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Fretting phenomenon occurs when two bodies in contact undergo small repetitive relative motion such that the localized surface and subsurface material properties are altered leading to damage or failures. Fretting conditions are obtained by controlling externally applied parameters such as load, frequency of displacement, displacement amplitude. Material properties which influence fretting behavior include hardness, ductility, hardening behavior. External parameters like surface roughness, temperature also play a role in deciding the extent of damage. Based on fretting conditions and specimen geometry, various fretting modes can be classified. Rotational fretting is one such damage mode, observed in industrial applications such as cable ropes under tension used for support in construction industry and variable stator vanes (VSVs) in compressors of turbines. In spite of industrial and engineering relevance, rotational fretting has received little attention. In the present work, rotational fretting of self-mated AISI 4340 material pair was studied, with the objective of characterizing subsurface damage induced by fretting. AISI 4340 (EN 24) is a low alloy martensitic steel with an excellent combination of strength, ductility and toughness. It is widely used in high strength cyclic loading applications like gears, bearings, automobile pistons and aircraft landing gears as well as in low corrosion, high strength offshore applications. It can be readily machined and surface hardened which makes it useful for wear related applications. A novel rotational fretting test set up, capable of operating under various test loads, frequencies, displacement amplitudes and temperatures was used to perform experiments. Specimens were subjected to a combination of normal load and rotational displacement and caused to mutually contact on non-conformal curved surfaces which simulate a bearing or bushing geometry. Fretting results were primarily determined by the frictional torque versus angular displacement plots. The running condition response was linked to the fretting material response regime. Surface and subsurface characterization studies of fretted regions were conducted using Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM). TEM studies revealed varying levels of fretting induced plastic deformation within the fretted contact zone. Good correlation with available literature relating to formation of dislocation cells and presence of high dislocation density in the fretting damaged regions was established. Although quantifying the dislocation density as a damage indicator is a challenge, it is proposed that a microstructural feature based approach has the potential to be developed into a useful tool for life assessment and life prediction studies.

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.

The general problem of an anticrack, present in a simple domain and subject to general remote loading is solved using distributed line forces, acting as strain nuclei, along the line of the anticrack. Subsequently, both dislocations and point forces are used as strain nuclei to achieve mixed boundary value conditions. The influence function for a pair of forces applied to the faces of a semi-infinite notch is found and finally this is used to find the true closure length and interfacial contact pressure. When a sharp-edged indenter is pressed into a half plane material in the half-plane is displaced and 'laps around' the edges of the punch, possibly making contact with the side faces. This phenomenon is quantified within (coupled) half-plane theory, and applied first to an idealised indenter having the cross section of a trapezium, and then to a semi-infinite indenter. The latter allows an asymptotic form to be found which, through a generalised stress intensity factor may be collocated into the edge of any notionally sharp-edged indentation problem. The effect of surface strains on the local slip angle, when an infinite cylinder is slid skew-wise across an elastically similar half-plane is found. It is shown that local frictional orthogonality is not completely consistent with global orthogonality. The problems of a square-ended and an almost square-ended rigid punch sliding with both plane and anti-plane velocity components are studied. It is shown that, for a truly complete contact, if the contacting body is incompressible, convection effects are absent. Introducing either: (a) local rounding or (b) finite compressibility of the contacting body into the problem introduces convection, giving rise to an inconsistency between the global and local requirement of the orthogonal friction law. The state of stress in a three-quarter-plane undergoing antiplane shear deformation is studied, due to the presence of a screw dislocation along one of the projection lines extending from the free surfaces. A simple, accurate formula for the state of stress along the line is found, providing a useful kernel for the solution of crack and contact edge slip problems. The state of stress induced in an axi-symmetric solid formed from a half-space and a bonded semi-infinite rod, by a family of ring dislocations of arbitrary Burgers vector is found. Particular care is given to the interaction between the Cauchy singularity near the dislocation core and the geometric singularity at the rod/half-space junction. Torsional contact between a semi-infinite elastic rod with square ends and an elastically similar half-space was then solved using the ring dislocations as influence functions. This provides an excellent illustration of the imposition of orthogonality condition for a complete contact.

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Thesis (M.S.)--Mechanical Engineering, Georgia Institute of Technology, 2005. Directed by Richard Neu. / Johnson, Steven, Committee Member ; McDowell, David, Committee Member ; Neu, Richard, Committee Chair. Includes bibliographical references.

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Mecânica, 2017. / Submitted by Gabriela Lima (gabrieladaduch@gmail.com) on 2017-12-04T17:49:57Z No. of bitstreams: 1 2017_GabrielMagalhãesJuvenalAlmeida.pdf: 83803985 bytes, checksum: 8ff18524c3dc296320de503f8217bb6c (MD5) / Approved for entry into archive by Raquel Viana (raquelviana@bce.unb.br) on 2018-02-01T17:41:41Z (GMT) No. of bitstreams: 1 2017_GabrielMagalhãesJuvenalAlmeida.pdf: 83803985 bytes, checksum: 8ff18524c3dc296320de503f8217bb6c (MD5) / Made available in DSpace on 2018-02-01T17:41:41Z (GMT). No. of bitstreams: 1 2017_GabrielMagalhãesJuvenalAlmeida.pdf: 83803985 bytes, checksum: 8ff18524c3dc296320de503f8217bb6c (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) e Eletronorte. / O fenômeno de fadiga por fretting causa enormes prejuízos, principalmente para os setores elétrico e aeronáutico, ao danificar e reduzir a vida útil dos componentes que presenciam este tipo de fadiga, e ainda hoje, muitos dos efeitos causados pelo problema de fadiga por fretting continuam desconhecidos. Este trabalho tem como propósitos principais a validação de metodologias utilizadas para prever a direção de iniciação de trincas no caso de fretting, além de analisar a influência de parâmetros experimentais sobre a direção de propagação destas trincas. Para alcançar tal fim, dados disponíveis na literatura conjuntamente com testes conduzidos pelo autor foram utilizados para comparar os resultados numéricos obtidos combinando as metodologias propostas e critérios multiaxiais (Fatemi-Socie, Smith-Watson-Topper e Modified Curve Wöhler Method) com as direções experimentais de propagação das trincas. Os resultados apontaram que dentre os critérios em estudo, o de SWT se mostrou superior ao atingir os melhores resultados e que a utilização do Método da Distância Crítica trouxe melhora no desempenho desses critérios, inclusive na captura dos efeitos observados pela variação dos parâmetros analisados. / The fretting fatigue phenomenon causes huge losses, mainly to energy and aviation industries, by reducing the life of many components which experience this kind of fatigue and currently, many of the effects caused by the problem of fretting fatigue remain unknown. The main goals of this dissertation are the validation of methodologies used for prediction of crack path propagation on fretting fatigue cases and the analysis of the influence of experimental parameters on the direction of these cracks. To achieve these goals, data available in literature and experimental tests conducted by the author were used to compare the numerical results obtained using different methods and multiaxial criteria (Fatemi-Socie, Smith-Watson-Topper and Modified Wöhler Curve Method) with the experimental results. The results indicate that among the multiaxial criteria in analysis, the SWT has proved itself to be better than the others and the utilization of the Method of Critical Distance has improved the performance of these criteria, as well as the capture of the effects caused by variation of the experimental parameters in study.

Tese (doutorado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Mecânica, 2017. / Texto parcialmente liberado pelo autor. Conteúdo restrito: Capítulos 4 e 5. / Submitted by Raquel Almeida (raquel.df13@gmail.com) on 2018-01-04T18:22:52Z No. of bitstreams: 1 2017_BarbaraMarieCélineFerry_PARCIAL.pdf: 3017479 bytes, checksum: b23c85c14a5f22650fc965f93bbbf89d (MD5) / Approved for entry into archive by Raquel Viana (raquelviana@bce.unb.br) on 2018-02-21T18:37:40Z (GMT) No. of bitstreams: 1 2017_BarbaraMarieCélineFerry_PARCIAL.pdf: 3017479 bytes, checksum: b23c85c14a5f22650fc965f93bbbf89d (MD5) / Made available in DSpace on 2018-02-21T18:37:40Z (GMT). No. of bitstreams: 1 2017_BarbaraMarieCélineFerry_PARCIAL.pdf: 3017479 bytes, checksum: b23c85c14a5f22650fc965f93bbbf89d (MD5) Previous issue date: 2018-02-20 / A fadiga por fretting está relacionada com o processo de dano, localizado na fronteira de contato entre dois corpos submetidos a cargas de fadiga. A previsão desse fenômeno é de grande importância na análise, por exemplo, da vida de lâminas de discos de turbinas. Na fadiga por fretting, o campo de tensão é máximo na superfície de contato, sendo observado um alto gradiente de tensão sob essa superfície. A diferença de escala entre experimentos realizados em laboratórios e os sistemas industriais, motivaram, nessa pesquisa, uma investigação da influência do efeito de tamanho na previsão de vida em fadiga por fretting. Para quantificar o efeito do gradiente de tensão e o efeito de tamanho, diferentes testes foram realizados na Universidade de Brasília em um equipamento servo-hidráulico com dois atuadores especialmente desenvolvido para ensaios de fadiga por fretting. Os parâmetros de testes foram definidos de forma que induzissem diferentes gradientes de tensão nos corpos de prova e posteriormente foram ajustados de modo que o volume solicitado sob a região de contato fosse o mesmo. Após os ensaios, para investigar os mecanismos de dano, os corpos de prova foram analisados por meio de um microscópio confocal laser. Foi demostrado nesta tese que para a liga Ti-6Al-4V, uma abordagem não local, baseada no campo de velocidades em uma determinada área ao redor da região de contato consegue prover boas previsões de vida em fadiga por fretting. Uma análise da influência das forças de fadiga nos processos de iniciação e propagação de trincas foi realizada e indicaram que essas forças não podem ser negligenciadas. De fato, se cerca de 75% dos mecanismos de iniciação de trinca em fadiga por fretting são controlados por tensões de contato (cisalhantes e pressão de contato) a consideração das tensões normais possibilita realizar previsões de vida mais realistas. O estudo do efeito do tamanho foi dividido em duas fases. A primeira investigou a influência do volume solicitado, reduzindo a largura de contato, porém, o gradiente de tensão sob a área de contato e a área de dano dentro da zona de deslizamento foram mantidas constantes. Na segunda, mantendo os parâmetro experimentais σB,max/p0 e Q/fP constantes, a influência da área de dano no interior da zona de deslizamento foi isolada enquanto que a área de dano sob a zona de deslizamento foi reduzida. Os resultados experimentais foram analisados utilizando o critério de fadiga da Curva Modificada de Wöhler em conjunto com a Teoria da Distância Crítica. Foi observado que nenhum desses dois parâmetros influenciam significativamente a vida em fadiga por fretting. Assim, o termo “efeito de tamanho” deve ser analisado somente com base no efeito do gradiente. / Fretting fatigue refers to the damage process localized at the frontier of the contact between two contacting bodies subjected to fatigue loadings. The prediction of this phenomenon is of major importance in determining, for instance, the lifetime of fan’s disk. In the vicinity of the contact front, the stress field inherited from the contact loads is maximal at the surface and displays a strong gradient under the contact. The difference of scale between the laboratory’s experiments and the industrials’ system motivated the study of the impact of the size effect for the determination of the lifetimes. To quantify the effect of the stress gradient and of the size effect, tests were carried out on a two vertical-actuators fretting-fatigue rig at the University of Brasilia, with experimental conditions ensuring different stress gradient and later different volume solicited under the contact. Damage mechanisms were studied using post-mortem analysis with a confocal microscope on some contact elements tested. It was shown on this thesis, for a Ti-6Al-4V alloy, that a nonlocal approach, based on equivalent velocity field on a determined area around the contact, leads to good expectation for the determination of fretting fatigue lives. The influence of the bulk stress for the description of the fretting fatigue crack initiation and propagation was also determined and it appears that it could not be neglected for the determination of the crack initiation boundary. As a matter of fact, if around 75% of the crack initiation mechanism in fretting fatigue is controlled by the contact stresses, i.e. shear stress and contact pressure, the consideration of the normal stress allows to obtain more realistic prediction. The study of the size effect was divided into two phases. First the influence of the volume stressed was investigated by reducing the width of the contact but maintaining the stress gradient under the contact and the damaged area within the slip zone constant. Then, the influence of the damaged area within the slip zone was isolated by maintaining the experimental parameters, i.e. σB,max/p0 and Q/fP, constant while the damaged area under the slip zone was reduced. The experimental results were analysed by applying a fatigue criterion, the Modified Wöhler Curve Method, in conjunction with the Theory of the Critical Distance. It was found that none of these two parameters influences significantly the fretting fatigue lifetimes, and so the term ‘size effect’ usually referenced in the literature as a damaging effect should refer only to the gradient effect.

Les endommagements provoqués par le fretting sont multiples et peuvent causer de sévères disfonctionnements. Il est donc nécessaire d’étudier le fretting, en particulier dans le cas des alliages de titanes fréquemment employés dans l’aéronautique. Les endommagements générés par fretting peuvent être de l’usure, de la fissuration ou bien une combinaison des deux. La distinction entre ces deux comportements entraine régulièrement une dichotomie dans le choix des sujets traités. L’étude présentée ici fait le choix de rassembler en une seule démarche les études d’usure et de fissuration. Cette approche permet d’avoir une vision d’ensemble du comportement en fretting et fretting-fatigue d’un contact aube-disque dans un compresseur haute pression. Afin de respecter les contraintes industrielles, l’étude est réalisée à haute température (450°C) avec un contact plan sur plan revêtu. Pour réaliser cette étude, un dispositif expérimental original a été mis en place et validé. Les premiers résultats tribologiques montrent un effet majeur de la pression de contact sur le comportement tribologique de l’interface. Le coefficient de frottement du traitement de surface étudié diminue quand la pression de contact augmente. Une hypothèse d’expulsion du lubrifiant solide inclus dans le dépôt est proposée pour expliquer ce phénomène. Les résultats d’usure et notamment les analyses physicochimiques montrent un comportement sacrificiel du dépôt qui est usé préférentiellement au contre-corps. Cette caractéristique est bénéfique car dans l’application industrielle le contre-corps (le disque) doit être protégé en priorité par rapport à la pièce revêtue (l’aube). Les résultats d’usure dans la configuration industrielle sont complétés par une étude plus fondamentale mettant en évidence l’influence de la fréquence et du cycle de chargement du contact. La morphologie des traces d’usure est modifiée par ces deux facteurs, et le taux d’usure énergétique est également modifié. L’étude de la fissuration est menée en fretting simple et en fretting-fatigue. La fissuration du contre-corps non revêtu est modifiée par l’application d’un dépôt sur le poinçon revêtu. L’effet est principalement observable sur la longueur maximale de fissure, qui est divisée par deux dans le cas revêtu. Les résultats en fretting-fatigue sont également modifiés par la présence du revêtement, dont l’effet est plus présent pour les grands nombre de cycles. Enfin, une représentation des résultats sous forme de diagramme polaire normalisé est proposée afin de donner une image claire de l’ensemble des performances du dépôt. / Fretting damage is a major cause of defect. It is mandatory to study fretting in order to improve material performances, especially for titanium alloys used in aeronautics. Fretting induces wear, cracking or both damages in bodies in contact. The usual topics of fretting studies deal with one of these damages. In the one presented here, wear and cracking are studied simultaneously. This point of view allows a global approach of the blade-disk contact behavior in case of fretting in a turbojet high pressure compressor. Due to industrial constraints, the temperature of this study is 450°C and the contact geometry is coated plane on plane. This study is performed on an original experimental setup made for it. This setup enables fretting-fatigue tests at constant fretting force even if fatigue force varies. The first’s results regard tribological behavior. A significant effect of pressure is shown: the more the pressure, the smaller the coating friction coefficient. The given hypothesis is an expulsion of solid lubricant contained in surface treatment. Wear results show a sacrificial behavior of the coating. The surface treatment is worn preferentially than counter-body. From an industrial point of view, this characteristic is a good way to protect the uncoated counter-body (disk) instead of coated part (blade). In parallel, another study shows effect of frequency and load variation during cycle in a more fundamental case. Wear scar profile and wear rate is modified by these two parameters. Plain fretting tests and fretting-fatigue tests are performed to study fretting cracking process. Fretting induced cracking on counter-body is modified by coating on the punch. Maximal crack length is twice as short in coating condition as in uncoated condition. In fretting-fatigue, the coating is more efficient in high cycle fatigue. As a conclusion, a polar diagram is used in order to present global results and performances of the coating.