"INTRODUCTION When two bodies@ one or both of whose surfaces are curved@ are brought into contact and subjected to a normal load@ a nominal ""point contact"" becomes an elliptical area as a result of elastic deflections within the bodies. Some typical examples of such contacts are shown in Sketch 2.1. Two limiting cases may be identified. In the first@ the contact area is circular@ for example@ sphere on sphere@ (a) in Sketch 2.1@ sphere on plane@ (b)@ identical cylinders crossed at right-angles@ (c). In the second limiting case@ a nominal ""line contact"" becomes a strip@ for example@ cylinder on cylinder with parallel axes@ (e)@ cylinder on plane@ (f )@ cylinder in groove with parallel axes@ (i). The elastic deflections imply the presence of stress fields within and on the surface of the bodies. These stress fields are characterised by the values at each point of the six components of the stress tensor@ defined in Section 3. Data Item No. 78035 (Reference 1) deals with the calculation of stresses and contact dimensions for normally loaded contacts. The maximum values of all the stress components then occur along the line of symmetry@ normal to the surface and passing through the centre of the ellipse@ and much of the information of interest could be presented by a plot of the values of the stress components@ and of quantities derived from them@ against position along this line. The present Item@ the second in a series of which Item No. 78035 is the first@ considers the effect on the stress fields of the addition of tangential shear stresses over the surface of the ellipse@ the ratio of the shear stress to the normal stress having everywhere a constant value@ equal to the coefficient of friction for gross slip. The inclusion of these shear stresses destroys the symmetry of the field@ and the maximum values no longer necessarily occur on the axis of symmetry. This complicates the presentation of the results of calculations of the stress field@ and the coverage of the effect of different combinations of the various factors@ such as coefficient of friction@ Poisson's ratio@ axis ratio of ellipse of contact@ et cetera@ is less comprehensive than in Item No. 78035. Some linear interpolation will often be required in the application to practical cases of the results presented in this Item@ and worked examples are provided. Further results@ not included here@ will be available to all holders of this Item in a forthcoming ESDU Memorandum (Reference 2). In the application of the information in the present Data Item to the solution of practical problems@ it will be assumed that the essential quantities@ the maximum compressive stress and the lengths of the axes of the ellipse of contact@ have been calculated from the information given in Data Item No. 78035. It will also be assumed that the values of these quantities are unaffected by the imposition of the tangential stresses. This latter assumption is not strictly valid if the elastic properties of the two bodies are different@ but in general the effects of the difference are small. This point is discussed further in Section 8.3. Shear stresses of the form assumed arise in the case of gross sliding between dry (unlubricated) bodies. The distribution of shear stresses is more complicated if the tangential forces are insufficient to cause gross sliding@ but the assumption of gross sliding will result in higher values of the stresses than will occur in other circumstances@ that is@ the situation that has been assumed is the worst that could arise. The stress distribution may differ from that assumed if the surfaces are lubricated@ but the results given in this Data Item are valid for boundary lubrication@ and are approximately correct for the limiting case of very thin films in elastohydrodynamic lubrication@ that is@ with low surface velocities and low lubricant viscosities. It is planned to cover the case of elastohydrodynamically lubricated bodies in a further Item in this series. Analytical expressions for the stress fields in the two limiting cases of circular and line contact under combined normal and tangential loading have been available in the literature for some time and are well known (References 3 to 6 inclusive and Derivations 21 and 22)@ but solutions for the general elliptical contact are more complicated@ involve elliptic integrals@ and have been published only recently (Reference 7@ Derivations 23 to 25 inclusive). A surprising feature of the results of these treatments is that the stress fields vary very little with what would appear to be important factors@ such as the axis ratio of the ellipse@ the direction of the force of friction@ and Poisson's ratio. Indeed@ in many cases@ the values of the various stress criteria@ discussed later@ vary by not more than 5 per cent over the range of circular contact@ line contact with friction parallel to the short axis@ and line contact with friction parallel to the long axis. Results for elliptical contacts with any general direction of the force of friction may be expected to fall also within this range. The depths at which the maxima occur are@ however@ more sensitive to the axis ratio. The value of the coefficient of friction can have a major influence on the stress field@ but only if it is above 0.1??0.2.This means that many contacts of practical interest@ e.g. those lubricated by a boundary or elastohydrodynamic mechanism@ may be treated as normally loaded@ that is@ without tangential stresses. Many users of this Item will be concerned with the failure of materials. There are many modes of failure@ and the behaviour of materials approaching failure may be very complicated. For accurate and reliable prediction of failure@ a detailed model of the behaviour of the material is required together with a detailed knowledge of the variation of the individual stress components with space and with time. It is planned to issue a further Item covering the calculations of the individual stress components@ including the general elliptical contact with friction acting in any direction. In the present Item@ attention is concentrated on three simplified models of failure: Plastic yielding of ductile materials (Section 4) Cracking of brittle materials (Section 5) Fatigue failure under repeated stressing (Section 6) For each failure mode@ an appropriate failure criterion is defined according to the current state of knowledge@ and charts are provided from which the value of this criterion may be read. It is emphasised that this treatment is over-simplified@ and that very few materials behave exactly in the manner assumed@ but this simplification is acceptable in most cases. It is necessary to distinguish between materials with uniform properties@ that is@ those in which the critical value of the failure criterion is independent of the position@ and those with non-uniform properties. The best known example of a material with non-uniform properties is case-hardened steel@ in which the critical value of a failure criterion will depend on depth below the surface. For uniform materials@ only the overall maximum value of the failure criterion is of interest@ its position being of less consequence@ but for non-uniform material it is necessary to take into account the variation of the failure criterion with depth below the surface. Results covering these cases are presented separately in the various sections. Another vital distinction is between static stress fields@ in which the stress experienced by a given element of material remains constant in time@ and cyclic stress fields@ such as those in rolling contacts@ in which a given element of material is subjected to a range of stresses as it traverses the contact zone. The stresses often fall to zero as the material leaves the contact zone@ only to be re-applied at the next approach. In some cases the materials of one body may be stressed statically@ and that of the other cyclically. This distinction between static and cyclic loading is important mainly in connection with Section 4@ plastic yielding of ductile materials@ while Section 6@ fatigue failure@ is concerned wholly with cyclic stressing. The various calculation procedures appropriate in each of these individual cases are summarised for easy reference in Table 7.1. A list of the figures@ showing the ranges of the variables covered in each@ is given in Table 7.2."