo. Finalmente são apresentadas as conclusões sobre as metodologias utilizadas e sobre a importância de levar em conta a não proporcionalidade de um estado de tensões multiaxial oscilantes. / It is known throughout human history the large amount of accidents linked to action of cyclic loading. For over 100 years, methodologies take into account the fatigue phenomenon of new components projects. Existing methodologies for assessing the fatigue life are empirical and have been successfully applied in the determination of fatigue life of the component when it is subjected to uniaxial loading or proportional multiaxial loading. But the experimental evidence has shown that when the request is multiaxial and not proportional, the laws mentioned above are no longer adequate. Thus the classical criteria used not correctly predict component life. In this context, this paper analyzes some of the methodologies of multiaxial fatigue non proportionate available in the relevant literature. The results obtained with these methods are compared with the results so obtained and using the proportional multiaxial fatigue methodology. To compare the methods mentioned is an example of simple request, and also the analysis component of an agricultural machine requested by a history of typical strains, obtained from the machine field testing on a test track. Finally conclusions on the methodologies used and the importance of taking into account the non-proportionality of a state of oscillating multiaxial stresses are presented.

É conhecida ao longo da história da humanidade a grande quantidade de acidentes vinculados à ação de cargas cíclicas. Há mais de 100 anos, metodologias levam em conta o fenômeno de fadiga em projetos de novos componentes. As metodologias existentes para avaliar a vida em fadiga são empíricas e têm sido aplicadas com sucesso na determinação da vida do componente em fadiga quando o mesmo é submetido a carregamento uniaxial ou a carregamento multiaxial proporcional. Mas a evidencia experimental tem mostrado que quando a solicitação é multiaxial e não proporcional, as leis antes mencionadas deixam de ser adequadas. Dessa forma os critérios clássicos utilizados não preveem corretamente a vida do componente. Neste contexto o presente trabalho avalia algumas das metodologias de fadiga multiaxial não proporcionais disponíveis na bibliografia especializada. Os resultados obtidos com estes métodos são comparados entre sim e com os resultados obtidos utilizando a metodologia de fadiga multiaxial proporcional. Para comparar as metodologias citadas é apresentado um exemplo de solicitação simples, e também a análise do componente de uma máquina agrícola solicitada por um histórico de tensões típicas, obtida a partir do teste da máquina em campo. Finalmente são apresentadas as conclusões sobre as metodologias utilizadas e sobre a importância de levar em conta a não proporcionalidade de um estado de tensões multiaxial oscilantes. / It is known throughout human history the large amount of accidents linked to action of cyclic loading. For over 100 years, methodologies take into account the fatigue phenomenon of new components projects. Existing methodologies for assessing the fatigue life are empirical and have been successfully applied in the determination of fatigue life of the component when it is subjected to uniaxial loading or proportional multiaxial loading. But the experimental evidence has shown that when the request is multiaxial and not proportional, the laws mentioned above are no longer adequate. Thus the classical criteria used not correctly predict component life. In this context, this paper analyzes some of the methodologies of multiaxial fatigue non proportionate available in the relevant literature. The results obtained with these methods are compared with the results so obtained and using the proportional multiaxial fatigue methodology. To compare the methods mentioned is an example of simple request, and also the analysis component of an agricultural machine requested by a history of typical strains, obtained from the machine field testing on a test track. Finally conclusions on the methodologies used and the importance of taking into account the non-proportionality of a state of oscillating multiaxial stresses are presented.

For decades, structural engineers have been using various conventional design approaches for assessing the strength and stability of framed structures for various loads. Today, engineers are still designing without some critical information to insure that their stability assessment yields a safe design for the life of the structure with consideration for extreme loads. Presented in this thesis is new critical information provided from the study of stability analysis and design of steel framed structures accounting for extreme loads associated to load patterns that may be experienced during their lifetime. It is conducted in five main parts. A literature survey is first carried out reviewing the previous research of analyzing frame stability including the consideration of initial geometric imperfections, and also evaluating research of the analysis and design of the increased usage of cold-formed steel (CFS) storage racks. Secondly, the elastic buckling loads for single-storey unbraced steel frames subjected to variable loading is extended to multi-storey unbraced steel frames. The formulations and procedures are developed for the multi-storey unbraced steel frames subjected to variable loading using the storey-based buckling method. Numerical examples are presented as comparisons to the conventional proportional loading approach and to demonstrate the effect of connection rigidity on the maximum and minimum frame-buckling loads. Thirdly, the lateral stiffness of axially loaded columns in unbraced frames accounting for initial geometric imperfections is derived based on the storey-based buckling. A practical method of evaluating column effective length factor with explicit accounting for the initial geometric imperfections is developed and examined using numerical examples. The fourth part is an investigation of the stability for multi-storey unbraced steel frames under variable loading with accounting for initial geometric imperfections. Finally, the stability of CFS storage racks is studied. The effective length factor of CFS storage racks with accounting for the semi-rigid nature of the beam-to-column connections of such structures are evaluated based on experimental data. A parametric study on maximum and minimum frame-buckling loads with or without accounting for initial geometric imperfections is conducted. The proposed stability analysis of multi-storey unbraced frames subjected to variable loading takes into consideration the volatility of live loads during the life span of structures and frame buckling characteristics of the frames under any possible load pattern. From the proposed method, the maximum and minimum frame-buckling loads together with their associated load patterns provides critical information to clearly define the stability capacities of frames under extreme loads. This critical information in concern for the stability of structures is generally not available through a conventional proportional loading analysis. This study of work ends with an appropriate set of conclusions.

For decades, structural engineers have been using various conventional design approaches for assessing the strength and stability of framed structures for various loads. Today, engineers are still designing without some critical information to insure that their stability assessment yields a safe design for the life of the structure with consideration for extreme loads. Presented in this thesis is new critical information provided from the study of stability analysis and design of steel framed structures accounting for extreme loads associated to load patterns that may be experienced during their lifetime. It is conducted in five main parts. A literature survey is first carried out reviewing the previous research of analyzing frame stability including the consideration of initial geometric imperfections, and also evaluating research of the analysis and design of the increased usage of cold-formed steel (CFS) storage racks. Secondly, the elastic buckling loads for single-storey unbraced steel frames subjected to variable loading is extended to multi-storey unbraced steel frames. The formulations and procedures are developed for the multi-storey unbraced steel frames subjected to variable loading using the storey-based buckling method. Numerical examples are presented as comparisons to the conventional proportional loading approach and to demonstrate the effect of connection rigidity on the maximum and minimum frame-buckling loads. Thirdly, the lateral stiffness of axially loaded columns in unbraced frames accounting for initial geometric imperfections is derived based on the storey-based buckling. A practical method of evaluating column effective length factor with explicit accounting for the initial geometric imperfections is developed and examined using numerical examples. The fourth part is an investigation of the stability for multi-storey unbraced steel frames under variable loading with accounting for initial geometric imperfections. Finally, the stability of CFS storage racks is studied. The effective length factor of CFS storage racks with accounting for the semi-rigid nature of the beam-to-column connections of such structures are evaluated based on experimental data. A parametric study on maximum and minimum frame-buckling loads with or without accounting for initial geometric imperfections is conducted. The proposed stability analysis of multi-storey unbraced frames subjected to variable loading takes into consideration the volatility of live loads during the life span of structures and frame buckling characteristics of the frames under any possible load pattern. From the proposed method, the maximum and minimum frame-buckling loads together with their associated load patterns provides critical information to clearly define the stability capacities of frames under extreme loads. This critical information in concern for the stability of structures is generally not available through a conventional proportional loading analysis. This study of work ends with an appropriate set of conclusions.

Les rails de Chemins de fer sont soumis à de la fatigue de roulement due au passage répété des roues de train, ce qui induit différents types de fissures, telles que les Squats. Ces fissures sont soumises à un chargement de mode mixte non-proportionnel I + II + III, dans des proportions variables le long du front, avec des phases de compression, ce qui rend la prédiction de leur trajet et de leur vitesse délicate.La cinétique de fissuration en mode I a été déterminée dans de l’acier à rail R260, pour des rapports R positifs et négatifs, ainsi que la cinétique de mode mixte II & III corrigée des effets de frottement. Les Facteurs d’Intensité des Contraintes (FICs) effectifs ont été obtenus à partir des sauts de déplacements dans le plan et hors plan mesurés en surface, le long de la fissure. De ces lois cinétiques, il ressort que ni le mode I seul, ni les modes de cisaillement seuls ne peuvent expliquer la fissuration des rails. C’est donc la combinaison des trois modes, suivant des trajets de chargement complexes, qui en est responsable.Des essais de fissuration par fatigue en mode mixte non-proportionnel I + II ont ensuite été réalisés, suivant des trajets de chargement représentatifs de ceux subis par les squats. La stéréo corrélation d’images a été utilisée pour obtenir les champs de déplacements en pointe de fissure. Les méthodes classiques de mesure des FICs à partir de champs de déplacements n’étant pas adaptées, du fait des efforts de contact et frottement entre les lèvres de fissure, de nouvelles méthodes ont été développées. Les trajets et vitesses de fissuration ont été étudiés au regard de ces FICs effectifs. Il apparait que la prédiction du trajet à partir du critère de la contrainte tangentielle maximale n’est pas très fiable, mais peut être améliorée par la prise en compte de la plasticité en pointe de fissure ainsi que des efforts de contact/frottement entre les lèvres de fissure. Les vitesses de propagation obtenues se corrélèrent bien avec une combinaison des trois FICs effectifs dans une loi de type « Paris ».De ces essais, il ressort que du fait de la rugosité de la fissure, l’enchevêtrement d’aspérités et le frottement réduisent considérablement les FICs effectifs. Et cela même en l’absence de compression normale, ce qui ne peut être modélisé par une simple loi de Coulomb. De plus, l’usure des lèvres de fissure a aussi une forte influence sur les FICs effectifs. Le challenge pour les applications structurelles est donc non seulement de choisir le critère de bifurcation et la loi cinétique les plus appropriés, mais également de prendre en compte la rugosité et l’usure des lèvres de fissure, afin d’estimer correctement les FICs effectifs à utiliser dans ces modèles.Pour les applications industrielles, une approche d’ingénieur, simplifiée, a été proposée afin de prendre en compte le frottement induit par la rugosité dans l’estimation des trajets de chargements effectifs à partir des trajets nominaux. Cette approche a été validée sur des essais de mode mixte séquentiel I + II & III. / Rails are submitted to Rolling Contact Fatigue due to repeated passages of train wheels, which induces several types of cracks, such as Squat-type cracks. Those cracks undergo non-proportional mixed-mode I + II + III loading, including compression phases, in variable proportions along the crack front, making the prediction of their paths and growth rates a challenge.Mode I crack growth kinetics, for positive and negative R ratios, were first determined in R260 steel, as well as friction-corrected crack growth kinetics for fully-reversed combined mode II and III. The effective Stress Intensity Factors (SIFs) were deduced from the measured in-plane and out-of-plane crack face sliding displacements. From those kinetic laws, it was deduced that neither pure mode I, nor pure shear mode loadings can explain the crack growth rates observed in rails. A combination of those three loading modes, according to complex loading paths had thus to be prospected.Non-proportional mixed-mode I + II fatigue crack growth tests were then performed, following representative loading paths. Stereo digital image correlation was used to measure the near-tip displacement field. Post-treatment methods generally used to deduce the effective SIFs from these fields were inappropriate because of contact and friction stresses along the crack face. New methods were thus developed. The crack paths and growth rates were analyzed, using the effective SIFs. Crack path prediction by the maximum tangential stress criterion was found not to be very reliable, but substantially improved when crack tip plasticity and the presence of contact and friction stresses along the crack faces were taken into account. The measured crack growth rates correlated well with a combination of the three effective SIFs in a Paris-type law.From these experiments, it appears that due to crack face roughness, asperities interlocking and friction substantially reduce the effective SIFs, even without any normal compression, which cannot be captured by a simple Coulomb’s law. Besides, crack faces wear also has a large influence on the effective SIFs. The challenge for structural applications is thus not only to choose the most appropriate bifurcation criterion and crack growth law, but also to take crack face roughness and wear into account, in order to estimate the correct effective SIFS to use in these models.For industrial applications, a simple engineering approach was proposed to integrate roughness-induced friction in the estimation of the effective loading path from the nominal one. This approach was validated on sequential mixed-mode I + II & III experiments.

Fatigue analysis is a critical stage in the design of any structural component. Typically fatigue is analysed during post-processing, but as the size of the analysed component increases, the amount of data stored for the analysis increases simultaneously. This increases the computational and memory requirements of the system, intensifying the work load on the engineer. A continuum mechanics approach namely ’Continuous time fatigue model’, for fatigue analysis is available in a prior study which reduces the computational requirements by simultaneously computing fatigue along with the stress. This model implements a moving endurance surface in the stress space along with the damage evolution equation to compute high-cycle fatigue. In this thesis the continuous time fatigue model is compared with conventional model (ie.Cycle counting) to study its feasibility. The thesis also aims to investigate the continuous time fatigue model and an evolved version of the model is developed for non-proportional load cases to identify its limitations and benefits.

Le travail s’intéresse aux effets d’un pré-écrouissage cyclique axial ou en torsion sur le comportement cyclique et la durée de vie en fatigue sous sollicitation axiale à température ambiante d’un acier inoxydable austénitique 304L. Les essais cycliques séquentiels à amplitude de déformation croissante ou décroissante montrent que la courbe cyclique du 304L est non-unique. Cette caractéristique est liée à la persistance de l’état microstructural généré pendant les cycles d’amplitude de déformation maximale de la première séquence. En augmentant le nombre des séquences, l’acier 304L montre une tendance vers une courbe cyclique asymptotique, l’écrouissage semble se stabiliser. Des essais de fatigue sous chargement axial ont été réalisés sur des éprouvettes vierges ou pré-écrouies en traction-compression ou en torsion. Les durées de vie ont été sensiblement réduites pour les éprouvettes pré-écrouies. Ce phénomène est lié à la formation de structures de dislocations denses héritées de la phase de pré-écrouissage. Cependant, l’augmentation de l’amplitude de déformation en fatigue réduit l’effet du pré-écrouissage. / This study investigates the effects of loading history on the cyclic stress-strain curve and fatigue behavior of 304L stainless steel at room temperature. Tension-compression tests were performed ont the same specimen under controlled strain, using several loading sequences of increasing or decreasing amplitude. The results showed that fatigue life is significantly reduced by the previous loading history. A previously developed method for determining the effect of prehardening was evaluated. Microstructural analyses were also performed; the microstructures after preloading and their evolution during the fatigue cycles were characterized by TEM. The results of these analyses improve our understanding of the macroscopic properties of 304L stainless steel and can help us identify the causes of failure and lifetime reduction.

[pt] A avaliação da propagação de trincas de fadiga inclui a identificação da direção da trinca, o conhecimento do Fator de Intensidade de Tensões (SIF) equivalente, a determinação de uma taxa de crescimento de comprimento de trinca por número de ciclos da/dN e o estabelecimento de uma regra de propagação de trinca conectando SIF e da/dN, como uma regra de tipo Paris. Quando ocorrem cargas mistas e não proporcionais, esses parâmetros ainda não são totalmente compreendidos. Esta tese trata de algumas das variáveis que influenciam a propagação de trincas sob carregamento no modo misto não proporcional. A técnica de Correlação de Imagens Digitais (DIC) foi utilizada para a aquisição de imagens de corpos de prova submetidos a carregamento proporcional e não proporcional cíclico. Dois tipos de corpos de prova foram utilizados. Primeiramente, dois corpos de prova planos foram testados; um disk compact tension (DCT, em inglês) e um compact tension modificado (C (T) em inglês). Eles foram submetidos a carregamento cíclico induzindo o modo I de abertura de trinca ou modos I e II de abertura de trinca proporcionais. Em segundo lugar, os dados DIC adquiridos anteriormente, e em outro lugar, para cinco tubos finos sujeitos a carregamento cíclico foram analisados. Os tubos finos tiveram entalhes usinados a partir dos quais as trincas por fadiga iniciaram e se propagaram. Esses cinco tubos finos foram submetidos a diferentes casos de carga proporcional e não proporcional. Um corpo de prova tipo tubo fino foi exposto a carga axial e apresentou modo de abertura de trinca tipo I. Os outros quatro foram submetidos a carregamento de torção ou carga axial-torcional mista e exibiram todos os três modos de abertura de trinca I, II e III. Os campos de deslocamento adquiridos experimentalmente com a técnica DIC foram processados para calcular independentemente o SIF para cada modo de abertura existente usando formulações de mecânica de fratura elástica linear (MFLE). Uma formulação delas utilizou dados de deslocamento de campo completos adquiridos em pequenas áreas que circundavam a ponta da trinca. Outra formulação usou dados adquiridos de um par de pontos localizados ao longo dos flancos opostos das faces da trinca. Os SIFs determinados foram usados para encontrar os SIFs equivalentes e faixas de SIF equivalentes usando o critério da tensão máxima de tração (para ambas as versões 2D e 3D de combinações dos modos I-II e modos I-II-III respectivamente) que implicitamente incluíram o ângulo de propagação de trinca. Verificou-se que a inclusão do SIF no modo III experimentalmente determinado efetivamente faz diferença nas faixas do SIF e dos SIF equivalentes estimados. A curva da/dN versus faixa do SIF equivalente foi elaborado com as taxas de crescimento de trinca medidas experimentalmente e as faixas de SIF que foram encontradas usando a suposição amplamente aceita de que as trincas cresceram na direção que maximiza a tensão de tração. Para isso, extensões do modelo de Schollmann et. al. e bem como o modelo de Erdogan-Sih, que são geralmente aplicados ao carregamento proporcional, foram usados para determinar os SIFs equivalentes e faixas de SIF equivalentes para os casos de carregamento proporcional e não proporcional. Finalmente, a segunda zona da regra de Paris (da/dN versus faixa do SIF equivalente) foi plotada para os cinco casos de carregamento nos tubos finos mostrando que eles caíram dentro de uma faixa razoavelmente fina e dispersa. / [en] Fatigue crack propagation assessment includes identifying the crack direction, knowing the equivalent Stress Intensity Factor (SIF) range, determining a crack length growth rate per number of cycles (da/dN), and establishing a crack propagation rule connecting the equivalent SIF and da/dN rate, such as a Paris type of rule. When mixed and non-proportional loading occur, those parameters are not fully understood yet. This thesis deals with some of the variables that influence crack propagation under non-proportional mixed mode loading. The Digital Image Correlation (DIC) technique was used to acquire images of test specimens subjected to cyclic proportional and non-proportional loading. Two types of specimen samples were used. Firstly, two different plate test specimens were tested; a disk compact tension (DCT), and a modified compact tension, C(T). They were subjected cyclic loading inducing crack opening mode I or proportional crack opening modes I and II. Secondly, the previously and elsewhere acquired DIC data for five thin tubes subject to cyclic loading were analyzed. The thin tubes had pre-fabricated slit-notches from which fatigue cracks initiated and propagated. Those five thin tubes were subjected to different cases of proportional and non- proportional loading. One tube specimen was exposed to axial loading and presented mode I crack opening. The other four were subjected to torsion loading or mixed axial-torsional loading and exhibited all three I, II and III crack-opening modes. The experimentally acquired DIC displacement fields were processed to independently calculate SIF for each existing opening mode using linear elastic fracture mechanics (LEFM) formulations. One formulation used full field displacement data acquired in small areas that surrounded the crack tip. Another formulation used data acquired from a pair of points located along the opposite crack flanks. The determined SIFs were used to find equivalent SIFs and equivalent SIF ranges using the maximum tensile stress criterion (for both 2D and 3D versions of combinations of modes I-II and modes I-II-III respectively) which implicitly included the crack propagation angle. It was found that the inclusion of the experimentally determined mode III SIF indeed makes a difference in the determined equivalent SIF and equivalent SIF ranges. A da/dN versus equivalent SIF ranges plot was drafted with the experimentally measured crack growth rates and the SIF ranges that were found by using the widely accepted assumption that the cracks grew in the direction that maximizes the tensile stress. For this, extensions of the Schollmann et. al. model as well as of the Erdogan-Sih model, which are generally applied to proportional loading, were used to determine equivalent SIFs and equivalent SIF ranges for the cases of proportional and non-proportional loading. Finally, the second stage of the Paris rule (da/dN versus SIF range) was plotted for the five thin tubes loading cases showing that they fell inside a reasonably thin scattered band.