The demand for lightweight materials in automobiles has been motivated by two factors: fuel economy and air pollution reduction. One of the first steps taken in automotive vehicle weight reduction was the use of aluminum alloys for both structural and non-structural parts. Although magnesium alloys, that have one fourth the density of steel and one third that of aluminum, have also been used in automobiles, however, their applications were limited to non-structural parts. Recently, interest has been focused on using magnesium alloys as structural materials for automotive load-bearing components. Load-bearing components in automobiles are usually subjected to multiaxial cyclic loading. Fatigue is considered to be a significant cause of ground vehicle component failure. Therefore, for magnesium alloys to be used for these components, an understanding of their fatigue behaviour is necessary. In this study, series of monotonic and cyclic tests were conducted on smooth specimens machined from AZ31B magnesium extrusion section. Two loading modes were considered in this investigation, axial and torsional. Monotonic tensile and compressive tests were performed at three different orientations, longitudinal (LD), i.e., parallel to the extrusion direction, 45° and transverse (TD) directions. Monotonic torsion tests were performed on specimens that were machined along the LD. Similarly, cyclic axial and torsional as well as multiaxial axial-torsional tests were performed on specimens that that were machined along the LD. Three different phase angles were considered for multiaxial tests: in-phase, and 45° and 90° out-of-phase. It was found that monotonic axial stress-strain behaviour is direction dependent due to the different deformation mechanisms involved. Significant yield anisotropy and sigmoidal-type hardening were observed. Twinning-detwinning deformation was considered as the major cause of these behaviours. On the other hand, monotonic torsional stress-strain curve had a linear hardening behaviour. Cyclic axial behaviour was found to be affected by twinning-detwinning deformation. Its most significant characteristics are: yield asymmetry, power-like hardening in compressive reversal and sigmoidal-type hardening in tensile reversal. This unusual behaviour was attributed to the contribution of three different deformation mechanisms: slip, twinning and detwinning. Due to yield asymmetry, significant positive mean stress was observed especially at LCF. Cyclic hardening was also observed and it was found to be associated with a substantial decrease in plastic strain energy density. Cyclic shear behaviour was symmetric and did not exhibit any of the aforementioned behaviours in cyclic axial loading. Two major observations were made from multiaxial tests. First, additional hardening due to nonproportionality was observed. Second, phase angle has no effect on fatigue life. Three fatigue life models were considered for multiaxial fatigue life prediction: Smith-Watson-Topper, Fatemi-Socie and Jahed-Varvani. The first two models are based on strain and are evaluated on specific critical planes. The third model is based on energy densities calculated from hysteresis loops. Strain- and energy-life curves had knees and pronounced plateaus. Therefore, it was not possible to model the entire fatigue life using Coffin-Manson-Type equations. Low cycle fatigue lives were predicted within ۬x scatter bounds using the Fatemi-Socie and the Jahed-Varvani models for all loading conditions which was not the case with Smith-Watson-Topper model. Total energy, the sum of plastic and positive elastic strain energy densities, was found to correlate fatigue lives for several wrought Mg-alloys under different loading conditions.

The demand for lightweight materials in automobiles has been motivated by two factors: fuel economy and air pollution reduction. One of the first steps taken in automotive vehicle weight reduction was the use of aluminum alloys for both structural and non-structural parts. Although magnesium alloys, that have one fourth the density of steel and one third that of aluminum, have also been used in automobiles, however, their applications were limited to non-structural parts. Recently, interest has been focused on using magnesium alloys as structural materials for automotive load-bearing components. Load-bearing components in automobiles are usually subjected to multiaxial cyclic loading. Fatigue is considered to be a significant cause of ground vehicle component failure. Therefore, for magnesium alloys to be used for these components, an understanding of their fatigue behaviour is necessary. In this study, series of monotonic and cyclic tests were conducted on smooth specimens machined from AZ31B magnesium extrusion section. Two loading modes were considered in this investigation, axial and torsional. Monotonic tensile and compressive tests were performed at three different orientations, longitudinal (LD), i.e., parallel to the extrusion direction, 45° and transverse (TD) directions. Monotonic torsion tests were performed on specimens that were machined along the LD. Similarly, cyclic axial and torsional as well as multiaxial axial-torsional tests were performed on specimens that that were machined along the LD. Three different phase angles were considered for multiaxial tests: in-phase, and 45° and 90° out-of-phase. It was found that monotonic axial stress-strain behaviour is direction dependent due to the different deformation mechanisms involved. Significant yield anisotropy and sigmoidal-type hardening were observed. Twinning-detwinning deformation was considered as the major cause of these behaviours. On the other hand, monotonic torsional stress-strain curve had a linear hardening behaviour. Cyclic axial behaviour was found to be affected by twinning-detwinning deformation. Its most significant characteristics are: yield asymmetry, power-like hardening in compressive reversal and sigmoidal-type hardening in tensile reversal. This unusual behaviour was attributed to the contribution of three different deformation mechanisms: slip, twinning and detwinning. Due to yield asymmetry, significant positive mean stress was observed especially at LCF. Cyclic hardening was also observed and it was found to be associated with a substantial decrease in plastic strain energy density. Cyclic shear behaviour was symmetric and did not exhibit any of the aforementioned behaviours in cyclic axial loading. Two major observations were made from multiaxial tests. First, additional hardening due to nonproportionality was observed. Second, phase angle has no effect on fatigue life. Three fatigue life models were considered for multiaxial fatigue life prediction: Smith-Watson-Topper, Fatemi-Socie and Jahed-Varvani. The first two models are based on strain and are evaluated on specific critical planes. The third model is based on energy densities calculated from hysteresis loops. Strain- and energy-life curves had knees and pronounced plateaus. Therefore, it was not possible to model the entire fatigue life using Coffin-Manson-Type equations. Low cycle fatigue lives were predicted within ۬x scatter bounds using the Fatemi-Socie and the Jahed-Varvani models for all loading conditions which was not the case with Smith-Watson-Topper model. Total energy, the sum of plastic and positive elastic strain energy densities, was found to correlate fatigue lives for several wrought Mg-alloys under different loading conditions.

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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.

Les élastomères présentent une diversité d’utilisation et des caractéristiques mécaniques spécifiques (grandes déformations, comportement dissipatif, ...) qui en font une famille de matériaux très utilisés dans l’industrie. Lors de leur fonctionnement, les pièces réelles subissent des sollicitations complexes. Comprendre les phénomènes induits par la fatigue multiaxiale constitue ainsi un enjeu important dans la phase de conception industrielle. Le matériau utilisé au cours de cette étude est un polychloroprène (CR), fourni par la société Hutchinson et présent dans les poulies découpleuses. Celui-ci possède une réponse dissipative en grandes déformations. Son comportement est modélisé à partir de lois de comportements viscohyperélastiques suivant deux approches : une méthode analytique impliquant un calcul simple en un point d’un cylindre et l’autre utilisant un calcul éléments finis implémenté dans ANSYS. Une campagne expérimentale en fatigue multiaxiale est alors réalisée, en traction-torsion afin de tester l’énergie dissipée comme critère de fatigue multiaxial. Celui-ci présente des résultats intéressants. Des diagramme de Haigh ont été établis afin de mettre en évidence le phénomène de cristallisation. Des analyses post-mortem ont été menés avec un microscope électronique à balayage et expose des spécificités morphologiques liées à la sollicitation vue par le matériau. / Due to their interesting mechanical behavior (large strain, dissipative behavior ...) and their diversity, elastomers are more and more used in industry. In service conditions, rubber components are subjected to complex loadings. Therefore, understanding phenomena induced by multiaxial fatigue constitutes an important issue in the industrial conception’s step. The material used in this work is a polychloroprene rubber, provided by Huchinson society and dedicated to silent-block’s applications. This elastomer possess a dissipative component at large strains. This behavior is determined following two approaches : an analytic method, implying a simple calculation at a local point of a cylinder and a finite elements analysis implemented with ANSYS software. An experimental investigation in multiaxial fatigue is then realized to test the dissipated energy density as a multiaxial fatigue criterion. This parameter obtained interesting results. Haigh diagrams has been built to point out crystallization phenomenon. Post-mortem analyses has been carried out with a scanning electronic microscope and exposes morphological specificities related to the material’s sollicitation.

abstract: A new critical plane-energy model is proposed in this thesis for multiaxial fatigue life prediction of homogeneous and heterogeneous materials. Brief review of existing methods, especially on the critical plane-based and energy-based methods, are given first. Special focus is on one critical plane approach which has been shown to work for both brittle and ductile metals. The key idea is to automatically change the critical plane orientation with respect to different materials and stress states. One potential drawback of the developed model is that it needs an empirical calibration parameter for non-proportional multiaxial loadings since only the strain terms are used and the out-of-phase hardening cannot be considered. The energy-based model using the critical plane concept is proposed with help of the Mroz-Garud hardening rule to explicitly include the effect of non-proportional hardening under fatigue cyclic loadings. Thus, the empirical calibration for non-proportional loading is not needed since the out-of-phase hardening is naturally included in the stress calculation. The model predictions are compared with experimental data from open literature and it is shown the proposed model can work for both proportional and non-proportional loadings without the empirical calibration. Next, the model is extended for the fatigue analysis of heterogeneous materials integrating with finite element method. Fatigue crack initiation of representative volume of heterogeneous materials is analyzed using the developed critical plane-energy model and special focus is on the microstructure effect on the multiaxial fatigue life predictions. Several conclusions and future work is drawn based on the proposed study. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2016

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.

The master’s thesis deals with the fatigue life prediction under multiaxial cyclic loading. First, the fatigue process is discussed and the methods for fatigue life prediction under uniaxial and multiaxial loading are described. In the practical part, the accuracy of selected criteria is assessed based on experimental data obtained on cylindrical samples made of 1.2210 steel that were tested under synchronous symmetric axial-torsion loading. Application of criteria requires to determine the fatigue strength under pure axial and torsional loading.