Surface effect in nanoscale adhesive contact

Using the well-known Lennard-Jones potential and a recently proposed surface energy density-based elastic theory, we analyze the adhesive contact behavior between a rigid spherical nano-indenter and an elastic half-space in this paper. With the help of Newton's method of iterations and arc-length continuation algorithm, both contact pressure and normal displacement at the indented surface are obtained numerically, based on which the load-approach curves are further achieved. It is found that the surface effect could be characterized by only one intrinsic length, i.e., the ratio of bulk surface energy density to shear modulus of the indented material. Comparison of the results with or without surface effect shows that the surface effect leads to a smaller pull-off force. Moreover, for the case of a zero-external loading, the corresponding approaches become smaller than the classical predictions, which qualitatively agree with the existing experimental findings. This indicates the elastic substrate becomes hardened due to the surface effect. All the study should have contributions to the deep understanding of surface effect on nanoscale adhesive contact behaviors.