Elastic and elastic-perfectly plastic analysis of an axisymmetric sinusoidal surface asperity contact

Abstract

Closed-form finite-element empirical models are available for elastic and elastic–plastic spherical and sinusoidal contact. However, some of these models do not consider the effect of interaction with adjacent asperities or require extensive numerical resources because they employ a full 3-D model. Therefore this work has analysed and quantified the behaviour of an elastic and elastic- perfectly plastic axisymmetric sinusoidal surface in contact with a rigid flat for a wide range of material properties and different values of the amplitude to wavelength ratio from initial to complete contact (high load). The numerical results agreed well with the Hertz model and the Jackson–Green elastic–plastic spherical contact model at low loads. Empirical equations for elastic and also elastic-perfectly plastic cases are formulated for the contact pressure, contact area and surface separation. From the current analysis, it is found that it is not any single parameter, but different combinations of material properties and surface roughness that govern the whole contact behaviour. The critical value of the amplitude of the sinusoidal asperity below which it will deform completely elastically from initial to complete contact is established. At low values of amplitude normalized by the critical amplitude, it was found that the contact behaved similar to a spherical contact, with the average pressure (hardness) always remaining lower than three times the yield strength. However, at higher values the average pressure increased toward a value as high as six times the yield strength at complete contact. All of these equations should be useful in rough surface contact modelling, lubrication analysis, electrical contact modelling and in many other applications.