Receding Contact Problem of Multi-Layered Elastic Structures Involving Functionally Graded Materials

Jie Yan,Cong Wang

doi:10.3390/cryst12030354

Abstract

This paper studies a receding contact problem of a functionally graded layer laminate pressed against a functionally graded coated homogeneous half-plane substrate by a rigid flat indenter. The shear modulus of the functionally graded materials with a constant Poisson’s ratio is modeled by an exponential function which varies along the thickness direction. Both the governing equations and the boundary conditions of the receding contact problem are converted into a pair of singular integral equations using the Fourier integral transforms, which are numerically integrated by the Chebyshev–Gauss quadrature. The contact pressure and the contact size at both contact interfaces are eventually obtained iteratively, as developed from the steepest descent algorithm. Extensive parametric studies suggest that it is possible to regulate the contact pressure and contact size by constructing the top layer from a soft functionally graded material.

Highlights

Crystals 2022, 12, 354. https://For a multi-layered structure, according to the variation of the contact size between different layers under an external load, three contact types can be identified: advancing contact, if the contact size becomes larger; Stationary contact, if the contact size remains unchanged; and receding contact, if the contact size becomes smaller
Our simulation results show that the corresponding normalized receding contact half-length is 1.3243, which is almost identical to the results reported by the early literature [48,49]
The minimum stationary contact pressure and the maximum receding contact pressure are both negatively correlated with the indenter size

Summary

Introduction

Crystals 2022, 12, 354. https://For a multi-layered structure, according to the variation of the contact size between different layers under an external load, three contact types can be identified: advancing contact, if the contact size becomes larger; Stationary contact, if the contact size remains unchanged; and receding contact, if the contact size becomes smaller. Among these, receding contact has not been well studied, since it rarely occurs in a single-layer structure. For multi-layered structures, receding contact may give rise to several adverse effects, including layer peeling, delamination fracture, etc. A variety of methods have been adopted to study the receding contact problems of multi-layered homogeneous elastic structures. By using Fourier transform method, Comez et al [1] studied the receding contact problem of double elastic layers indented by a rigid cylindrical indenter. By using Fourier transform method, Adibelli et al [3] studied the receding contact problem between a coated layer and a half-plane loaded by a rigid cylindrical indenter. Yaylaci and Birinci [4] analyzed a double receding contact problem between two elastic layers and two elastic quarter-planes by using an integral transform technique, further verified by the finite element method [5]

Methods

Results

Conclusion