Contact and Adhesion Analysis Considering a Variation of Surface Stresses

1st Report, A Comparison of Fundamental Theory and Hertz Theory

Abstract

The adhesion contact analysis using the theory of elasticity is presented in the paper. The boundary condition considering the surface stresses, which are originated from surface energy, was employed for the surfaces of indenter and substrate. Furthermore, it was supposed the surface stresses in an adhesion region are different from that in non-adhesion region and are reduced from the original surface stresses. In the present analysis, a paraboloidal indenter is pressed into the substrate and adhesion occurs between two surfaces of the indenter and the substrate. The surfaces at the adhesion regions of the indenter and the substrate deformed inward due to the variation of the surface stresses. This means that the attractive force between the adhesion region occurs for maintaining the contact of the regions and the pall-off force of the indenter from the substrate is needed. The distribution of contact pressure, the surface profile of adhesion region and adhesive force between the indenter and the substrate were precisely examined. The results in the analysis were compared with those in the Hertz theory. The total force between the indenter and the substrate was about the value of 0.04 to 0.06 reduced from the dimensionless contact load based on Hertz theory.