This work analyzes partial slip contact problems in the theory of linear viscoelasticity using both the semi-analytical method and nite element method. Such problems arise in metal-polymer contacts in orthopedic implants and similar applications. The boundary conditions of such problems are inherently mixed and vary with time, thus restricting the use of classical correspondence principle, which have been the basic approach for most of the solved problems in viscoelasticity. In the present semi-analytical approach, the governing equations for the vis-coelastic partial-slip contact are formulated as a pair of coupled Singular Integral Equations (SIEs) for a pin-plate geometry using the viscoelastic analogues of Green's functions. The formulation is entirely in the time-domain, avoiding Laplace transforms. Both Coulomb and hysteretic e ects are considered, and arbitrary load histories, including the bidirectional pin loads and remote plate stresses, are allowed. Moreover, the contact patch is allowed to advance and recede with no restrictions. The presence of viscoelastic behavior necessitates the application of the stick zone boundary condition in convolved form, and also introduces additional convolved gap terms in the governing equations, which are not present in the elastic case. Transient, as well as steady-state contact tractions, are obtained under load-hold, unload-hold, unload-reload, cyclic bidirectional (fretting) and remote plate loading for a three-element delayed elastic solid. A wide range of loads, loading rates, friction coeficients and the conforming nature of the contact are considered. The contact size, stick-zone size, indenter approach, maximum pressure, Coulomb energy dissipation are tracked during fretting. The edge-of-contact stresses and the subsurface stresses for the viscoelastic plate due to the contact tractions are determined by solving an equivalent traction boundary value problem. It is found that the viscoelastic fretting contact tractions for materials with delayed elastic nature shakedown just like their elastic counterparts. However, the number of cycles to attain shakedown states is strongly dependent on the ratio of the load cycle time to the relaxation time constant of the viscoelastic material. In monotonic load-hold case, the viscoelastic steady-state tractions agree well with the tractions from an equivalent elastic analysis using the shear modulus at infinite time. Whereas, the viscoelastic fretting tractions in shakedown differ considerably from their elastic counterparts. This is due to the fact that the contact patch does not increase monotonically in fretting-type(cyclic) loading. Hence, an approximate elastic analysis misleads to an incorrect edge-of-contact stresses. During fretting, the edge-of-contact hoop stress also shakedown and reaches its peak value at the trailing edge-of-contact when the horizontal pin load reaches its maximum. Moreover, the peak tensile of the edge-of-contact hoop stress increases with the increase in the Coulomb friction coefficient. In cyclic loading, Coulomb dissipation in a cycle at steady-state is almost independent of the rate at which the load is cycled. However, the viscous energy dissipated in a cycle is a strong function of the ratio of the load cycle time to the relaxation time constant. The steady-state cyclic hysteretic energy dissipation typically dominates the cyclic Coulomb dissipation, with a more pronounced difference at slower load cycling. However, despite this, it is essential to model an accurate viscoelastic fretting contacts including the effects of both viscous and Coulomb friction dissipation to obtain accurate contact stresses. A 12-element generalized Maxwell solid with long time scales representing a well characterized viscoelastic material like PMMA is also studied. The material chosen is of slowly relaxing nature and the ratio of the instantaneous shear modulus(G0) to the modulus at the infinite time(G1) is almost equal to 1000. In such cases, the material is effectively always in a transient state, with no steady edge-of-contact. As a consequence, the location of the peak hoop stress keeps on shifting when the load cycle is repeated. Interestingly, the rate at which the viscoelastic material relaxes affects the contact tractions. It is observed that the rapidly relaxing materials show qualitatively different tractions in the partial slip, with local traction spikes close to the edges-of-contact and concomitant high-stress gradients. On the other hand, finite element method is also used to analyze the partial slip viscoelastic contacts. In FEA, the pin-plate geometry is modeled using a custom mesh maker, where a 2D-continuum plane strain element is used for the plate and rigid element for the pin. The technique uses 'ABAQUS Standard' solver to solve the contact problem. Finite element analysis for a wide range of loads comparable with the SIE technique is performed. The tractions and contact sizes for various load cases such as unload-reload, fretting-type cyclic loads from both SIE and FEA agrees well. In certain conditions, there exist multiple contact arcs or stick zones that are currently difficult to solve with SIE's. However, such problems are treated using FEA and one such problem is illustrated.

Byl studován kontakt mezi koulí a deskou pod tangenciálním zatížením ve vodě. Jako zdroj střižných kmitů byl použit akustický rezonátor (křemíkové mikrováhy – QCM). Kontakt koule s povrchem resonátoru indukuje změnu resonanční frekvence a šířky pásma. Byla měřena změna frekvence f a změna šířky pásma v závislosti na amplitudě oscilací. S rostoucí amplitudou docházelo k poklesu f a růstem , což je chování typické pro parciální skluz. Díky aplikaci Cattaneo-Mindlinova modelu byl vypočítán kontaktní poloměr a třecí koeficient. Kontaktní poloměr při nízké amplitudě stoupal při zvětšujícím se normálovým zatížením. Tato závislost se dobře shodovala s JKR modelem. Třecí koeficient se nacházel v odpovídajícím rozsahu. Při zvyšování externí normálové síly, docházelo k nepatrnému snižování hodnoty třecího koeficientu. Toto chování je vysvětleno příspěvkem adhezivních sil k totální normálové síle. Výpočtem byly získány dva typy třecích koeficientů, první ze změny frekvence f a druhý ze změny šířky pásma . Tyto dvě hodnoty se spolu shodovaly z ± 20 % pro měření prováděná ve vodě, zatímco pro dvě měření prováděných na hydrofilním povrchu ve vzduchu se lišila. Tento nesoulad poukazuje na nedostatek Cattaneo Mindlinovy teorie a mohl by být vysvětlen přítomností kapilárních sil.

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L’optimisation du dimensionnement des structures passe par une meilleure connaissance de leur mode d’endommagement. Cette étude se focalise donc sur la caractérisation de l’endommagement du contact aube/disque des moteurs aéronautique. Cet assemblage mécanique est soumis a une combinaison d’un effort normal (force centrifuge) et tangentiel (dynamique de l’aube). La portée du disque en Ti-6Al-4V subi donc un chargement complexe de type fretting fatigue. Ce type de sollicitation entraine, entre autre dégradation, de la fissuration dont la modélisation expérimentale et numérique est rendue difficile par les limitations des moyens et des connaissances actuelles. Le premier objectif de ce travail de thèse est de développer un moyen d’essai et une instrumentation associée afin d’étudier de façon qualitative et quantitative la fissuration d’un contact Ti-6Al-4V/Ti-6Al-4V. Le second but est d’utiliser les données issues de ce moyen expérimental afin de proposer un modèle de prédiction des durées de vie de cet assemblage. Un montage inédit de fretting fatigue double vérin mono-contact a été mis en place avec une instrumentation nouvelle pour ce type d’essai : suivi de fissuration par suivi de potentiel et par émission acoustique. Une attention particulière a été apportée aux calibrations et aux méthodologies expérimentales. Ce banc d’essai permet notamment de simuler des efforts de fretting applique en phase ou alors de telle manière a simuler un vrai cycle de vol. Cet outil a permis de décrire quantitativement les premières courbes de Wohler en fretting à amorçage (Effort de fretting vs Nombre de cycles à amorçage) pour deux configurations de contact (cylindre/plan et plan/plan). Les impacts des différents paramètres de fretting sur l’amorcage ont pu être quantifies. Les paramètres influant sont : la configuration du contact, les niveaux des efforts appliques et leur mode de combinaison (cycles en phase ou cycles de type vol). De plus des courbes de cinétique de propagation des fissures ont pu être extraites des différents essais, montrant un fort impact du fretting sur les vitesses de propagation des fissures. Une analyse qualitative via l’émission acoustique a montré un mécanisme d’amorçage et de propagation en 3 étapes suivant la perte d’influence du contact. Un modèle de prédiction de l’amorçage et de simulation de la propagation des fissures a été mis en place. Bien que limite dans la prise en compte des effets gradients (approches non locales), ce modèle se montre très performant surtout dans sa capacité à utiliser les données expérimentales dans l’identification des lois d’amorçage ou de propagation. Ce travail a donc permis d’importantes avancées dans la compréhension des mécanismes de fissuration et dans leur modélisation ouvrant ainsi la porte vers une prédiction fiable de l’endommagement des contacts aube/disque. / Optimization of structures design requires a better understanding of their damage process. This study focuses on the characterisation of the blade/disk contact damaging process on aircraft engines. That mechanical structure is subjected to a normal load (centrifugal forces) combined with a tangential force (blade dynamic). Thus the Ti-6Al-4V disk seat sees a complex fretting fatigue loading. This type of solicitation can generate a series of degradations like cracking. Experimental and numerical simulation of this damaging is very difficult considering the present state of arts. The first aim of this work is to develop a new experimental set-up with the appropriate instrumentation in order to conduct a qualitative and a quantitative analysis of the cracking in a Ti-6Al-4V/Ti6-Al-4V contact. The second goal is to build a life prediction numerical model that would be able to use the data obtain with the new experimental tests. The new dual-actuator fretting-fatigue set-up is now operational. It allows to run single contact test under different loading combinations: fretting and fatigue loads can be applied in phase or in a way to simulate the real ‘in flight’ conditions. New instrumentations have been added in order to follow the crack initiation and propagation: potential-drop technique and acoustic emission. Thanks to this new test procedure, the first fretting Wöhler curve to crack nucleation have been described (fretting load vs number of cycles to crack nucleation) for two contact geometries (cylinder on flat and flat on flat). The separate influences of fatigue and fretting parameters have been determined. The mains parameters are: the contact characteristics, the stress level and the force combination modes (‘in phase’ cycles or ‘in-flight’ cycles). Moreover, the very first crack propagation kinetics have been drowned. Also, a major influence of the fretting on the crack propagation has been exposed. The qualitative analysis conducted with the acoustic emission has revealed a three steps crack propagation process. The crack propagation process evolves with the decrease of the contact influence. A model has been developed in order to predict crack initiation and propagation lives. Even if the model suffers from a major limitation due to the difficult considerations of the stress gradient effects, it has shown very good results through its ability to directly include experimental data. This work has led to major breakthroughs in the understanding of the cracking mechanisms and their simulation. This forms solid foundations for future predictions of the blade/disk interface durability.