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.

Microtrusses are hybrid materials composed of a three-dimensional array of struts capable of efficiently transmitting an externally applied load. The strut connectivity of microtrusses enables them to behave in a stretch-dominated fashion, allowing higher specific strength and stiffness values to be reached than conventional metal foams. While much attention has been given to the optimization of microtruss architectures, little attention has been given to the strengthening mechanisms inside the materials that make up this architecture. This thesis examines strengthening mechanisms in aluminum alloy and copper alloy microtruss systems with and without a reinforcing structural coating. C11000 microtrusses were stretch-bend fabricated for the first time; varying internal truss angles were selected in order to study the accumulating effects of plastic deformation and it was found that the mechanical performance was significantly enhanced in the presence of work hardening with the peak strength increasing by a factor of three. The C11000 microtrusses could also be significantly reinforced with sleeves of electrodeposited nanocrystalline Ni-53wt%Fe. It was found that the strength increase from work hardening and electrodeposition were additive over the range of structures considered. The AA2024 system allowed the contribution of work hardening, precipitation hardening, and hard anodizing to be considered as interacting strengthening mechanisms. Because of the lower formability of AA2024 compared to C11000, several different perforation geometries in the starting sheet were considered in order to more effectively distribute the plastic strain during stretch-bend fabrication. A T8 condition was selected over a T6 condition because it was shown that the plastic deformation induced during the final step was sufficient to enhance precipitation kinetics allowing higher strengths to be reached, while at the same time eliminating one annealing treatment. When hard anodizing treatments were conducted on O-temper and T8 temper AA2024 truss cores, the strength increase was different for different architectures, but was nearly the same for the two parent material tempers. Finally, the question of how much microtruss strengthening can be obtained for a given amount of parent metal strengthening was addressed by examining the interaction of material and geometric parameters in a model system.

Microtrusses are hybrid materials composed of a three-dimensional array of struts capable of efficiently transmitting an externally applied load. The strut connectivity of microtrusses enables them to behave in a stretch-dominated fashion, allowing higher specific strength and stiffness values to be reached than conventional metal foams. While much attention has been given to the optimization of microtruss architectures, little attention has been given to the strengthening mechanisms inside the materials that make up this architecture. This thesis examines strengthening mechanisms in aluminum alloy and copper alloy microtruss systems with and without a reinforcing structural coating. C11000 microtrusses were stretch-bend fabricated for the first time; varying internal truss angles were selected in order to study the accumulating effects of plastic deformation and it was found that the mechanical performance was significantly enhanced in the presence of work hardening with the peak strength increasing by a factor of three. The C11000 microtrusses could also be significantly reinforced with sleeves of electrodeposited nanocrystalline Ni-53wt%Fe. It was found that the strength increase from work hardening and electrodeposition were additive over the range of structures considered. The AA2024 system allowed the contribution of work hardening, precipitation hardening, and hard anodizing to be considered as interacting strengthening mechanisms. Because of the lower formability of AA2024 compared to C11000, several different perforation geometries in the starting sheet were considered in order to more effectively distribute the plastic strain during stretch-bend fabrication. A T8 condition was selected over a T6 condition because it was shown that the plastic deformation induced during the final step was sufficient to enhance precipitation kinetics allowing higher strengths to be reached, while at the same time eliminating one annealing treatment. When hard anodizing treatments were conducted on O-temper and T8 temper AA2024 truss cores, the strength increase was different for different architectures, but was nearly the same for the two parent material tempers. Finally, the question of how much microtruss strengthening can be obtained for a given amount of parent metal strengthening was addressed by examining the interaction of material and geometric parameters in a model system.