Analysis of Contact Mechanics for Flat Stamps on Graded Coatings Using Shifted Legendre Polynomials of the First Kind.

Abstract

This study investigates the contact mechanics of graded coatings, focusing specifically on the early fracture behavior of these materials under rigid flat stamp sliding contact loading. The problem is formulated as a weakly singular Fredholm integral equation of the second kind, in this paper we will utilize shifted Legendre polynomials of the first kind in a matrix-vector format to approximate this integral. The singularity in the kernel is addressed analytically to facilitate the analysis [1].The primary objective of this research is to derive analytical benchmark solutions that allow us to explore the influence of numerous factors, such as material inhomogeneity constants, the coefficient of friction, and characteristic length parameters, on the critical stresses that may impact the fatigue and fracture behavior of the coatings so The branch on integral equations is one of the most important bases for addressing initial, boundary, and mixed value problems. This is because it may convert any of these problems into a boundary integral equation