A generalized Maugis-Dugdale solution for adhesion of power-law graded elastic materials. (September 2021) - Jin, Fan; Tang, Qiqin; Guo, Xu; Gao, Huajian
Abstract: The present paper provides a generalized Maugis-Dugdale analytical model of adhesive contact between an axisymmetric rigid punch of arbitrary shape and a graded elastic half-space with Young's modulus varying with depth according to a power-law. Based on the principle of superposition and an equivalent indentation method to solve an axisymmetric external crack problem, a series of closed-form solutions are derived for power-law punch profiles which reduce to the existing solutions for homogeneous isotropic materials and for paraboloidal geometries as special cases. A complete transition between the JKR and DMT type models is captured through a generalized Tabor parameter. Finite element analysis is performed to validate the obtained analytical solutions and examine the effect of interaction potential form on the pull-off force. Further important findings from this study include: (1) The pull-off force for non-paraboloidal punch profiles is found to be largely dependent on the form of the interaction potential, which is distinct from the familiar paraboloid case; (2) For the so-called Gibson solid, the independence of the pull-off force on the Tabor parameter is valid only for the paraboloidal punch profiles; (3) A three-dimensional adhesion map has been constructed to aid the appropriate choice of different contact models involving power-law graded elastic materials.