Modeling cracks and inclusions near surfaces under contact loading

• Solution for cracks and inclusions near surface under contact loading.
• Interactions among all the cracks and inclusions.
• Interactions between subsurface micro-defects and surface loading body.
• Accurate description of surface pressure and subsurface stress field.

In this work, a semi-analytic solution is developed for multiple cracks and inhomogeneous inclusions of arbitrary shape beneath a half-space surface subject to contact loading. The contacting surfaces can have roughness. The solution takes into account the interactions among all the inclusions and cracks as well as the interactions between them and the surface loading body. Thus, it is capable of providing an accurate description of the surface contact area and pressure and the subsurface stress field. In developing the solution, each inhomogeneous inclusion is modeled as an homogeneous inclusion with initial eigenstrain plus unknown equivalent eigenstrain using Eshelby’s equivalent inclusion method; each crack of mixed modes I and II is modeled as a distribution of glide and climb dislocations with unknown densities. As a result, the inhomogeneous half-space contact problem is converted into a homogenous half-space contact problem with unknown surface contact area and pressure distribution. All the unknowns are integrated by a numerical algorithm and then determined iteratively by using the conjugate gradient method. Computational efficiency is achieved by using the fast Fourier transform algorithm. The solution is general and robust and will potentially have wide applications for reliability analysis of heterogeneous materials, in particular their wear and contact fatigue analysis.