Two-dimensional adhesion mechanics of a graded coated substrate under a rigid cylindrical punch based on a PWEML model

The paper aims at the contact mechanics of functionally graded coated substrate by taking into the adhesion effect. The coating-substrate structure is indented by a cylindrical punch to form a contact region where the adhesion forces are described by using the Maugis adhesion model. A piece-wise exponential multi-layered (PWEML) model is used to simulate the functionally graded materials with arbitrary spatial variation of material properties. This model divided the functionally graded coating into several sub-layers in which the elastic parameter varies as exponential form. Using the Fourier transform technique and the Transfer matrix method, the boundary value problem for adhesive contact of graded coated substrate is reduced to the singular integral equation. Some numerical results are presented to analyze the influence of gradient index on the pull-out force, contact stresses and adhesion region. The results can be applied to improve the performance of the coating by adjusting the gradient index.