On the two-dimensional solution of both adhesive and non-adhesive contact problems involving functionally graded materials

Abstract

This paper presents a semi-analytical algorithm for the determination of the contact half width and surface pressure which results from both adhesive and non-adhesive contact problems involving functionally graded materials (FGM). The inhomogeneously elastic solid comprises a graded elastic coating whose shear modulus depends exponentially on the vertical coordinate and a homogeneously elastic substrate. The solid is assumed to be in a state of plane strain and thus a two-dimensional analysis is performed within this work.Using the work of Chidlow et al. (2011a) as a starting point, we derive a pair of integral equations which may be used to determine approximations to the contact pressure when either the surface deflection or the deflection gradient is known over the contact region. As these integral equations are non-singular, we use Galerkin's method to approximate the contact pressure and it is found that relatively small trial spaces allow accurate computation of the pressure. Information about the prescribed load is then used to formulate an iterative algorithm to determine the contact half width. A selection of numerical results are presented using this method and it is found that the solutions computed here compare favourably with those of other authors. A further investigation is then conducted into the solution of adhesive contact problems using the assumptions of Maugis (1992) and Johnson and Greenwood (2008) to inform the nature of the adhesive stresses outside of the contact. It is found that both JKR-like and DMT-like behaviour can be observed in contact problems involving FGMs.

Modelling adhesive contact problems involving a layered elastic solid and cylindrical indenter using Lennard Jones potential

“…The converse is true for the soft coating as an increase in coating thickness here leads to an decrease in the applied maximum pressure and an increase in the maximum surface deflection. These trends are in accord with the observations of Chidlow et al [31]. The sub-surface stress fields given in figure 9 correspond to the pressure curves presented in figures 8c and 8d.…”

“…Johnson and Sridhar [30] also presented an adhesive model, based on the original JKR model, for a layered solid with a homogeneous elastic coating. Lately, Chidlow et al [31] investigated the e↵ects of surface adhesion between a rigid cylindrical indenter and a layered solid when in contact using Maugis's Dugdale model.…”

A Semi-Analytical Solution Method for the Adhesive Contact Between a Rigid Punch and Multi-Layered Functionally Graded Material

“…It is observed that as the ratio h 1 /a h increases, the predicted contact half-width for the hard coating decreases yet the maximum pressure in the contact increases whilst the converse is true for a soft coating. This is an observation that has been made by other authors (e.g Teodorescu et al [5], Chidlow et al [6] and indicates that softer coatings are less likely to fail under pressure than harder coatings.…”

“…The reader is referred to Chidlow et al [6] for the definition of the matrices appearing above and the remaining constants within the transition layer and substrate. We note however that the constants P n , n ∈ N are the coefficients in the Fourier series representation of the pressure and are defined as…”

Analysing the effects of sliding, adhesive contact on the deformation and stresses induced within a multi-layered elastic solid

“…Sergici et al [19] applied a Maugis type adhesive model to investigate the contact between a spherical indenter and an elastic layered solid. More recently, Chidlow et al [20] and Chong and Chidlow [21] introduced surface adhesion via the Dugdale and Lennard-Jones potential respectively to simulate a rigid cylindrical geometry indenting a graded elastic layered solid comprising a FGM perfectly bonded to a homogeneous substrate.…”