Mechanics of axisymmetric adhesive contact of rough surfaces involving power-law graded materials

In the present paper, the mechanics of axisymmetric adhesive contact of rough surfaces involving power-law graded materials is investigated analytically. A series of general analytical solutions have been obtained with use of the cumulative superposition and equivalent energy release rate approaches. These solutions provide closed-form expressions of equilibrium relations among applied load, indentation depth and contact radius. Based on these solutions, an effective macroscopic description of the contact evolution is obtained for a general punch profile with surface roughness. Our analysis results reveal that the simultaneous presence of surface roughness and graded material properties can influence the pull-off force and energy dissipation due to adhesion hysteresis significantly. Moreover, it is found that both the adhesion strength and toughness can be optimized by adjusting the surface topography and material parameters of power-law graded solids appropriately. The analytical results obtained in this paper include the corresponding solutions for homogeneous isotropic materials as special cases and therefore can also serve as the benchmarks for checking the validity of numerical solution results.