Mechanical and Civil Engineering Seminar

The multiscale features of rough surfaces lead to approximately linear relations between macroscale physical quantities, such as normal force, electrical contact conductance, friction force, etc., even when the microscale relations between these quantities are highly non-linear. Surfaces are often found to be quasi-fractal at fine scales, in which case the resulting contact problem is best approached by considering the incremental change in the statistical distribution of (for example) contact pressure when the high frequency cutoff is slightly extended, and then us- ing inductive arguments. The parameters of macroscale phenomena are generally determined by deviations from fractality, or by the occurrence of a length scale in the governing physical laws such as the constitutive equation. Some important quantities, including incremental stiffness and electrical contact resistance, are de- termined by the coarse scale roll-off of the power spectral density, and rigorous bounds can then be established using relatively unsophisticated numerical models. By contrast, although multiscale arguments provide a plausible explanation of Coulomb s law of friction, the friction coefficient is determined at the fine scale and is therefore difficult to predict.

If two conforming bodies are in nominally static contact but subjected to vi- bration, microslip will occur between some of the contacting asperities, leading to fretting fatigue and hysteretic damping. The energy dissipation per unit nom- inal area can be related to the tangential contact stiffness, using an extension of a general result for elastic contact problems due to Ciavarella and Ja¨ger. Since this stiffness is determined at the coarse scale, it proves unecessary to investigate the morphology of the fine scale microslip process. A general sinusoidal loading cycle shows that energy dissipation (and hence potential fretting damage) is sig- nificantly higher when the oscillations in normal and tangential forces are out of phase with each other.