Critical analysis of randomly rough surfaces for contact mechanics through statistical simulation

Abstract

Surface roughness is a fundamental aspect of fracture, fatigue and wear. The complexity of a fracture surface affects the energy for crack propagation and strongly influences crack closure during fatigue. It defines contact stiffness and plays a dominant role in friction and wear. The micromechanical processes which produce the small-scale surface topography are so complex that it is often reasonable to model roughness as random processes which may be stationary or non-stationary (fractal). This work briefly summarises some methods used for the simulation of randomly rough surfaces and their characterisation. Their numerical efficiency allows for large-scale statistical simulation of contact behaviour, which was analysed through a generalised version of the classical Greenwood-Williamson model. Proper use of statistical techniques, such as analysis of variance and response surface analysis, allows to reduce the amount of simulations required to determine the effects of the model parameters. An increase of RMS-roughness and fractal dimension, as well as a reduction of yield strength, reduce contact stiffness. This can be expected from the mathematics and physics of the problem. An increase in the size of the model does not reduce the statistical spread of the results, as can be expected for non-stationary random processes. This means that very large models are not required in advanced numerical simulation. Less promising is the observation that an increase in model size produces a higher contact stiffness. This observation is due to an oversimplification in the Greenwood-Williamson model, as will be illustrated by the results of finite element simulations.