Mechanics of Fretting Fatique

In the design of any mechanical structural component, two criteria play very important parts. These are: the avoidance of yield, and the avoidance of brittle fracture. It is relatively easy to design against yield; this simply requires the determination of a composite stress parameter from the individual stress components, and this parameter is maintained below the value of the yield stress at all points. Design against brittle fracture is more difficult; this requires not only the determination of the state of stress within an object, but also some speculation on the form, location, and origin of initial defects, which often grow by the process of fatigue during the service life of the component, and may reach a critical value leading to brittle fracture. This latter criterion forms the basis of the study of fracture mechanics. There is now an excellent range of introductory textbooks on this subject, such as those by Gdoutos (1990, 1993), Ewalds and Wanhill (1984), and Broek (1982, 1989). It is important to recognise at the outset that the fatigue life of a crack has two quite distinct elements, and that the relative proportion of the total life expended in each portion will vary tremendously. These two phases are the initiation or nucleation phase, and the propagation stage. In welded structures, or those components made from castings of indifferent quality there will pre-exist a number of defects of appreciable size, due to the presence of inclusions, slag, or lack of weld penetration. In these components there is no initiation time, so that the entire life of the component is expended in propagation. However, most critical components in high-technology applications are not manufactured by these routes, and the surface finish is usually very good. There are therefore no pre-existing macroscopic defects, and it is very difficult to speculate where they may form. Indeed, it is the designer’s job to ensure that the geometry of the components is such as to reduce the chances of initiation to a minimum! This is normally done by avoiding stress raisers such as fillets, keyways, screw threads and abrupt changes of section. All these measures are concerned with keeping the stress state as uniform as possible, and are successful when the possible sites of initiation lie on a free surface. However, where there is a connection between two components, such as a collar heat shrunk onto a shaft, another form of crack initiation, which is much more aggressive than that prevalent at a free surface becomes possible. This is the phenomenon of fretting.

Two fundamental features are present in any fretting problem: first, the contact must be experiencing shear tractions and this normally means that a resultant tangential force is transmitted from one body to another. Secondly, there must be some degree of relative tangential displacement between the contacting surfaces so that slip takes place during cyclic variation of the applied load. In Chapter 2, two types of contact were analysed:

In this chapter a range of more difficult concepts arising in the analysis of contacts will be discussed. This chapter may therefore be omitted at first reading and studied after crack analysis techniques have been mastered. Three specific topics are covered, viz. the influence of elastic material mismatch, contacts subjected to torsion, and the presence of layers in the contacting bodies, including the influence of finite thickness. All of these extensions to the basic theory may be made in closed form, and represent the development of concepts introduced in chapters 2 and 3. There exists, however, a wide range of practically occurring contacts where neither the half-plane nor strip approximations is justified, for example where a contact occurs very close to the edge of a block of material. Under these conditions a completely numerical scheme may be unavoidable. Even where the half-space assumption may be retained, many problems arise which are neither axi-symmetric nor plane — these may profitably be analyzed using a numerical scheme, but based on a half-space influence function formulation, which provides a computationally more efficient strategy than the finite element technique. These numerical approaches to the analysis of contacts are also discussed in the present chapter.

The phenomenon of fretting fatigue arises as a result of surface interaction between two contacting bodies and it is therefore important to investigate the nature of the surfaces in some detail in order to understand the phenomenon in any meaningful way. Real surfaces are invariably complex and differ quite markedly from the smooth abrupt transitions from elastic solid to free space which have been assumed so far in this book. For example the surface of a metal component may consist of a number of layers, as depicted in fig. 5.1 for a typical metal. The bulk of the metal component will form a substrate. On top of this will be a layer of material which will typically have been exposed to large amounts of plastic deformation during the manufacturing process.

The object of studies of fretting is ultimately to be able to quantify the rate of fatigue crack growth, and to be able to describe the conditions under which cracks do not arise, or at any rate do not grow. Traditional approaches to the quantification of fatigue have relied on the assumption that the nominal stress in the absence of the crack is sufficient to determine its behaviour. The classical experiments of Wöhler were designed to measure the fatigue life of railway axles under fully reversing stress, which was calculated from elementary bending theory. A graph of the number of cycles to failure against the bending stress became known as an S-N curve (Dieter, 1961), and subsequent experimental work has enabled the influence of mean stress to be taken into account. However, a bulk approach to fatigue under a multi-axial state of stress has never been fully developed (Toor, 1975 a,b). Further, the initiation and propagation elements of fatigue crack growth cannot be separated by this approach.

So far, we have presented several of the elements of calculation necessary to analyse a range of idealised fretting contacts. They merely provide tools for determining the state of stress, strain and displacement, but do not, in themselves, permit production of initiation or crack propagation criteria, without extensive experimental data. The object of fretting fatigue tests must be to permit monitoring of fretting fatigue crack propagation and, more importantly, initiation, under laboratory conditions, so that the influence of different load histories, surface treatments, surface finishes and indeed underlying materials may be found. There are three general categories of tests which might be envisaged, viz.

Fatigue cracks may propagate either from an existing flaw, such as an inclusion or a defect in a weld, or they may grow from damage nucleated as part of the early stages of fatigue itself. It is into this second category that fretting fatigue falls. The fretting process must first initiate an embryo crack and then propagate it in order to produce a failure. The life of a component suffering fretting fatigue may therefore be conveniently divided into initiation and propagation phases. In contrast to plain fatigue the initiation phase of fretting fatigue life is often, although not always, quite short. In reality the term fretting fatigue encompasses a range of conditions from mild contact tractions accompanying bulk stress amplitudes sufficient to cause failure in plain fatigue, to severe fretting in the presence of relatively low bulk stresses. The spectrum of loading conditions can be conveniently summarised in a diagram such as that shown in fig. 8.1. It is possible for fretting fatigue to affect significantly both crack initiation and crack propagation. Thus, a full understanding of fretting fatigue requires a consideration of the effect of fretting on both initiation and propagation phases of crack life. Initiation occurs at a microscopic scale and a detailed understanding can be achieved only by a micromechanics analysis, although some progress can be made by considering bulk properties of the contact. In contrast, once a crack has developed and is larger than several material grain sizes, it should be possible to explain its propagation by employing the same techniques of fracture mechanics as are used for other types of fatigue. Indeed, crack growth depends entirely on conditions at the crack tip and it is impossible for a crack to ‘distinguish’ whether the propelling stresses arise from a contact loading or from some other far field. Thus, the analysis of crack propagation would appear to be far more tractable than that of initiation and it will be addressed first. Crack initiation will be discussed further in Chapter 9.

In a study of a field such as fatigue, which depends at least partly on an ever more refined understanding of materials phenomena, there can be no final statement completely explaining the physics of the problem. In the case of some kinds of failure, such as yield, or brittle fracture of a flawed component, it is, nevertheless, possible to make simple concise statements which are of immediate usefulness to the engineering designer. In attempting to quantify fretting fatigue, even this is not possible, principally because of our incomplete understanding of the nature of crack initiation, and partly because the process is a stochastic one, depending on the vagaries of the material crystallography, surface topography and cleanliness. We should remind ourselves that the life of a crack is conveniently categorised as a two-stage process; first the crack nucleates, usually from the surface and from pre-existing defect, no matter how small that defect may be. It is this phase of the life which is so critically dependent on the quantities cited, and which is difficult to quantify. Secondly, the crack propagates, in a direction and at a rate controlled also by the state of stress, but this phase is somewhat less sensitive to the material properties obtaining within the individual grains. There is a considerable body of experimental evidence to show that fretting influences both of these processes. The goal of an engineering approach to the analysis of fretting fatigue is to quantify the effects, so as to allow the designer to estimate component life reliably using the results of basic materials tests.