Over the past few decades various models of different formats have been developed to correctly evaluate and predict the strength of materials. However, these models are limited in certain environmental conditions in implementing the effect of material's thickness into their models. As such an there was a need to consider the basics of mechanical engineering and to try and define the trend, thickness has upon the behaviour of materials with respect to environmental conditions. The work consisted of a representation of tensile testing testing of common engineering alloys across a wide range of temperature, strain rate and thickness. Acquisition of high strain rate data and extended strain data (split-hopkinson, bulge forming and plane strain compression). A review of existing graphical techniques and limited applications using strength reduction factors, as well as applying the accepted empirical formulae, Johnson-Cook, Armstrong-Zerrili, Ramberg-Osgood and Hollomon. Later, recognising a need for a new approach as with a universal (quartic) polynomial fit to all plastic flow curves in which coefficients are T, ε̇ and t̄ dependant. Adoptation of a common numerical procedure for strain intercept ε0 and cut-off instability co-ordinates (σi, εi)- each as the solution to the roots of a quartic. Therefore, a proposal of the flow curve tables allowing interpolation and extrapolation, a numerical representation of any previous "Atlas of Curves". Subsequently, leading to reconstruction of the full stress-strain curve with the addition of elastic strain calculated from the modulus applicable to the specific test condition by further testing of these data from literature; both improving the existing and producing new empirical and simulation based models to analyse the materials, which will be subjected to dynamic loading as well as temperature and strain rates variations. The main objective of the work, was involved in creating a polynomial fit to describe the three physical conditions in terms of coefficients and to verify the findings in a FEA package, ABAQUS. A new process in reading the stress-strain data. By means of such development an instability study of strain limits based on Considére criteria was developed which illustrated the ways to prolong the instability limit. A secondary study of this work relates to creating a bridge between the micro-structure and macro-structure of the tested materials. A series of correlations and trends were developed to further signify the shift in micro-structural restructuring, whilst the material is under load. Another important aspect of the work consists, of carrying out an analytical study on Ramberg-Osgood equation. Ramberg-Osgood equation has been at the forefront of many engineering advancement. However it can yet be improved and reformatted by means of defining a set value for its variable constants. As such a fix ƞt value based on a best-fit approach was developed which was analytically tested.

Exergy utilization calculations have been in the past repeatedly used to quantify the quality and quantity of energy used in thermal energy processes. This thesis is an attempt to derive a common language exergy utilization and compare for the first time two entirely different manufacturing processes, namely material processing by a mechanical method of straining of the material and simple heating of the same mass of the material using exergy utilization as a metric. The exergy utilization of material processing is determined by performed work and utilized heat transfer using 1) Ramberg-Osgood equation and 2) Lumped heat capacitance method. A comparison of these two methods is presented.

In this paper we present novel analytic and finite element solutions to 1-D straight rods made of Ramberg-Osgood and Hollomon type materials. These material models are studied because they are a more accurate representation of the material properties of certain metals used often in manufacturing than the simpler composite linear types of stress/strain models. Here, various types of loads are considered and solutions are compared against some linear models. It is shown that the nonlinear models do have manageable solutions, which produce important differences in the results - attributes which suggest that these models should take a more prominent place in engineering analysis.

O presente trabalho tem como objetivo investigar o comportamento elasto-plástico em baixas deformações do fio máquina laminado em aço AISI 1045 destinado a trefilação e processos subsequentes de beneficiamento. Inicialmente, foi obtido material de quatro diferentes lotes de fabricação, sendo todas as amostras retiradas após a etapa de pré-endireitamento do processo de trefilação. O material foi caracterizado através de análise da composição química, metalográfica, determinação de tamanho de grão e segregação. Além disso, o comportamento elasto-plástico do material em ciclos de tração e compressão foi investigado, identificando-se o efeito Bauschinger para três diferentes temperaturas. Os modelos numéricos de Ramberg-Osgood e Ludwig-Hollomon foram utilizados para a definição de uma modelo numérico da curva para utilização em trabalhos futuros de simulação computacional. O modelo de Ludwig-Hollomon foi avaliado como mais satisfatório para baixas deformações e foi então utilizado para o cálculo da curva média de quatro lotes. A partir de curvas de escoamento de aço similar obtidas da literatura, foi possível obter-se uma extrapolação da curva para diferentes taxas de deformação, além da taxa de 0.05s-1, original dos ensaios: 1.6 s-1, 8 s-1, e 40 s-1. / The purpose of this work is to investigate the elastic-plastic behavior at low strains of steel rolled coil AISI 1045 intended for cold-drawing and subsequent processes. First, the material was withdrawn from four different manufacturing batches and all samples were taken from the pre-straightening process step. The material was characterized by means of chemical and metallography analysis, grain size and segregation. Furthermore, the elastic-plastic behavior in tension and compression cycles was investigated and the Bauschinger effect was identified for three different temperatures. The numerical models Ramberg-Osgood and Ludwig-Hollomon were the models used in this work to define the flow curve which can be used in future computer simulation works. The analysis showed that the Ludwig-Hollomon model is more adequate for low strains ranges. Ludwig-Hollomin was used to calculate the average flow curve based on the curves of the four batches. By using literature flow curves of similar steels, it was possible to make an extrapolation and to obtain flow curves at different strain rates beyond the experimental one: 1.6 s-1, 8 s-1, e 40 s-1.

O presente trabalho tem como objetivo investigar o comportamento elasto-plástico em baixas deformações do fio máquina laminado em aço AISI 1045 destinado a trefilação e processos subsequentes de beneficiamento. Inicialmente, foi obtido material de quatro diferentes lotes de fabricação, sendo todas as amostras retiradas após a etapa de pré-endireitamento do processo de trefilação. O material foi caracterizado através de análise da composição química, metalográfica, determinação de tamanho de grão e segregação. Além disso, o comportamento elasto-plástico do material em ciclos de tração e compressão foi investigado, identificando-se o efeito Bauschinger para três diferentes temperaturas. Os modelos numéricos de Ramberg-Osgood e Ludwig-Hollomon foram utilizados para a definição de uma modelo numérico da curva para utilização em trabalhos futuros de simulação computacional. O modelo de Ludwig-Hollomon foi avaliado como mais satisfatório para baixas deformações e foi então utilizado para o cálculo da curva média de quatro lotes. A partir de curvas de escoamento de aço similar obtidas da literatura, foi possível obter-se uma extrapolação da curva para diferentes taxas de deformação, além da taxa de 0.05s-1, original dos ensaios: 1.6 s-1, 8 s-1, e 40 s-1. / The purpose of this work is to investigate the elastic-plastic behavior at low strains of steel rolled coil AISI 1045 intended for cold-drawing and subsequent processes. First, the material was withdrawn from four different manufacturing batches and all samples were taken from the pre-straightening process step. The material was characterized by means of chemical and metallography analysis, grain size and segregation. Furthermore, the elastic-plastic behavior in tension and compression cycles was investigated and the Bauschinger effect was identified for three different temperatures. The numerical models Ramberg-Osgood and Ludwig-Hollomon were the models used in this work to define the flow curve which can be used in future computer simulation works. The analysis showed that the Ludwig-Hollomon model is more adequate for low strains ranges. Ludwig-Hollomin was used to calculate the average flow curve based on the curves of the four batches. By using literature flow curves of similar steels, it was possible to make an extrapolation and to obtain flow curves at different strain rates beyond the experimental one: 1.6 s-1, 8 s-1, e 40 s-1.

O presente trabalho tem como objetivo investigar o comportamento elasto-plástico em baixas deformações do fio máquina laminado em aço AISI 1045 destinado a trefilação e processos subsequentes de beneficiamento. Inicialmente, foi obtido material de quatro diferentes lotes de fabricação, sendo todas as amostras retiradas após a etapa de pré-endireitamento do processo de trefilação. O material foi caracterizado através de análise da composição química, metalográfica, determinação de tamanho de grão e segregação. Além disso, o comportamento elasto-plástico do material em ciclos de tração e compressão foi investigado, identificando-se o efeito Bauschinger para três diferentes temperaturas. Os modelos numéricos de Ramberg-Osgood e Ludwig-Hollomon foram utilizados para a definição de uma modelo numérico da curva para utilização em trabalhos futuros de simulação computacional. O modelo de Ludwig-Hollomon foi avaliado como mais satisfatório para baixas deformações e foi então utilizado para o cálculo da curva média de quatro lotes. A partir de curvas de escoamento de aço similar obtidas da literatura, foi possível obter-se uma extrapolação da curva para diferentes taxas de deformação, além da taxa de 0.05s-1, original dos ensaios: 1.6 s-1, 8 s-1, e 40 s-1. / The purpose of this work is to investigate the elastic-plastic behavior at low strains of steel rolled coil AISI 1045 intended for cold-drawing and subsequent processes. First, the material was withdrawn from four different manufacturing batches and all samples were taken from the pre-straightening process step. The material was characterized by means of chemical and metallography analysis, grain size and segregation. Furthermore, the elastic-plastic behavior in tension and compression cycles was investigated and the Bauschinger effect was identified for three different temperatures. The numerical models Ramberg-Osgood and Ludwig-Hollomon were the models used in this work to define the flow curve which can be used in future computer simulation works. The analysis showed that the Ludwig-Hollomon model is more adequate for low strains ranges. Ludwig-Hollomin was used to calculate the average flow curve based on the curves of the four batches. By using literature flow curves of similar steels, it was possible to make an extrapolation and to obtain flow curves at different strain rates beyond the experimental one: 1.6 s-1, 8 s-1, e 40 s-1.

A vast array of high value parts in land- and air-based turbomachinery are subjected to non-isothermal cycling in the presence of mechanical loading. Crack initiation, growth and eventual failure more significantly reduce life in these components compared to isothermal conditions. More accurate simulation of the stress and strain evolution at critical locations of components, as well as test specimens, can lead to a more accurate prediction of remaining life to a structural integrity specialists. The focus of this thesis is to characterize the effects of thermomechanical fatigue (TMF) on generic turbomachinery alloy. An expression that can be used to estimate the maximum and minimum stress under a variety of loading conditions is formulated. Analytical expressions developed here are modifications of classic mechanics of materials methods (e.g. Neuber's Rule and Ramberg-Osgood). The novel models are developed from a collection of data based on parametric finite element analysis to encompass the complex load history present in turbine service conditions. Relevance of the observations and formulated solutions are also explored for the case of a tensile specimen containing a v-shaped notch. Accurate estimations of non-isothermal fatigue presented here endeavor to improve component lifing and decrease maintenance costs.

Cette thèse est une contribution à la compréhension du comportement des composites carbone-époxy en compression par l’étude de l’influence des constituants (fibres et matrices). L’incidence d’un chargement mécanique d’amplitude constante ou variable sur la durabilité est étudiée et un modèle numérique permettant la prédiction de la résistance résiduelle est proposé. Une première partie des travaux s’intéresse aux mécanismes spécifiques engagés dans la résistance en compression. Un modèle analytique est retenu pour une confrontation expérimentale. Ce modèle propose de considérer d’une part le micro-flambage de la fibre comme contenu par le comportement en cisaillement de la matrice (Budiansky et Fleck, 1993). En complément, une partie supplémentaire de structure considérant, entre autres, l’influence du gradient de déformation induit dans une sollicitation en flexion 4 points est étudiée (Grandidier, 2002). Afin de valider la pertinence du modèle, une campagne expérimentale est menée sur six matrices époxy différentes (de fragile à ductile) dans des empilements stratifiés monolithiques identiques réalisés en cuisson autoclave. Ces résultats ont permis de valider la capacité du modèle à prédire l’influence de la rigidité de la matrice sur la résistance en compression. Le partie micro-flambage est validée pour la prise en compte de la matrice. La partie effet de structure (gradient ici) est validée par une comparaison avec des résultats supplémentaires obtenus sur des éprouvettes sandwich sollicitées en flexion. Ces dernières éprouvettes ont fait l’objet d’une conception spécifique afin de favoriser la rupture en compression pure (sans gradient de déformation). Une seconde partie est consacrée à l’étude de la durabilité en compression. Une campagne expérimentale d’essais de fatigue est menée en flexion 4 points sur les éprouvettes sandwich précédemment conçues. Les essais sont conduits à une fréquence de 10 Hz et différents rapports de charge dans une optique de dégager l’évolution de la résistance résiduelle. Un modèle numérique de changement d’échelles (stratifié, plis, constituants) est parallèlement développé, basé sur la dégradation et la plasticité de la matrice. On fait l’hypothèse de simplicité thermo-rhéologique de la matrice pour établir des courbes de maitresses à partir d’une série d’essais identifiés (fluage, relaxation, fatigue…). On utilise les propriétés résiduelles du pli (rigidité, résistance) pour estimer un indicateur d’endommagement. Ce dommage est répercuté dans les propriétés de la matrice au moyen d’une loi de dégradation linéaire. Une loi de cumul de dommage de type Miner est alors introduite pour tenir compte de la variabilité des chargements appliqués. Un solveur micro- mécanique est développé pour extraire le comportement non-linéaire du pli en cisaillement tenant compte de la dégradation. Ce comportement est paramétré par une loi de Ramberg-Osgood utilisée dans le modèle analytique validé précédemment. Les travaux des deux parties permettent donc la mise en place d’un outil de prédiction de la résistance résiduelle des plis sollicités dans un chargement biaxial plan, avec en particulier le traitement de la compression / This PhD dissertation is a contribution to the modelling of Carbon-Fiber-Epoxy-Polymer laminates, undergoing specifically compression loadings, according to components. The aim is to build a design tool for composites structures taking into account this compression specificity for dimensioning racing yachts parts (masts, daggerboards, foils), which is the expertise of HDS/GSea-Design, the company associated to this work. Emphasis was put on the influence of linear or non-linear properties of each phase by varying the type of fibre (from high stiffness to high strength) and the type of matrix (from brittle to ductile). The effect of a mechanical loading, static, constant (creep, relaxation) or variable (fatigue) on durability is studied and a numerical model for predicting the residual strength is proposed. The first part of this work deals with the mechanisms involved in compressive strength. An analytical model is used for an experimental validation. It considers a contribution linked to the micro-buckling of the fibre as contained by the shear behaviour of the matrix (Budiansky et Fleck [1993]). It considers also a contribution of the deformation gradient induced for instance in a bending loading (Gardin et al. [2002]). To validate this model, an experimental campaign was conducted on six different epoxy matrices (from brittle to ductile) on identical monolithic stackings processed in autoclave. The results allowed the validation of the model capability to predict the influence of the matrix stiffness on the compressive strength of unidirectional laminas. Taking into account the matrix behaviour validates the micro-buckling contribution. Regarding the deformation gradient contribution, it is validated through a comparison using additional experimental results on sandwich samples in bending. The latter samples were specifically designed to favour a pure compression fracture (without any deformation gradient). The second part examines durability in compression. Another experimental campaign with fatigue tests was conducted with four points bending tests on the same sandwich samples. Experiments were carried out at 10 Hz and different load ratios were used to study their influence on the compressive residual strength. A numerical model involving different scales (laminate, laminas, fibres and matrix) is developed in parallel (Huang et al. [2012a]), based on the degradation and the plasticity of the matrix. The assumption of thermo-rheological simplicity of the matrix is made to build master curves from dedicated experiments (creep, relaxation). We then use the residual properties (stiffness, strength) of the ply to estimate a damage level. This latter parameter is used to modify the elastic stiffness of the matrix with a linear law. A Miner-type cumulative law is used in fatigue to take into account the different possible loadings. A micro-mechanical solver is developed to extract the non-linear shear behaviour of the ply accounting for this degradation. This behaviour is described by a Ramberg-Osgood law used in the analytical model described in the first part of this work. The joint contributions of these two parts allowed us to program a numerical tool for predicting the residual strength of plies undergoing a biaxial in- plane loading, being monotonous, constant or with a variable amplitude, with emphasis on the particular case of compression loading.

We will create a class of generalized ellipses and explore their ability to define a distance on a space and generate continuous, periodic functions. Connections between these continuous, periodic functions and the generalizations of trigonometric functions known in the literature shall be established along with connections between these generalized ellipses and some spectrahedral projections onto the plane, more specifically the well-known multifocal ellipses. The superellipse, or Lam\'{e} curve, will be a special case of the generalized ellipse. Applications of these generalized ellipses shall be explored with regards to some one-dimensional systems of classical mechanics. We will adopt the Ramberg-Osgood relation for stress and strain ubiquitous in engineering mechanics and define a general internal bending moment for which this expression, and several others, are special cases. We will then apply this general bending moment to some one-dimensional Euler beam-columns along with the continuous, periodic functions we developed with regard to the generalized ellipse. This will allow us to construct new solutions for critical buckling loads of Euler columns and deflections of beam-columns under very general engineering material requirements without some of the usual assumptions associated with the Ramberg-Osgood relation.

In this thesis the Ramberg-Osgood nonlinear model for describing the behavior of many different materials is investigated. A brief overview of the model as it is currently used in the literature is undertaken and several misunderstandings and possible pitfalls in its application is pointed out, especially as it pertains to more recent approaches to finding solutions involving the model. There is an investigation of the displacement of a cantilever beam under a combined loading consisting of a distributed load across the entire length of the beam and a point load at its end and new solutions to this problem are provided with a mixture of numerical techniques, which suggest strong mathematical consistency within the model for all theoretical assumptions made. A physical experiment was undertaken and the results prove to be inaccurate when using parameters derived from tensile tests, but when back calculating parameters from the beam test the model has a 14.40% error at its extreme against the experimental data suggesting the necessity for further testing.