Adhesive contact on power-law graded elastic solids: The JKR-DMT transition using a double-Hertz model

A cohesive zone model of axisymmetric adhesive contact between a rigid sphere and a power-law graded elastic half-space is established by extending the double-Hertz model of Greenwood and Johnson (1998). Closed-form solutions are obtained analytically for the surface stress, deformation fields and equilibrium relations among applied load, indentation depth, inner and outer radii of the cohesive zone, which include the corresponding solutions for homogeneous isotropic materials and the Gibson solid as special cases. These solutions provide a continuous transition between JKR and DMT type contact models through a generalized Tabor parameter mu. Our analysis reveals that the magnitude of the pull-off force ranges from (3 + k)pi R Delta gamma/2 to 2 pi R Delta gamma, where k, R and Delta gamma denote the gradient exponent of the elastic modulus for the half-space, the radius of the sphere and the work of adhesion, respectively. Interestingly, the pull-off force for the Gibson solid is found to be identically equal to 2 pi R Delta gamma, independent of the corresponding Tabor parameter. The obtained analytical solutions are validated with finite element simulations. (C) 2013 Elsevier Ltd. All rights reserved.