A probabilistic wear model for brittle materials based on micro contact

A theory for the wear of brittle materials is presented. It follows the Greenwood Williamson model of the elastic contact between two rough surfaces. The asperities constituting the roughness are assumed to have spherical shape of radius R{dollar}sb{lcub}rm S{rcub}{dollar} at their summits; the center of curvature is assumed not to be displaced by the normal forces of contact, but the spheres are elastically deformed according to the Hertzian theory. The heights of the asperity summits are distributed according to a statistical distribution, which is taken to be Gaussian in the numerical computation. The Greenwood Williamson model calculates the total real contact area between the surfaces and the total normal contact force as a function of the separation of the surfaces. The wear theory formulates a criterion for the removal, by fracture of an asperity that makes contact with the opposite surface: fracture is assumed to occur when the elastic deformation of the asperity, caused by the opposite surface, reaches a critical value. A crack that is parallel to the surface then develops, producing a wear particle. Incorporating this model into the statistical contact model of Greenwood and Williamson produces a prediction of the expectation value of the total volume of material removed by wear as a function of the roughness parameters of the surface, the contact pressure and materials properties such as Young's modulus and the fracture toughness. The predictions of the theory agree reasonably well with the results of measurements of the wear rate of several ceramics rubbing against a surface presenting a controlled and constant roughness (a metal wheel with diamond grit) by Lancaster. The theory is also used to predict the dependence of ceramic wear on the contact load. It predicts that the wear volume increases linearly with the contact load when the friction is high, the surface is rough and the material is brittle; the wear volume increases with a higher power of the load when the friction is lower, the surfaces are smooth and/or the material is relatively tough. The linear wear case also corresponds to higher wear rates than the superlinear. These findings are qualitatively confirmed by observations of ceramic wear: the wear of silicon nitride is relatively rapid and increases linearly with load, the wear of alumina and zirconia is much milder and increases with a higher power of load. The present wear theory offers the first rational explanation of these observations.