Wear 258 (2005) 924–934 A method for calculating boundary friction and wear A.A. Torrance ∗ Department of Mechanical and Manufacturing Engineering, Trinity College, Dublin 2, Ireland Received 25 June 2004; received in revised form 9 August 2004; accepted 23 September 2004 Available online 2 December 2004 Abstract Starting from a rigid-plastic model of asperity sliding, a finite element model of elastoplastic asperity sliding is developed. Its results are encapsulated in closed form correlations with non-dimensional groups selected on the basis of the rigid-plastic solution. This permits friction and wear coefficients to be predicted for some simple sliding contacts using techniques of surface characterisation previously used successfully to predict friction. The predictions compare well with experimental measurements, and illustrate the relative importance of different parameters, surface texture, mechanical properties, and the nature of the third body, on the friction and wear of the contact. An easy to use software package allows the model to be applied to a wide range of contacts to estimate the influence of different parameters on their friction and wear. © 2004 Elsevier B.V. All rights reserved. Keywords: Boundary lubrication; Wear; Surface texture; Third body; Modelling 1. Introduction In engineering design, it is customary to use the wear equation proposed by Archard [1] to calculate the volume of material V removed when a surface of hardness H v slides a distance S under a load F n : V = KF n S 3H v (1) The attractive simplicity of this equation conceals the prob- lems of its practical application, for the coefficient K is found to depend on a whole range of different factors, which can cause it to vary over several orders of magnitude for a given set of materials and lubricants. In order to predict with any precision the influence of con- tact conditions upon K, it is first necessary to have a satisfac- tory model of the mechanics of wear. One possibility, which has been suggested by several workers [2–10], is to calculate the surface plastic strain produced by asperity interaction, then to use a damage rule to relate it to the wear rate. This requires a model which predicts the extent and rate of strain ∗ Tel.: +353 1 6081729; fax: +353 1 6795554. E-mail address: atorrnce@tcd.ie. due to sliding, and the amount of strain needed to produce wear particles. The starting point of such a model must be an idealisation of asperity contacts which allows the calcula- tion, from the rheology of the interface and the mechanical properties of the wearing surface, of the strains imposed by an asperity sliding across it. This must be combined with a damage rule, so that the rate of d´ ebris generation can be found. Finally, a way of characterising surface texture must be found which allows the result for a single asperity to be extended to a real surface. A first attempt at such a synthesis was made over ten years ago [2], in which strain was predicted with a rigid-plastic asperity deformation model, originally developed by Green [11] and Challen and Oxley [12]. A simple, constant shear stress rheology was used to model the interface, and the ef- fect of the surface texture of the wearing surfaces was in- corporated using slope statistics, unambiguously determined from a physically significant bandwidth of the surface profile [13]. Agreement of the predictions with experimental results was satisfactory. However, the damage rules used were spec- ulative, and have since been shown to be incorrect [8,14]. Moreover, it has become clear that a rigid-plastic model of asperity interaction severely overestimates surface strains for most practical engineering surfaces, and that an elastoplastic 0043-1648/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2004.09.074