A Numerical Contact Model Based on Real Surface Topography
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A numerical finite element contact model is developed to make use of the high precision surface topography data obtained at the nanoscale by atomic force microscopy or other imaging techniques 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 to contact in previous steps. Method accuracy 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 for the high precision models. Applicability of extrapolation from lower precision models is presented. The real contact area estimates for micrometer-size tribology test machine surfaces are calculated and convergence behavior with mesh refinement is investigated.
KeywordsContact mechanics Finite elements Boussinesq solution
We acknowledge Graham Wabiszewksi (University of Pennsylvania) for the MEMS surface images, the Microelectronics Development Laboratory at Sandia National Laboratories for the samples, Matthew A. Hamilton (Exactech, Inc), and W. Gregory Sawyer (University of Florida) for useful discussions. This work was partially supported by the National Science Foundation, grant CMMI 1200019, and by the US Department of Energy, BES-Materials Sciences, under Contract DE-FG02-02ER46016.
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