A multi-scale discrete stochastic model of linear wear and pitting based on fracture mechanics: Parametric model analysis—Wear and pitting for the case of highly compressive residual stresses

An innovative stochastic multi-scale approach to modeling of 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 ordinary differential equations for the probabilities of the solid surface to be located at certain levels are derived. The equations of the systems involve the rates of the damage probabilities produced by a cyclic loading acting on the solid surface located at one level on other levels located below. These damage probabilities are calculated based on the unified approach to 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 created by these stresses at the tips of small cracks. The model has been analyzed theoretically through theorems as well as extensively numerically. A multitude of numerical results is presented.