K.L. Johnson

Contact mechanics and the wear of metals

Abstract It is commonly observed that metallic wear debris takes the form of thin platelets, leading to the term ‘delamination wear’. Modelling this phenomenon has proved a stiff challenge in Contact Mechanics since the fractures which give rise to wear particles lie parallel, or nearly so, to the surface; i.e. on planes of maximum compressive stress. Sectioning the surface layer beneath a wear track has revealed it to have acquired severe plastic strains, which suggests that the cracks are ductile fractures, driven by plastic strain rather than elastic stress intensity. The paper reviews recent research into the progressive plastic deformation of surfaces in repeated sliding: the process known as ‘ratchetting’. Included is an analysis of ‘running-in’ of rough surfaces by repeated sliding and a discussion of the criterion of rupture under cyclic plastic strain.

The behaviour of transverse roughness in sliding elastohydrodynamically lubricated contacts

Recent calculations have shown that in a sliding elastohydrodynamically lubricated contact, any initial roughness largely disappears and is replaced by (often large) pressure variations. This paper gives an elementary analysis of the process for transverse roughness which provides the conditions under which it occurs, and allows the magnitude of the pressure ripples to be estimated. If the fluid is non-Newtonian, the behaviour will be very different.

Plastic flow and shakedown of the rail surface in repeated wheel-rail contact

Abstract Recent progress in modelling the near-surface plastic deformation caused by repeated wheel-rail contact is reported. A simple non-linear kinematic hardening law is described which is capable of predicting the response of rail steel to sliding contact loading. This hardening law is incorporated into a theory of elastic-plastic sliding contact. Particular attention is paid to the deformation at the surface caused by high tractive loads, since this appears to be the most common form of deformation leading to wear and fatigue of railway track. Shakedown limits are calculated for various combinations of contact loading relevant to railway practice, and an approximate technique is used to calculate the plastic flow that occurs when the shakedown limit is exceeded. The predictions of the theory are compared with experimental measurements of plastic flow in disks.

A surface roughness parameter in Hertz contact

Abstract The influence of surface roughness on the accuracy with which the Hertz theory of elastic contact predicts the contact pressure and contact area between a sphere and a plane is examined theoretically and experimentally. Statistical theories of surface contact suggest that the influence of surface roughness is governed primarily by a single non-dimensional parameter α defined by α ue5fc σR a 0 2 where σ is the combined roughness of the two surfaces, R is the radius of the sphere and a 0 is the contact radius for smooth surfaces given by the Hertz theory. Experimental measurements of contact area correlate well with this parameter. Provided that the value of α is less than about 0.05, errors in the application of the Hertz theory due to roughness of the surfaces are not likely to exceed about 7%.

The steady state sliding of rough surfaces

Abstract The changes in surface topography which take place when two rough surfaces of different hardnesses are in continuous sliding have been analysed. It is shown that the surfaces “shake down” to a steady state which is perfectly elastic only if the nominal contact pressure is below a critical limit. This shakedown limit is shown to be dependent upon the roughness characteristics of the hard surface, the hardness of the soft surface, the contact modulus and the coefficient of friction between them. Continuous sliding under conditions in which the shakedown limit is exceeded leads to the accumulation of plastic strain and hence to an increase in wear. Tests on a copper specimen in lubricated sliding contact with a hard steel surface of varying roughness showed that the wear rate decreased to a negligible value when the nominal pressure was reduced to values within the shakedown limit.

A model for the mild ratchetting wear of metals

Abstract A mechanism of metallic wear is proposed in which laminar wear debris is generated by a process of plastic ratchetting brought about by repeated pummelling of the softer wearing surface by the asperities on a harder mating surface. Wear rate is found to be approximately proportional to (load) 1.5 and an increasing function of a single non-dimensional parameter termed the plasticity index for repeated sliding which relates the roughness of the hard surface to the limiting elastic strain of the softer wearing surface. For small values of this parameter the wear rate becomes negligibly small and a shakedown state obtains in which the deformation of the surface is entirely elastic and ratchetting effectively stops. The hardness of the wearing surface and the coefficient of friction at the interface influence the wear rate through their influence on the value of the plasticity index.

The role of surface asperities in transmitting tangential forces between metals

Abstract When metallic bodies are placed in contact under normal and tangential forces, the material in the region of the contact surface is deformed. The object of this investigation was to compare the relative magnitudes of the deformation of the surface asperities with the deformation of the bulk of the bodies when tangential forces less than limiting friction are applied. The tangential compliance of bodies of different hardness and surface roughness was measured. Of the specimens examined, there was evidence of full plastic deformation of the asperities only on a soft, artificially rough, surface during the first application of the tangential force. Such deformation made only a small contribution to the total tangential compliance of the bodies. During subsequent applications of the tangential force, the asperities behaved entirely elastically and their deformations were then negligible. It is concluded that an elastic theory, ignoring surface roughness, can be used to predict accurately the behavior of typical engineering surfaces in contact under normal and tangential forces.

Plastic ratchetting as a mechanism of erosive wear

Abstract Many researchers have observed plate-like wear debris in tests on erosion of ductile metals at near normal impingement. We propose that this is due to ‘plastic ratchetting’ of a thin surface layer, which is progressively extruded out in the form of thin slivers which subsequently break off to provide wear debris. The process is driven by the repeated random impacts of the erodent. During the impact high contact stresses are generated. If these exceed the elastic limit then localised plastic flow takes place. As a result the material strain hardens and protective residual stresses are developed promoting shakedown, i.e. steady-state behaviour which is entirely elastic. However, if the impact stresses are high enough it is shown that shakedown is impossible and plastic ratchetting would be expected, i.e. small increments of plastic strain are accumulated leading to progressive extrusion of a thin layer of plastically deformed material. The proposed mechanism has been modelled by using the kinematical shakedown theorem of the theory of plasticity. A similar mechanism leading to wear has been shown to take place in lubricated sliding, where slivers of a softer surface are extruded by the pummelling action of the asperities on a harder counterface (A. Kapoor and K.L. Johnson, Proc. R. Soc. London, Ser. A, 445 (1994) 367–381).

A review of the theory of rolling contact stresses

Abstract Recent developments in the theory of rolling contact stresses are reviewed. They follow three main lines: 1. (1) elastic stresses due to slip and friction at the contact interface, 2. (2) pressures developed in elasto-hydrodynamic lubricating films and 3. (3) the influence of inelastic (visco-elastic or plastic) behaviour of the material of the rolling solids. The theory of dry rolling contact of elastic solids is now at an advanced state of development. Studies of lubricated rolling and inelastic deformation are restricted to the two-dimensional problems of rolling cylinders. It has been possible however to put forward a tentative theoretical load-carrying capacity for lubricated metal rollers, above which continuous permanent deformation will take place. It is suggested that the strength of actual rolling surfaces falls below the theoretical limit due to non-homogeneity of the material and the roughness of the surfaces. These effects are at present beyond the scope of theory but would well repay study.

Surface corrugations spontaneously generated in a rolling contact disc machine

Abstract A flexibly mounted disc machine has been developed which permits the vibrations excited by rolling contact to be studied in isolation from their surroundings. The principal mode of vibration is a “contact resonance” in which the discs oscillate on the “spring” provided by their elasticity in the vicinity of their point of contact. Vibration in this mode has been observed to lead to the spontaneous generation of corrugations on the surface of the softer disc in two different circumstances : 1. (a) Brass discs, dry or lubricated, progressively developed corrugations by plastic deformation. 2. (b) Duralumin discs, carefully degreased, developed corrugations by ‘stick-slip’ wear when sliding accompanied rolling.