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.

No description available.

Motivated by the structure of the normal surface stress of the extended Hertzian approach [1] given due to terms of the form r^2n*(a^2-r^2)^(1/2) (n=0, 2, 4, 6…) it seems attractive to evaluate the complete elastic field also for shear loadings of this form. The reason for this lays in the demand for analytical tools for the description of mixed loading conditions as they appear for example in scratch experiments. [1] N. Schwarzer, "Elastic Surface Deformation due to Indenters with Arbitrary symmetry of revolution", J. Phys. D: Appl. Phys., 37 (2004) 2761-2772

Composites are materials which cater to the present and future needs of many demanding industries, such as aerospace, as they are weight-sensitive for a given requirement of strength and stiff ness, corrosion resistant, potentially multi-functional and can be tailored according to the application. However, they are in particular difficult to join as they cannot be easily machined, without introducing damages which can eventually grow. Any structure is as strong as its weakest joint. Most of the joints belong to the category of mechanically-fastened joints and they pose enormous challenges in modeling due to contact phenomena, nonlinearity and stress concentration factors. It is therefore a necessity to construct an efficient model that would include all the relevant contact phenomena in the joints, as it has been pointed out in literature that damage typically initiates near the joint holes. The focus of this work is to describe the construction of an asymptotically-correct model using the Variational Asymptotic Method (VAM). Amongst its many potential applications, VAM is a well-established analytical tool for obtaining the stress and strain fields for beams and shells. The methodology takes advantage of the small parameter that is inherent in the problem, such as the ratio of certain characteristic dimensions of the structure. In shells and beams, VAM takes advantage of the dimension-based small parameter(s), thereby splitting the problem into 2-D + 1-D (for beams) and 1-D + 2-D (for shells), in turn offering very high computational efficiency with very little loss of accuracy compared to dimensionally unreduced 3-D models. In this work, the applicability of VAM is extended to two-dimensional (2-D) and three-dimensional (3-D) frictionless contact problems. Since a generalised VAM model for contact has not been pursued before, the `phantom0 step is adopted for both 2-D and 3-D models. The development of the present work starts with the construction of a 2-D model involving a large rectangular plate being pressed against a rigid frictionless pin. The differential equations governing the problem and the associated boundary conditions are obtained by minimizing the reduced strain energy, augmented with the appropriate gap function, by using a penalty method. The model is developed for both isotropic and orthotropic cases. The boundary value problem is solved numerically and the displacement field obtained is compared with the one obtained using commercial software (ABAQUSr) for validation at critical regions such as the contact surfaces. Banking on the validation of the 2-D model, a 3-D model with a pin and a finite annular cylinder was constructed. The strain energy for the finite cylinder was derived using geometrically exact 3-D kinematics and VAM was applied leading to the reduction in the strain energy for isotropic and orthotropic materials in rectangular and cylindrical co-ordinates. As in the 2-D case, the reduced strain energy, subject to the inequality constraint of the gap function, is minimized with respect to the displacement field and the corresponding boundary value problem is solved numerically. The displacements of the contact surface and the top surface of the annular cylinder are compared with those from ABAQUS and thus validated. The displacement fields obtained using the current 2-D and 3-D models show very good agreement with those from commercial finite element software packages. The model could be re ned further by using the gap function derived in this work and applying it to a plate model based on VAM, which could be explored in the future.

Grease-lubricated journal bearings are widely used in heavy duty applications, such as construction equipment, agriculture- and forest machines. The main purpose of the grease-lubricated journal bearing is solely to create sustainable rotation of a given application. However, purpose seldom decides complexity of journal bearing design. Depending on application, parameters such as Load , Material  and Lubrication immensely increase complexity of the design. Tribology is a highly interdisciplinary subject, which requires knowledge concerning physics, chemistry, metallurgy and solid mechanics. Tribological aspects of a design are frequently regarded as irrelevant. Tribological issues are commonly enlightened in combination with structural design weaknesses. The main aim of the thesis was to analyze two cylinder joints found in a Komatsu Forest 951 crane and establish root cause to the structural and tribological issues. Outline of the approach was divided into three main targets: 1. Investigate mechanical and tribological aspects of the crane design. 2. Understand how these aspects influence the life time of the bearings. 3. Summarize the analysis and suggest improvements based on the discovery. Fundamental structural and tribological design guidelines regarding grease-lubricated journal bearings have been presented in this thesis. Damaged components such as cylinders, pins and journal bearings have been examined at Komatsu Forest’s factory in Umeå. Further, a scanning electron microscopy study has been done at Luleå University of Technology, to determine predominant wear mechanisms in the harvester crane joints. A non-linear finite element model of the crane has been designed to represent pressure distribution in the contact between bearing and pin. The finite element analysis gives a good approximation of the contact but leaves room for further refinements. Temperatures, in the contacts, have not been identified and will be measured outside the time frame of the master’s thesis. Design changes, with respect to discovered structural and tribological issues have been suggested. The suggested improvements can potentially increase the life time of lift cylinders, pins and journal bearings.

[pt] Este trabalho tem como finalidade comparar e analisar diferentes modelos numéricos na análise do processo de queda de blocos com diferentes geometrias, para que seja possível determinar os riscos à infraestrutura e à população local que este evento pode causar. Foram utilizados o software RAMMS e o programa de modelagem PFC3D para simulação de queda de blocos. O primeiro foi desenvolvido pelo instituto suíço WSL, o software utiliza a dinâmica não suave (nonsmooth), não havendo penetração dos blocos com a superfície, e as leis de contato são feitas por restrições. O segundo utiliza o método dos elementos discretos através de dinâmica de contato suave. Na primeira parte do trabalho foram realizadas simulações de casos simples de queda de blocos para ambos os modelos, a fim de analisar o principal parâmetro do contato rocha-solo de cada programa com o alcance das rochas. O modelo de contato no programa PFC3D utilizado foi o método linear, e depois foi adicionada uma força de resistência ao rolamento para que o modelo conseguisse reproduzir o comportamento de solos mais macios. Os modelos foram simulados para casos reais, primeiro foram aplicados para uma encosta na BR116, onde um evento de deslizamento já tinha ocorrido. Foram realizadas simulações com os dois modelos na região, comparando-os e analisando com os vestígios deixados pelo evento. Outro caso estudado foi o de blocos susceptíveis ao deslizamento no bairro Glória, no município de Petrópolis. E por último, foram criados modelos para analisar o comportamento da vegetação em ambos os modelos. Com os resultados obtidos, conclui-se que o PFC3D consegue simular o processo de queda com melhor precisão através do auxílio da força de resistência ao rolamento. Para ambas simulações, o caso da BR116 e o do bairro Glória, os modelos apresentarem uma mesma tendência quanto a trajetória do bloco, mas melhorias na calibração do modelo linear com resistência ao rolamento precisam ser realizadas para que melhores resultados sejam obtidos. A presença de vegetação se mostrou como um mecanismo muito eficiente para perdas de energia no sistema, diminuindo significativamente a velocidade dos blocos. / [en] The aim of this work is to compare and analyze different numerical models on the rockfall process with different geometries, to determine the risks to the local infrastructure and population. It was used the software RAMMS and the modeling program PFC3D to simulate rockfall events. The first software was developed by the Swiss institute WSL, it uses the nonsmooth dynamics system, it is a dynamic behavior where there is no penetration between the rock and the surface and the contact laws are created by restrictions laws. And the second one uses the discrete element method applying the smooth dynamics system to simulate the event. On the first part of the work, numerical models were created on both models to simulate simple cases of rockfall events, to compare the main soil-rock parameter of both modeling program with the distance reached of the rocks. The contact model used on the PFC3D program was the linear method, and after the first simulations was added a rolling resistance force to the model reproduce soft. Both models were applied to real cases, the BR116 was the first case modeled, where some natural hazards have already happened. The results of the numerical simulations were compared and analyzed. It was also created a model to simulate the rockfall event of the Gloria neighborhood, in Petropolis; rocks that could fall were determined and simulations for those blocks were performed, the deposition area and the blocks trajectory of each model were examined. And finally, it was studied the vegetation effect of each model and its particularities. Through the results, it is possible to conclude that the PFC3D can simulate the rockfall process with better accuracy using the rolling resistance method. For both simulation, the BR116 and the Gloria neighborhood, the models showed the same tendency of the blocks trajectory, but it is necessary to improve the calibration of the rolling resistance coefficient. The existence of the vegetation revealed as a very effect lose energy mechanism on the system, decreasing significantly the velocity of the blocks.

Ce travail de thèse Cifre, réalisé dans le cadre de la collaboration avec la société Elbi, porte sur la modélisation de la géométrie et de la cinématique du système vis à rouleaux. Ce travail analyse la cinématique et la géométrie du mécanisme de vis à rouleaux satellites (RSM) pour fournir une base fondamentale pour soutenir ses diverses applications. Un modèle 3D du système vis à rouleaux est développé. Un code numérique a été développé en fonction de la géométrie et la cinématique du système de vis à rouleaux. Le champ d’effort et le champ de pression en fonction des défauts de forme et de la géométrie sont obtenus dans ce travail. Ensuite, un modèle 3D du moment de frottement dans le contact entre les surfaces de la vis à rouleaux est développé. La vitesse de glissement et la force de frottement se produisant entre vis/rouleau et entre rouleau/écrou a été calculé conformément à la cinématique, la géométrie et les erreurs de forme. L’efficacité, les pertes par frottement et la durée de vie du mécanisme de la vis à rouleaux en fonction des défauts de forme, de la cinématique et de la géométrie sont obtenues. Ces résultats numériques montrent le rendement important du système de vis à rouleaux en fonction des défauts de forme (autour de 97%). Par ailleurs, une partie expérimentale a été faite sur un banc d’essais électromécanique en collaboration avec le laboratoire Ampère d’Insa de Lyon afin de comparer les résultats expérimentaux avec les résultats théoriques. Ces expériences nous permettent de découvrir plusieurs sources de pertes de frottement dans l’ensemble du banc d’essais, ce qui confirme le faible rendement obtenu expérimentalement (autour de 50 %) pour tout l’ensemble (vérin électromécanique, réducteur). Quelques optimisations ont été effectuées pour améliorer l’efficacité de l’ensemble. Mais il reste difficile de quantifier l’efficacité de système (vis-rouleaux-écrou) expérimentalement. Pour cela, des essais manuels effectués en utilisant le système vis à rouleaux seul confirme les résultats numériques. Une autre partie expérimentale (en utilisant les machines MTM et HFRR) a été faite afin d’obtenir l’influence du lubrifiant sur le coefficient de frottement. Quatre huiles de différentes caractéristiques ont été utilisées. Ces huiles ont été utilisées sur le banc d’essais, mais l’influence du lubrifiant sur le rendement de l’assemblage n’est pas obtenue à cause de la rugosité importante des surfaces de contact du système vis à rouleaux. / This PhD work, carried out in collaboration with the Elbi company concerns the modeling of the geometry and the kinematics of the roller screw system. This work analyzes the ki- VII Résumé nematics and the geometry of the planetary roller screw mechanism (RSM) to provide a fundamental basis to support its various applications. A 3D model of the roller screw system is developed. A numerical code has been developed as a function of the geometry and the kinematics of the roller screw system. The force and the contact pressure distribution as a function of form errors and geometry are obtained in this work. Then, a 3D model of the frictional moment was developed. The sliding speed and the frictional force (between screw/roller and roller/nut) was calculated as a function of the kinematics, the geometry and the form error. Efficiency, frictional losses and the lifetime of the roller screw mechanism as a function of the form errors, the kinematics and geometry are obtained. These numerical results show the high efficiency of the roller screw system (around 97 %). Furthermore, experiments were performed on an electromechanical bench in collaboration with the laboratory Ampére of INSA Lyon, to compare these results with theoretical predictions. These experiments reveal several sources of friction losses, which confirms the low efficiency obtained experimentally (around 50 %) for the complete system (electromechanical actuator and gearbox). Some optimizations have been made to improve the efficiency of the assembly. But it remains difficult to quantify the efficiency of the set (screw-roller-nut) experimentally because of the presence of many sources of friction. To attain this goal, manual tests using the single roller screw system confirm the numerical results. Furthermore, another experimental part (using the HFRR and MTM Machines) was carried out to obtain the influence of the lubricant on the friction coefficient. Four oils of different characteristics were used. These four oils were used on the test bench, but the influence of the lubricant on the performance of the system was not obtained due to the high roughness of the contact surfaces of the roller screw system.