Previous delamination mechanism maps for coatings/substrates system cannot predict the critical conditions for de lamination nucleation under adhesive contact loads, because the effects of surface adhesion on delamination are not considered. In this paper, the finite element simulation of a rigid sphere in adhesive contact with an elastic coating on an elastic-plastic substrate is undertaken to clarify interface crack initiation and growth, in which the surface adhesion of the indenter/coating contact system is modeled by nonlinear spring elements with a force-displacement relationship derived from a Lennard-Jones potential, and the coating/substrate interface is represented by an irreversible cohesive zone law. By conducting parametric studies, delamination mechanism maps considering surface adhesion are constructed. It is found that increasing the adhesion work will initiate delamination nucleation, and the critical indentation depth increases with increasing the interfacial cohesive energy in the presence of the surface adhesion. For relatively stronger adhesion, the higher the coating elastic modulus or the coating thickness is, the greater the critical indentation depth becomes. However, for relatively weaker adhesion, increasing the coating elastic modulus will decrease the critical indentation depth, and increasing the coating thickness will increase the critical indentation depth for lower indentation depths, but an opposite trend occurs for higher indentation depths. (C) 2017 Elsevier B.V. All rights reserved.