The effect of edge compliance on the adhesive contact between a spherical indenter and a quarter-space. (February 2019) - Stan, Gheorghe
Highlights: A boundary element method was developed to examine the frictionless, adhesive contact between a rigid spherical indenter and an elastic quarter-space. The adhesive coupling was modeled as a Maugis interaction with continuous transition between the DMT and JKR adhesive limits. The model provides solutions for the load dependencies of the indentation depth and contact stiffness for various values of the adhesion parameter and position from the edge of the quarter-space. The developed methodology can be used for contact mechanics analysis on a sample with edge geometries to correctly separate the material and geometrical contributions to the measured indentation response of the sample. Abstract: In this work, the effect of the edge compliance on the adhesive, frictionless contacts near the edge of a quarter-space is analyzed in terms of stress, deformation, and contact stiffness. The study relies on the numerical implementation of the conjugate gradient method (CGM) to adhesive contacts near the edge of a quarter-space. It extends the previous CGM developed for contact analysis of non-adhesive and adhesive contacts on half-space to the matrix formulation of the quarter-space problem. The considered adhesive contact interaction is in terms of the Maugis–Dugdale model to provide insight into the transitional behavior from non-adhesive to various type of contact adhesive regimes. It is found that the edge compliance affects the contact mechanics of adhesive contacts as a function of position, applied force, and adhesive parameter. The analysis provides calculations for quantities like depth indentation and contact stiffness that can be found directly in indentation-type experiments performed on samples with edge geometries. Such understanding and characterization of edge contacts can be used to unambiguously account for the mechanical response of nanoscale structures near their edges and detect possible mechanical variability introduced by fabrication and processing. Graphical abstract: