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Abstract: 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. [Copyright &y& Elsevier]

A theoretical model of a power-law graded elastic half-space in contact with a randomly rough rigid surface is established by combining the Greenwood–Williamson rough contact model and the JKR type adhesion model for power-law graded materials. The rough surface is modeled as an ensemble of non-interacting asperities with identical radius of curvature and Gaussian distributed heights. By applying the JKR type theory for power-law graded solids to each individual asperity of the rough surface, the total normal forces for the rough surface are derived for loading and unloading stages, respectively, and a prominent adhesion hysteresis associated with dissipation energy is revealed. Our results include the solutions for homogeneous materials and Gibson solids as special cases and describe the complete transition between these two limiting situations. A dimensionless adhesion parameter, which influences both the total pull-off force and the energy dissipation due to adhesive hysteresis, is also identified. It is found that a small adhesion parameter results in higher energy dissipation and pull-off force, while a large adhesion parameter leads to lower energy dissipation and pull-off force. [ABSTRACT FROM AUTHOR]