Formulation of a multi-scale discrete stochastic model of linear wear and pitting based on fracture mechanics: An example of wear results

A completely new stochastic multi-scale approach to modeling linear wear and pitting/micropitting processes has been developed. This approach is the extension of the approaches for modeling fatigue pitting and coating delamination and is also based on fracture mechanics and fatigue crack growth. As wear and pitting/micropitting have a stochastic nature, infinite systems of linear stochastic equations for the probabilities of a solid surface to be located at certain levels are derived. The equations of the systems involve the local rates of the damage probabilities produced by a cyclic loading acting on a solid surface located at one level on other levels located below. These damage probabilities are calculated based on a unified approach to the fatigue growth of small cracks present in the solid material using approximations of the crack stress intensity factors. The latter are related to the acting subsurface stress and the stress intensity factors obtained based on a regular perturbation method. A numerical example of model prediction of wear is presented.