Elastohydrodynamic lubrication modeling for materials with multiple cracks

This paper presents a semi-analytic solution for multiple cracks beneath a half-space surface under elastohydrodynamic lubrication (EHL) contact. The solution not only takes into account the fluid-structure interactions in the EHL contact but also the interactions among all the cracks. In developing the governing equation, each crack of mixed modes I and II is modeled as a continuous distribution of climb and glide dislocations with unknown densities. With such a treatment, the original problem for materials with multiple cracks is converted into two subproblems: a homogeneous EHL contact problem with the fluid pressure distribution and the lubricant film thickness to be determined, and a half-space problem with unknown dislocation densities, which are iteratively obtained by a modified conjugate gradient method. A numerical algorithm is developed to integrate the two problems. The computational process is performed until the convergence of the displacements, which are the sum of the displacements due to the fluid pressure and the subsurface cracks. Sample cases are presented to analyze the pressure and lubricant film thickness profiles of EHL contact and the subsurface stresses for cracked materials.