A Finite Element Study of an Elastic- Plastic Axisymmetric Sinusoidal Surface Asperity in Contact Against a Rigid Flat with Strain Hardening

Abstract

With the advancement in science and the introduction of new technology, computational modelling of contact between rough surfaces has attracted a great deal of attention. Researchers have developed many rough surface contact models to simulate the elastic-plastic contact of spheres. Most of the early models of rough surface contacts assumed a cylindrical or spherical/ellipsoidal shape for the asperities on the surface, Sinusoidal models have also been introduced but not widely use until recently. However, at initial contact the spherical and sinusoidal cases are very similar and can both be described by the classic elastic Hertz contact case. However, there does not appear to exist a closed-form analytical model for elastic- plastic three dimensional sinusoidal contact. Elastic-plastic sinusoidal contact has recently become more important with the development of several multiscale contact models. This work uses a finite element model (FEM) to characterize elastic-plastic sinusoidal contact as it is pressed against a rigid surface. It is theorized that the sinusoidal asperity gives a better prediction of asperity interaction, especially for heavy loaded contacts. The current model is designed in such a way that it’s axisymmetric and the interactions with the adjacent asperities are considered by the effect of periodicity at the base of the asperity. The material of the three dimensional axisymmetric sinusoidal surface is modelled as an elastic-plastic, nonlinear isotropic power law hardening solid. This work also characterizes the pressure required to cause complete contact between the surfaces. Complete contact is defined as when there is no gap between the two surfaces in contact. In the end, the FEM model is used to produce equations which can be employed to approximately relate the area of contact to the contact pressure for elastic-plastic strain hardening sinusoidal contact. It was found that with the increase in hardening exponent and tangent modulus more pressure is required for complete contact to occur. The results are also curve fitted to provide an expression for the contact area over a wide range of cases for use in engineering applications.