Loading–unloading contact analysis of a fractal rough surface with functional gradation

Abstract

The present paper deals with a finite-element-based static loading–unloading analysis of a functionally graded rough surface contact with fractal characteristics. Two different gradation models, namely elastic and plastic gradations, are adopted. In these models, one out of yield strength and Young's modulus is varied spatially according to exponential functions, while the other is kept constant. In both these material models, separate inhomogeneity parameters control the variation of material properties. The gradation is such that throughout the top of the rough surface properties remain constant with variations in the depth direction being controlled by the above-mentioned parameters. Different fractal surfaces with different levels of roughness (governed by the values of fractal dimension and fractal roughness) have been analysed. The influence of the gradation parameters on the contact properties, viz. contact force, contact area, contact stress, etc., are investigated for both loading and unloading phases. It was found that for most of the loading phase, higher elastic, as well as plastic gradation parameter, causes higher contact force and contact area. However, in the case of the unloading of elastically graded surfaces, this trend is not maintained throughout. For the cases, where a substantial amount of yielding takes place during loading near the contact surface, the resulting contact area is found to be higher for the unloading phase in comparison with the same during the loading phase. The trend of plastic yielding at the vicinity of the contact surface is studied for varying gradation parameters. It is observed that the higher volume of yielded material is obtained for the higher value of elastic gradation parameter. On the other hand, the higher value of plastic gradation parameter causes more yielding to take place at the vicinity of the contact surface. Additionally, the effect of gradation on the energy dissipation due to plasticity after complete unloading is explored in detail.