Multiple Inhomogeneous Inclusions and Cracks in a Half Space Under Elastohydrodynamic Lubrication Contact

Abstract

A semi-analytic solution is presented for multiple inhomogeneous inclusions and cracks in a half-space under elastohydrodynamic lubrication contact. In formulating the governing equations, each inhomogeneous inclusion embedded under the contacting surfaces is modeled as a homogeneous inclusion with initial eigenstrains plus unknown equivalent eigenstrains by employing Eshelby's equivalent inclusion method, while each crack of mixed modes I and II is treated as a distribution of climb and glide dislocations with unknown densities according to the dislocation distribution technique. Such a treatment converts the problem into a homogeneous lubricated contact with disturbed deformation due to the inclusions and cracks. The unknowns in the governing equations are integrated by a numerical algorithm and determined iteratively by utilizing a modified conjugate gradient method. The iterative process is performed until the convergence of the half-space surface displacements, which involve the displacements due to the inhomogeneous inclusions and cracks as well as the fluid pressure. Samples are presented to demonstrate the generality of the solution.