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When a high voltage cable is transported throughout factory it is affected by sidewall pressure in cable bends between the roller supports and the cable. The problem is when the sidewall pressure is too high it will deform the cable which can have a negative impact on the conductivity of the cable. The roller supports can also get damaged because of fatigue. These negative consequences are the subject to exploration by implementing known analytical solution of contact mechanics developed by Hertz together with finite element analysis and experimental testing.   Two possible methods of measuring the radial force is studied to be able adjust the roller supports positions to reduce the sidewall pressure on the cable. The first one is to use the pressure film to determine the radial force. The second one is to by measuring the compression in cable to thereafter translate it to radial force by having the relation between compression and radial force for the specific cable.   Two different types of high voltage cables, a direct current (DC) cable and an alternating current (AC) cable is studied by using finite element method and experimental tests to see the relation between the compression and radial force in the cable. Also in these experimental tests the pressure films are used and evaluated to see if this measuring technique combined with Hertzian’s theory make it possible determining the radial force.   For the method of using the pressure films to determine the radial force the result shows it is difficult to translate the pressure from the films to radial force for a high voltage because of the cable’s armouring wires. The conclusion about these the pressure films is that they are good to use to describe the compression and can be used as relative measurement between the rollers but not for determine the radial force.   The result shows it is a possible to describe relation between compression and radial force for a high voltage cable and use this information to determine the radial force by measuring the compression. But the conclusion is that it is ineffective and less accurate way of measuring the radial force.   These results from this thesis are important for further research within the area and they help creating a greater understanding of sidewall pressure related problems in cables.

Nous proposons dans ce manuscrit une nouvelle méthode pour prendre en compte l’effet du gradient en Fretting-fatigue. Les champs mécaniques présents à proximité du front de contact sont décrits à travers des facteurs d’intensité non locaux. L’objectif est d’aboutir à une description du champ de vitesse sous la forme d’une somme de termes exprimés chacun comme le produit d’un facteur d’intensité (Is, Ia, Ic), qui dépend des chargements macroscopiques appliqués à l’ensemble et d’une fonction de forme (ds, da, dc), qui est liée à la géométrie locale du contact. Cette description est obtenue à travers un processus non intrusif de post-processing des résultats obtenus avec des calculs à éléments finis. De plus, elle a été pensée pour être implémentée dans un contexte industriel. En pratique, pour chaque chargement macroscopique et pour chaque géométrie, il est possible de calculer un ensemble de facteurs d’intensité non locaux qui permettent de décrire les champs mécaniques locaux près du front de contact. Cette description non locale a l’avantage d’être (i) indépendante de la géométrie du contact employé et (ii) utilisable dans des modèles à éléments finis utilisés dans l’industrie qui sont caractérisés par des maillages plus grossiers par rapport à ceux utilisés pour étudier le fretting-fatigue dans des milieux académiques. Une étude est menée pour vérifier que les facteurs d’intensité non locaux peuvent être utilisés pour transposer les résultats expérimentaux d’une géométrie à une autre. / In this manuscript a new method to describe the stress gradient effect in fretting-fatigue is proposed. It is based on the description of the mechanical fields arising close to the contact edges through nonlocal intensity factors. For this purpose, the kinetic field around the contact ends is partitioned into a summation of multiple terms, each one expressed as the product between intensity factors, Is, Ia, Ic, depending on the macroscopic loads applied to the mechanical assembly, and spatial reference fields, ds, da, dc, depending on the local geometry of the part. This description is obtained through nonintrusive post-processing of FE computation and is conceived in order to be easily implementable in the industrial context. As a matter of fact, for any given macroscopic load and geometry, a set of nonlocal intensity factors is computed that permits to characterize the mechanical fields close to the contact edges. Such nonlocal description has the advantage of being (i) geometry independent so that the nonlocal intensity factors can be used to compare laboratory test with real-scale industrial assembly, (ii) applicable to industrial FE models usually characterized by rougher meshes compared to the ones used to describe fretting-fatigue in the academic context. The procedure is applied to fretting-fatigue test data in order to verify whether the nonlocal intensity factors can be used to transpose experimental results to different contact geometries from the one in which they have been obtained.

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The measurement of the work of adhesion is of significant technical interest in a variety of applications, ranging from a basic understanding of material behavior to the practical aspects associated with making strong, durable adhesive bonds. The objective of this thesis is to investigate a novel technique using an elastica loop to measure the work of adhesion between solid materials. Considering the range and resolution of the measured parameters, a specially designed apparatus with a precise displacement control system, an analytical balance, an optical system, and a computer control and data acquisition interface is constructed. An elastica loop made of poly(dimethylsiloxane) [PDMS] is attached directly to a stepper motor in the apparatus. To perform the measurement, the loop is brought into contact with various substrates as controlled by the computer interface, and information including the contact patterns, contact lengths, and contact forces is obtained. Experimental results indicate that due to anticlastic bending, the contact first occurs at the edges of the loop, and then spreads across the width as the displacement continues to increase. The patterns observed show that the loop is eventually flattened in the contact region and the effect of anticlastic bending of the loop is reduced. Compared to the contact diameters observed in the classical JKR tests, the contact length obtained using this elastica loop technique is, in general, larger, which provides potential for applications of this technique in measuring interfacial energies between solid materials with high moduli. The contact procedure is also simulated to investigate the anticlastic bending effect using finite element analysis with ABAQUS. The numerical simulation is conducted using a special geometrically nonlinear, elastic, contact mechanics algorithm with appropriate displacement increments. Comparisons of the numerical simulation results, experimental data, and the analytical solution are made. / Master of Science

The thesis is concerned with the contact mechanics behaviour of non-conforming solids. The geometry of the solids considered gives rise to various contact configurations, from concentrated contacts with circular and elliptical configuration to those of finite line nature, as well as those of less concentrated form such as circular flat punches. The radii of curvature of mating bodies in contact or impact give rise to these various nonconforming contact configurations and affect their contact characteristics, from those considered as semi-infinite solids in accord with the classical Hertzian theory to those that deviate from it. Furthermore, layered solids have been considered, some with higher elastic modulus than that of the substrate material (such as hard protective coatings) and some with low elastic moduli, often employed as tribological coatings (such as solid lubricants). Other bonded layered solids behave in viscoelastic manner, with creep relaxation behaviour under load, and are often used to dampen structural vibration upon impact. Analytic models have been developed for all these solids to predict their contact and impact behaviour and obtain pressure distribution, footprint shape and deformation under both elastostatic and transient dynamic conditions. Only few solutions for thin bonded layered elastic solids have been reported for elastostatic analysis. The analytical model developed in this thesis is in accord with those reported in the literature and is extended to the case of impact of balls, and employed for a number of practical applications. The elastostatic impact of a roller against a semi-infinite elastic half-space is also treated by analytic means, which has not been reported in literature. Two and three-dimensional finite element models have been developed and compared with all the derived analytic methods, and good agreement found in all cases. The finite element approach used has been made into a generic tool for all the contact configurations, elastic and viscoelastic. The physics of the contact mechanical problems is fully explained by analytic, numerical and supporting experimentation and agreement found between all these approaches to a high level of conformance. This level of agreement, the development of various analytical impact models for layered solids and finite line configuration, and the development of a multi-layered viscoelastic transducer with agreed numerical predictions account for the main contributions to knowledge. There are a significant number of findings within the thesis, but the major findings relate to the protective nature of hard coatings and high modulus bonded layered solids, and the verified viscoelastic behaviour of low elastic modulus compressible thin bonded layers. Most importantly, the thesis has created a rational framework for contact/impact of solids of low contact contiguity.

Engineering assemblies are very frequently subject to fretting fatigue, which is a damage process that results when very small slip displacements arise at nominally stationary frictional interfaces. Fretting accelerates the initiation and early propagation of fatigue cracks, thereby causing significant reductions in the fatigue performance of many critical engineering components. A majority of the previous research on fretting fatigue has focused on incomplete (i.e. smooth-edged) contacts, while complete (i.e. sharp-edged) contacts have received less attention. The aim of this thesis is to contribute to the theoretical understanding of complete contacts, especially when they are subject to fatigue conditions. This problem is addressed in two separate ways. First, because fretting failures almost invariably initiate from the edge of contact, a detailed understanding of the conditions in this region should enable more accurate assessments of fatigue performance to be made. Thus, an asymptotic analysis is presented, which provides an accurate description of the contact edge under many conditions. This is done by using the elasticity solution for a semi-infinite notch to represent the state of stress near the contact edge in an asymptotic sense. Attention is then placed on the fact that cyclically loaded frictional contacts tend toward a steady-state response in which less frictional slip (and energy dissipation) occurs than in the first few load cycles. To investigate this effect, a numerical sub-structuring procedure is described, which significantly reduces the number of degrees of freedom in finite element models of frictional contact. This reduced model is then used to calculate the shakedown limit, i.e. the amplitude of cyclic load above which frictional slip is guaranteed to persist in the steady state. The sensitivity of the steady-state solution to the initial residual displacement state is then investigated, and it is shown that initial conditions can have a large influence on the steady-state behaviour of complete contacts.