Quelques développements sont démontrés dans cette thèse, du modèle de contact au modèle de roulement et du modèle de roulement-rotor à la technique de reproduction par bancs. Tout d’abord, la méthode de perturbation est étendue afin de prouver que la rigidité et l’amortissement distribués en état stable EHL ne remplissent pas les conditions transitoires et que les coefficients intégrés ne sont pas appropriés pour les analyses dynamiques. La loi de distribution de la rigidité et l’amortissement du film d’huile de l’EHL est proposée. En combinant l’état initial d’une solution stable avec l’amortissement et la rigidité distribués de l’EHL transitoire, les comportements du film d’huile peuvent être prédits. Par la suite, l’effet du contact en bordure entre le cylindre et le courant est pris en compte dans les transmissions de roulement. Les méthodes d’approximation première et seconde sont proposées pour interpréter numériquement cet effet. La méthode d’approximation première se concentre sur l’adoption de la méthode du coefficient d’influence pour reproduire l’effet de contact de même que l’utilisation du procédé de normalisation pour respecter les résultats empiriques ; alors que la méthode d’approximation seconde se concentre sur une manière analytique rapide de décrire la pression Hertz au contact entre le cylindre et le courant. Ensuite, les matrices de roulements pratiques sont utilisées pour développer un code de dynamiques 3D du roulement-rotor, basé sur des formules Hertz et EHL classiques. En temps-domaine, la méthode Adams quatre-ordres est améliorée pour résoudre les équations incrémentées des dynamiques non-linéaires. En fréquence-domaine, la méthode analytique de HB-AFT est particulièrement employée pour combler des matrices de roulement en 3D et des solutions d’état stable 3D. De plus, la méthode de continuation arc-longueur augmente la vitesse de calcul. En utilisant les deux méthodes, certains facteurs peuvent être considérés qualitativement et quantitativement, en incluant les états initiaux, l’amortissement, l’excentricité et les tensions internes et externes. Enfin, une technique alternative est proposée pour reproduire les comportements de contact à l’intérieur des roulements sous une forte charge et des vibrations à haute fréquence, lorsque les paramètres actifs sont en sous capacité du banc. Cette thèse apporte des visions nouvelles mais simples sur ce qui se produit sur les contacts roulants et longitudinaux d’un roulement circulaire ; sur comment modéliser et résoudre le système non-linéaire de roulement-rotor en domaines à la fois temps et fréquence ; et sur le moyen de reproduire des conditions de contact extrême à l’intérieur des roulements. / Some developments on bearing applications are emphasized in this thesis, from contact model to bearing model, and from bearing-rotor model to bench reproduction technique. First, perturbation method is extended to prove that steady-state EHL distributed damping and stiffness do not satisfy the transient conditions, and steady-state EHL lumped coefficients are not suitable for dynamic analysis. Distribution law of EHL oil film damping and stiffness is attemptly proposed. Combining initial state of steady-state solution with transient EHL distributed stiffness and damping, dynamic behaviors of oil film are predicted. Second, edge effect of roller/race contact is considered in bearing transmissions. First and second approximation methods are proposed to numerically interpret this effect. First approximation method concentrates on adopting influence coefficient method to replay edge effect as well as using normalization process to respect empirical results, while second approximation method focuses on a fast-analytical manner of describing Hertz pressure inside roller slice. Third, practical bearing matrices are used to develop 3D bearing-rotor dynamics code, based on classical Hertz and EHL formulas. In time domain, four-order Adams method is improved to solve incremental nonlinear dynamics equations; In frequency domain, analytical method of HB-AFT is particularly employed to bridge 3D bearing matrices and 3D steady-state solutions, besides, arc-length continuation method increases calculation speed. Using both methods, some factors can be considered qualitatively and quantitatively, including initial states, damping, eccentricity, internal and external excitations. Last, an alternative technique is proposed to reproduce contact behaviors inside bearings under heavy loading and high-frequency vibrations, when working parameters are beyond bench capacity. This thesis gives new but simple insights into what happens to rolling and longitudinal contacts of bearing roller, how to model and solve nonlinear bearing-rotor system in both time and frequency domains, and where a way is to reproduce extreme contact conditions inside bearings using bench.

Dans cette thèse, nous présentons et étudions une nouvelle formulation du problème de contact frottant entre deux corps élastiques se basant sur la méthode de Nitsche. Dans cette méthode les conditions de contact sont imposées faiblement, grâce à un terme additionnel consistant et stabilisé par un paramètre gamma. En premier lieu, nous introduisons, l’étude effectuée en petites déformations pour une version non biaisée de la méthode. La non-distinction entre une surface maître et une surface esclave permettera à la méthode d’être plus générique et applicable directement au problème d’auto-contact. Le cadre restrictif des petites déformations nous permet d’obtenir des résultats théoriques sur la stabilité et la convergence de la méthode. Ces résultats sont complétés par une validation numérique. Ensuite, nous introduisons l’extension de la méthode de Nitsche au cadre des grandes déformations qui est d’avantage pertinent pour les applications industrielles et les situations d’auto-contact. La méthode de Nitsche est formulée pour un matériau hyper-élastique avec frottement de Coulomb et se décline en deux versions : biaisée ou non. La formulation est généralisée à travers un paramètre theta pour couvrir toute une famille de méthodes. Chaque variante particulière a des propriétés différentes du point de vue théorique et numérique, en termes de précision et de robustesse. La méthode est testée et validée à travers plusieurs cas tests académiques et industriels. Nous effectuons aussi une étude de l’influence de l’intégration numérique sur la précision et la convergence de la méthode. Cette étude couvre une comparaison entre plusieurs schémas d’intégration proposés dans la littérature pour d’autres méthodes intégrales. / In this thesis, we present and study a new formulation of frictional contact between two elastic bodies based on Nitsche’s method. This method aims to treat the interface conditions in a weak sense, thanks to a consistent additional term stabilized with the parameter gamma. At first, we introduce the study carried out in the small strain framwork for an unbiased version of the ethod. The non-distinction between a master surface and a slave one will allow the method to be more generic and directly applicable to the self-contact problem. The restrictive framework of small strain allowed us to obtain theoretical results on the consistency and convergence of the method. Then, we present the extension of the Nitsche method to the large strain case more relevant for industrial applications and situations of self-contact. This Nitsche’s method is formulated for an hyper-elastic material and declines in the two versions: biased and unbiased. We describe a class of methods through a generalisation parameter theta . Particular variants have different properties from a numerical point of view, in terms of accuracy and robustness. To prove the accuracy of the method for large deformations, we provide several academic and industrial tests. We also study the influence of numerical quadrature on the accuarcy and convergence of the method. This study covers a comparison of several integration rules proposed in the literature for other integral methods.

Depuis l'utilisation des boulons au XVème siècle pour assembler deux pièces, les assemblages boulonnés posent des questions quant à la compréhension de leur fonctionnement et de leurs défaillances, telles que la variation de la tension de serrage entrainant, le desserrage, le dévissage, la perte d'étanchéité, l'initialisation de fissures, ... Pour comprendre leur fonctionnement, une méthodologie d'analyse tribologique a été mise en place, permettant de démonter un assemblage boulonné sans le desserrer, afin de ne pas modifier les conditions de contact lors du desserrage. Ainsi, toutes les interfaces d'assemblages (‘‘filets’’ écrou/vis et ‘‘autres que filets’’) formant des triplets tribologiques, ont été étudiées durant les trois phases de leur cycle de vie (fabrication, serrage, service) par le biais de cas-tests de matériaux différents. Un dialogue interactif entre les expérimentations (corrélations d'images, expertises) et la simulation numérique (Eléments Finis, Eléments Discrets) a permis de dégager des interprétations, notamment concernant les trois phases. Lors de la fabrication, le roulage des vis engendre des transformations tribologiques superficielles au niveau des sous-surfaces des filets formés. Le cœur des vis (noyau) restant non-déformé, ce procédé crée ainsi une différence de microstructure au sein de ces vis, ce qui est une source d'altération de leurs propriétés en fatigue. Lors du serrage, il se forme à l'interface ‘‘filets’’ une mixture de troisièmes corps ‘‘sec-solide’’, accommodant la vitesse entre la vis et l'écrou. Cette mixture résulte d'une réactivité entre une graisse utilisée pour le serrage et des particules, détachées d'un revêtement appliqué sur les filets d'écrous et/ou de vis. En fin de serrage, une partie de la mixture reste piégée entre les filets, jouant le rôle de maintien de la tension de serrage. Dans ces conditions, il apparaît que le frottement varie en fonction de la rhéologie de la mixture, conditionnant la variation de la tension de serrage. En service, des instabilités de contact (glissement, décollement, ...) ont été identifiées au niveau des interfaces. Ces instabilités engendrent dans les interfaces ‘‘autres que filets’’ la formation d'un troisième corps oxydé. Ce dernier constitue un surplus de matière qui peut entrainer l'augmentation des contraintes mécaniques dans les assemblages. A l'interface ‘‘filets’’ écrou/vis, il a été constaté que si la mixture de troisièmes corps piégée en serrage n'est pas cohésive, elle est extrudée des contacts, initialisant la perte de la tension de serrage. A partir de ces interprétations, des interactions entre plusieurs circuits tribologiques conduisent à converger vers un scénario de fonctionnement des assemblages boulonnés, permettant de solutionner leurs défaillances par la re-conception (mise en place de gorge de décharge, ...). / Since the use of bolts in the fifteenth century to assemble two parts, the bolted assemblies have the interrogations according to the understanding of their operating and failures occurring, such as the variation of the clamping force leading to, self-loosening, loss of sealing performance, cracks initialization, ... In order to understand their operating, a methodology focused on tribological approach was established, enabling to disassemble a bolted assembly without loosen its, allowing to not change the contact conditions during loosening. So, all the bolted assemblies interfaces (nut/screw ‘‘threads’’ and ‘‘others than threads’’) constituting tribological triplets, have been studied according to the three stages of their full life-cycle (manufacturing, tightening and service) using configurations of different materials. An interactive dialogue between the experiments (fields measuring by digital images correlation, tribological analysis) and the numerical simulation (Finite Element Method, Discrete Element Method) has led to interpretations about the three stages. During the manufacturing, the rolling of screws generates tribological superficial transformations in subsurfaces of machined threads. Contrariwise, inside the volume of these machined screws, there is no tribological transformation. So, this manufacturing process creates a difference of microstructure in these screws, that could be a source of their fatigue properties destruction. During the tightening, it produces at ‘‘threads’’ interface a ‘‘dry-solid’’ mixture of third bodies, accommodating the speed jump between the screw and the nut. This mixture is the result of a reactivity between a grease used for bolted tightening and the particles, detached by plastic flow from a coating initially applied on the threads of nuts and/or bolts. At the end of the process, a part of the mixture remains trapped in the threads, playing the role of maintaining the clamping force. In these conditions, it appears that the friction varies depending of the rheology of the mixture, conditioning the variation of the clamping force. In service, contact instabilities (slip, peeling off, ...) have been identified in the interfaces. These instabilities lead to the formation of an oxidized third body in ‘‘others than threads’’ interfaces. This oxidized third body represents a surplus of material and can increase mechanical stresses in the assemblies. In the nut/screw ‘‘threads’’ interface, it was found that if the mixture of third bodies trapped during the tightening stage is not cohesive, it is extruded, initializing the loss of clamping force. Based on the findings, the interactions between multiple tribological circuits lead to converge to a scenario of bolted assemblies operating, allowing to solve their failures by re-designing (create discharge grooves, ...).

Les Vibrations Induites par Frottement (FIV) sont un phénomène complexe qui surgit chaque fois deux surfaces subissent un glissement relatif. Pendant les dernières décennies, une quantité significative de œuvres expérimentales et numériques a traité des Vibrations Induites par Frottement, tandis que la simulation de l'excitation dynamique de contacts frictionnels a été toujours un vrai défi dans beaucoup de domaines de recherche industrielles. Dans ce cadre de recherche, ce travail est adressé à l'analyse des Vibrations Induites par Frottement, en développant des analyses en même temps expérimentales et numériques ; on propose une nouvelle approche numérique pour reproduire l'excitation dynamique locale du contact et son effet sur la réponse vibrationnel du système, sans augmentation significative des coûts de calcul. Le système mécanique, l'objet de l'analyse, est composé par deux poutres en acier en contact frictionnel dans un mouvement relatif ; la dynamique simple du système tient compte de la distinction entre la réponse de dynamique du système et l'excitation à haut débit venant du contact. Une campagne expérimentale paramétrique a été conduite pour analyser les effets de trois paramètres de contact principaux (la vitesse de glissement, la charge normale et la rugosité superficielle) sur la réponse du système vibrationnel, c'est-à-dire sur les vibrations induites. En parallèle, un modèle numérique a été mis en œuvre pour reproduire l'excitation dynamique locale du contact et son effet sur la réponse vibrationnel du système. Une nouvelle loi de friction a été présentée dans le modèle, proposant l'utilisation d'un terme provoquant une perturbation dans le coefficient de frottement pour simuler les effets de l'excitation au contact. Les inclusions de l'excitation dynamique locale, en raison des phénomènes de contact, par le terme de perturbation du coefficient de frottement, permettent de reproduire correctement les Vibrations Induites par Frottement sans présenter une représentation de la topographie superficielle réelle, qui a besoin d'un grand nombre d'éléments, économisant donc le temps de calcul. Des signaux différents pour le terme provoquant la perturbation ont été testés pour simuler correctement les vibrations mesurées. L'évolution du terme provoquant la perturbation récupérée par une méthode inverse a surligné les contributions spectrales différentes de l'excitation locale du contact. La comparaison entre les Vibrations Induites par Frottement mesurées et ceux simulés numériquement a montré une bonne corrélation, validant la loi de frottement proposée. Finalement, l'effet d'un changement de rugosité e de vitesse de glissement a été aussi simulé numériquement et corrélé avec les résultats expérimentaux. / Friction-Induced Vibrations (FIV) are a complex phenomenon which arises each time two surfaces undergo relative sliding. During the last decades, a significant amount of experimental and numerical works dealt with Friction-Induced Vibrations, while the simulation of the dynamic excitation from frictional contacts has always been a real challenge to face in many industrial research areas. In this research framework, this work is addressed to the investigation of the Friction-Induced Vibrations, carrying on at the same time experimental and numerical analyses; a new numerical approach is proposed to reproduce the local dynamic excitation from the contact and its effect on the vibrational response of the system, without significant increase of the computational time costs. The mechanical system, object of the investigation, is composed by two steel beams in frictional contact during relative motion; the simple dynamics of the system allows for distinguishing between the dynamics response of the system and the broadband excitation coming from the contact. A parametrical experimental campaign has been conducted to analyse the effects of three main contact parameters (the relative sliding velocity, the normal load and the surface roughness) on the system vibrational response, i.e. on the induced vibrations. In parallel, a numerical model has been implemented to reproduce the local dynamic excitation from the contact and its effect on the vibrational response of the system. A new friction law has been introduced in the model, proposing the use of a perturbative term in the friction coefficient in order to simulate the effects of the contact excitation. The inclusions of the local dynamic excitation, due to the contact phenomena, by the perturbation term of the friction coefficient allows to correctly reproduce the Friction-Induced Vibrations without introducing a representation of the real surface topography, which usually needs a large number of elements, saving then computational time. Different signals for the perturbative term have been tested to simulate correctly the measured vibrations. The evolution of the perturbative term recovered by an inverse method allowed for highlighting the different spectral contributions of the local excitation coming from the contact. The comparison between the measured Friction-Induced Vibrations and the ones simulated numerically showed good correlation, validating the proposed friction law. Finally, the effect in a change of the sliding velocity and surface roughness have been simulated numerically too and correlated with experimental results.

Les principaux mécanismes d'amortissement présents dans les transmissions par engrenages sont étudiés, en se basant sur une analyse transitoire du problème de lubrification élasto-hydrodynamique dans les contacts linéiques. Plusieurs modèles linéaires sont proposés suite à de nombreuses simulations numériques, permettant de prédire l’amortissement du lubrifiant dans les différentes conditions de contact, y compris les situations des pertes de contact momentanées suivies d’impact. Un modèle dynamique d’engrenage à un seul degré de liberté est présenté qui combine les contributions diverses du lubrifiant à l'amortissement structurel représentatif de la dissipation interne des engrenages. Un certain nombre de comparaisons avec des résultats expérimentaux est présenté pour une gamme de conditions de fonctionnement et de géométries d'engrenages, qui prouve la capacité du modèle à reproduire proprement le comportement dynamique des engrenages droits. On montre que l'amortissement associé au lubrifiant contribue essentiellement lors des pertes de contact et des chocs entre dentures se produisant au voisinage des vitesses critiques. Le cas des engrenages hélicoïdaux est analysé différemment du fait de l’absence de perte de contact pour ce type d’engrenage. Un modèle tridimensionnel simple est ainsi développé qui prend en compte la dissipation des différents éléments de la transmission. Un nombre de résultats est présenté qui, d'abord, confirme la contribution majeure de l'engrènement à l'amortissement global des engrenages droits, et, dans un second lieu, montre que les paliers constituent la principale source d'amortissement dans les transmissions par engrenages hélicoïdaux. / The primary damping mechanisms present in geared systems are investigated based on a transient analysis of the elasto-hydrodynamic lubrication problem for line contacts. Several linear models are derived from extensive numerical simulations, which make it possible to simulate the damping caused by the lubricant squeezing by the teeth with and without momentary contact losses and impacts. A one-degree-of-freedom gear dynamic model is set up which combines these lubricant damping sources along with structural damping that reproduces the internal dissipation in gear elements. A number of comparisons with benchmark experimental evidence are presented for a range of operating conditions and gear geometries, which prove that the proposed approach is sound in the case of spur gears. It is shown that the damping associated with lubricant squeezing contributes for the most part when contact losses and shocks between the teeth occur at critical speeds. The case of helical gears is analyzed differently since no contact loss occurs for such gears. A simple three-dimensional model is thus developed which accounts for the dissipation in the mechanical parts surrounding the gears. A number of results are presented which, first, confirm the primary contribution of the gear mesh to the overall damping in spur gears, and second, show that bearings constitute the main source of damping in helical gears transmissions.

L’adhérence et le frottement existent dans de nombreux systèmes techniques ainsi que dans les systèmes naturels. Ces deux phénomènes ont une influence importante sur la durabilité et l’efficacité des dispositifs techniques. Une approche reconnue pour ajuster précisément ces caractéristiques - outre le fait de modifier les propriétés physico-chimiques - est la texturation des surfaces en contact. Les surfaces de feuilles de plantes sont souvent décorées avec des morphologies de surface diverses, et présentent ainsi des fonctionnalités de surface remarquables. Cette thèse visait à réaliser une étude systématique de la mécanique de l’adhérence et du frottement sur des surfaces micro-structurées, répliquées à partir de surfaces de feuilles végétales, en contact avec une sonde qui s’inspire de l’organe adhérent d’un insecte. Les morphologies de surface de trois feuilles végétales différentes ont été directement transférées sur un polymère viscoélastique. Pour ce faire, trois approches différentes de reproduction ont fait l’objet d’une étude approfondie. La microscopie électronique à balayage et la microscopie confocale à balayage laser ont été utilisées pour l'évaluation qualitative et quantitative de la qualité de reproduction. Concernant l’étude de la mécanique du contact, un nano-indenteur a été modifié, permettant d’enregistrer les images in situ des contacts réels. Des tests de pull-off ont été menés afin d’évaluer quantitativement l’effet de la pré-charge sur la force d’adhésion et pour comprendre les modes distincts de collage/décollement. Des essais de frottement ont été effectués afin d’examiner l’effet de la charge normale et de la vitesse de glissement sur la force de frottement. Les résultats ont été discutés en fonction de la topographie de chaque surface. / Adhesion and friction exist in many technical systems as well as in natural ones. Both phenomena have a profound influence on the durability and efficiency of technical systems. A well-recognised way to tune these characteristics - besides altering the physicochemical properties - is the texturing of the interacting surfaces. Inspiringly, plant leaf surfaces are often decorated with diverse surface morphologies, and so show remarkable functionalities. This thesis aimed to perform a systematic investigation of adhesion and friction mechanics on micro-structured surfaces replicated from plant leaves, in contact with a probe, which was inspired from an insect’s adhesive pad. Surface morphologies of three different plant leaves were directly transferred onto a viscoelastic polymer. For this, three different replication approaches were comprehensively explored. Scanning electron microscopy and confocal laser scanning microscopy were used for the qualitative and quantitative evaluation of replication ability. For the contact mechanics investigation, a high-resolution nanoindenter was modified, with incorporating a unique feature to record the in-situ real-contact images. Pull-off tests were carried out to quantitatively evaluate the effect of pre-load on adhesion force characteristics and to understand distinct attachment-detachment modes. Friction investigations were performed to examine the effect of normal load and sliding speed on the friction force. Results were discussed with regard to each surface’s topography.

No description available.

Axisymmetric analysis of cylindrical contacts is considered in the context of axisymmetric assemblies such as shrink-fits. Fretting fatigue induces sub-critical cracks along the contact interface of press fits especially when they are subjected to vibration. The surface and near surface stresses play a major role in the fretting fatigue crack initiation process. Assuming near surface contact stresses to be largely independent of the actual geometry of components in contact, half-plane analyses and experimental results obtained from a strip configuration are often cited in the literature to predict and understand crack initiation in the actual components (ASTM STP 1425). This thesis starts with half plane and strip models for cylindrical contact such as in a shrink fitted shaft. Different traction profiles underpinning a typical fretting contact constitute a study of different geometrical parameters and friction coefficients. The cylindrical shrink fitted contact is considered using mixed boundary formulation. The different cases of contact such as full slip, partial stick-slip and full stick are considered. A formulation for cyclically varying tractions is attempted using dynamic elasticity. Finally, the problem of cylindrical cracks is highlighted to understand interface delamination in a fiber reinforced composite. Stress functions in conjunction with Fourier transforms are used for analysis. Dynamic potentials based on Helmholtz decomposition are used for dynamic loading.For static loading Love’s stress function is used for axisymmetric problems while Airy’s stress function is used for 2D problems. Solution procedures for solving traction boundary and mixed boundary conditions are described. Preliminary experiments are described to appreciate the contact stresses and crack initiation in cylindrical contact. Photoelastic fringes in a cylinder under a band of pressure illustrate fretting contact stresses concentrated close to the surface with the core of the cylinder relatively unstressed. Further, some material testing experiments using a specially designed cylindrical fretting rig demonstrated typical features of fretting fatigue crack initiation for providing the theoretical motivation. Fretting fatigue induces the initiation of a number of sub critical cracks along the contact interface of components in mechanical assemblies especially under vibration. The dominant crack among the initiated cracks may grow in size to the critical length in the presence of bulk cyclic loading finally resulting in fracture of the entire component. Fretting fatigue leads to unexpected failure of the component well below the expected life. It is therefore, critical to analyse, detect and control fretting. The blade root-disk joint in gas turbines as a critical example of fretting fatigue has spurred extensive research effort. There is relatively little literature available on cylindrical fretting in shrink fitted joint focused in this thesis. Analytical solutions for static fretting tractions are presented using both axisymmetric and plane elastic stress functions for later comparison. While Fourier transforms in conjunction with Airys stress functions are exploited for attacking plane problems, Loves axisymmetric stress functions are explored for cylindrical fretting. Near surface stresses are of great interest in fretting fatigue research. Although two dimensional models provide general understanding of stresses caused during fretting, these models become inadequate to explain the interaction of local stresses with the bulk stresses inevitably present in cylindrical components. Global stress analysis tools are desirable for estimating the fatigue life of components experiencing fretting. While numerical techniques immensely aid fatigue life estimation they have their limitation when it comes to coated components. Stress analysis of coated cylinders unveils the intricate influence of the elastic mismatch as well as the width of the loading for varying friction coefficients. Comparison of results obtained from axisymmetric elasticity with plane elasticity is discussed in detail. The validity and scope of relying on plane fretting results to cylindrical fretting contacts is examined by comparing the results obtained for three different traction profiles. Fretting is generally modeled as a stress boundary value problem wherein the normal and frictional shear stresses are prescribed on the cylindrical surface. In reality fretting generally turns out to be a mixed boundary value problem with unknown regions of stick and slip requiring prescribing traction and displacement simultaneously. This belongs to a formidable class of unsolved contact mechanics problems in cylindrical axisymmetric elasticity. The famous spherical axisymmetric Hertz problem has no cylindrical counterpart except in the limiting case of a cylinder of large radius. These aspects are investigated for studying the hub-shaft interfacial geometry. A conformal contact profile is considered to model a shrink fit; the contact pressure is zero at the ends of contact. The case of full slip condition is analysed assuming a frictionless contact. With friction, partial stick-slip condition is analysed. The unknown contact traction is resolved in terms of Chebyshev expansions whose unknown coefficients are solved using Schmidt method. The unknown contact length and stick zone length are determined through an iterative procedure. A rigid uneven undulating axisymmetric hub in total contact over an elastic shaft under full stick condition is analysed for obtaining the near surface stresses for a given value of hub penetration. Even though the stresses oscillate in fretting, almost all the analyses reported in the literature use static formulation. Understanding this need, a dynamic analysis for modeling fretting of a cylinder subjected to harmonic pressure and shear is attempted. The Pochhammer dispersion relation becomes a prerequisite for a dynamic analysis. The results show that the stresses do not decay away from the contact, in contrast to the static results. This shows the propagation of stresses along the axial direction. Further extension of the dynamic analysis to a layered cylinder is also described. The results obtained on contact stresses and contact tractions under the cylindrical contact represent a significant advance to the literature for modeling fretting fatigue crack initiation and propagation. Formulating cylindrical crack problems is somewhat similar to cylindrical contacts. Such cylindrical cracks arise from the debonding along the fiber-matrix interface of a composite. A unified formulation for the problem of a pressurised cylindrical crack as also a pair of 2D parallel cracks in infinite media is attempted using Love’s stress function in conjunction with Fourier transforms. The results obtained for stress intensity factors, strain energy release rate, mode mixity, crack opening and sliding displacements are compared with that of a 2D pair of parallel cracks obtained using the unified formulation. The asymptotic situation of a large crack length to spacing ratio is examined in detail. In the case of a pair of parallel cracks, this implies a single crack in mode-I as far as the total energy release rate is concerned while at the same time retaining an asymptotic value for the mode mixity. This unique feature of near field mixed mode blending smoothly to mode-I in the far field is also seen for the stress field around a symmetrically branched crack. Thus, this thesis presents a collection of cylindrical elastostatic and elastodynamic axisymmetric solutions to provide better understanding of fretting and delamination problems encountered in press fit assemblies.

Contrary to elastic deformation, plastic deformation of crystalline materials, such as metals, is size-dependent. Most commonly, this phenomenon is present but unnoticed, such as the effect of microstructural length scales. The grain size in metallic materials is a length scale that affects material parameters such as yield stress and hardening moduli. In addition, several experiments performed in recent years on specimens with geometrical dimensions on the micron scale have shown that these dimensions also influence the mechanical behaviour. The work presented in this thesis involves continuum modelling and simulation of size-dependent plastic deformation, with emphasis on thin films and the formulation of interface conditions. A recently published strain gradient plasticity framework for isotropic materials [Gudmundson, P., 2004. A unified treatment of strain gradient plasticity. Journal of the Mechanics and Physics of Solids 52, 1379-1406] is used as a basis for the work. The theory is higher-order in the sense that additional boundary conditions are required and, as a consequence, higher-order stresses appear in the theory. For dimensional consistency, length scale parameters enter the theory, which is not the case for conventional plasticity theory. In Paper A and B, interface conditions are formulated in terms of a surface energy. The surface energy is assumed to depend on the plastic strain state at the interface and different functional forms are investigated. Numerical results are generated with the finite element method and it is found that this type of interface condition can capture the boundary layers that develop at the substrate interface in thin films. Size-effects are captured in the hardening behaviour as well as the yield strength. In addition, it is shown that there is an equivalence between a surface energy varying linearly in plastic strain and a viscoplastic interface law for monotonous loading. In paper C, a framework of finite element equations is formulated, of which a plane strain version is implemented in a commercial finite element program. Results are presented for an idealized problem of a metal matrix composite and several element types are examined numerically. In paper D, the implementation is used in a numerical study of wedge indentation of a thin film on an elastic substrate. Several trends that have been observed experimentally are captured in the theoretical predictions. Increased hardness at shallow depths due to gradient effects as well as increased hardness at more significant depths due to the presence of the substrate are found. It is shown that the hardening behaviour of the film has a large impact on the substrate effect and that either pile-up or sink-in deformation modes may be obtained depending on the material length scale parameter. Finally, it is qualitatively demonstrated that the substrate compliance has a significant effect on the calculated hardness of the film. / QC 20100723

Most of the surfaces have roughness down to atomic scales. When two surfaces come into contact, the nature of the roughness determines the properties like friction and wear. Analysis of the rough surface contacts is always complicated by the interaction between the material size effects and the micro-geometry. Contact mechanics could be simplified by decoupling these two effects by magnifying the scale of roughness profile. Also, tailoring the roughness at different scale could show a way to control the friction and wear through surface micro-structure modifications. In this work, the mechanics of contact between a rigid, hard sphere and a surface with a well defined roughness profile is studied through experiments and finite element simulation. The well defined roughness profile is made up of a regular array of pyramidal asperities. This choice of this geometry was mainly dictated by the fabrication processes. The specimens were made out of an aluminium alloy (6351-T6) such that there could be a direct application of the results in controlling the tribological properties during aluminium forming. Experiments on the pyramidal aluminium surface is carried out in a 250 kN Universal Testing Machine (INSTRON 8502 system) using a depth sensing indentation setup. A strain gauge based load cell is used to measure the force of the indentation and a LVDT (Linear Variable Differential Transformer) is used to measure the penetration depth. The load and the displacement were continuously recorded using a data acquisition system. A 3-D finite element framework for studying the elastic-plastic contact of the rough surfaces has been developed with the commercial package (ABAQUS). Systematic studies of indentation were carried out in order to validate the simulations with the experimental observations. The simulation of indentation of flat surface is carried out using the implicit/standard (Backward Euler) procedure, whereas, the explicit finite element method (Forward Euler) is used for simulating rough surface indentation. It is found that the load versus displacement curves obtained from experiments match well with the finite element results (except for the error involved in determining the initial contact point). At indentation depths higher than a value that is determined mainly by the asperity height, the load-displacement characteristics are similar to that pertaining to indentation of a flat, smooth surface. From the finite element results, it is found that at this point, the elastic-plastic boundary is more or less hemispherical as in the case of smooth surface indentation. For certain geometries, it is found that there could exist an elastic island in the sub-surface surrounded by plastically deformed material. This could have interesting applications.