Analytical and numerical modeling of contact using atomic force microscopy images

Developments in techniques of surface imagery, like atomic force microscopy (AFM), permit detection of topography of surfaces at sub-nanometer precision. This opens doors to study the effects of topography on the contact of surfaces. In this thesis, two different approaches to model rough surface contact are explained. In the first part, a novel method is presented, which detects the multiscale features of the surface roughness with analysis of density, height, and curvature of summits on AFM images of actual silicon micro-electro-mechanical-system (MEMS) surfaces. The multiscale structure of roughness is then used in a contact model based on discrete hierarchical length scales and an elastic single asperity contact description. The contact behavior is shown to be independent of the scaling constant when asperity heights and radii are scaled correctly in the model. The real contact area estimate is discussed.;In the second part of the study, a numerical finite element contact model is developed to make use of the high precision surface topography data obtained while minimizing computational complexity. The model uses degrees of freedom that are normal to the surface, and uses the Boussinesq solution to relate the normal load to the long-range surface displacement response. The model for contact between two rough surfaces is developed in a step-by-step manner, taking into account the far-field effects of the loads developed at asperities that have come into contact in previous steps. Accuracy of the method is verified by comparison to simple test cases with well-defined analytical solutions. Agreement was found to be within 1% for a wide range of practical loads. Applicability of extrapolation from lower precision data is presented. The real contact area estimates for micrometer-size tribology test machine surfaces are calculated and convergence behavior with mesh refinement is investigated.