S.J. Chidlow

A New Solution Method for the Contact Mechanics of Graded Coatings

This paper attempts to solve analytically for the stresses present in a graded elastic solid resulting from pressure applied to its surface by computing the Airy stress function. The horizontal dimensions of the solid are assumed finite and hence we form the solution of the stress function as a Fourier series rather than an inverse Fourier transform. Finally, a selection of contour plots is presented to exhibit the behavior of this new model.Copyright

Determining the Sub-Surface Stresses in a Graded-Elastic Solid Using Fourier Series Decomposition

This paper describes a fully analytic solution method for the displacements and sub-surface stresses within a graded elastic layered solid. This method can be utilised to predict the local deformation of nano or micro-scale depositions under contacting conditions. The solid consists of two distinct layers which are considered to be perfectly bonded and comprise of a graded elastic coating whose shear modulus varies exponentially with the depth coordinate and an infinitely deep homogeneously elastic substrate. The solution given in this paper is generic and easily utilised to solve real problems as it requires only known physical characteristics of the solid under study and an applied surface pressure. As a result, this model is very cheap to use and can be easily integrated into tribological codes to predict local deflections.Copyright

Semi-Analytic Iterative Solution for the Adhesive Contact Between a Micro-Indenter and a Graded Elasticity Coating

This paper proposes a hybrid (semi-analytic) solution for determining the contact footprint and subsurface stress field in a two-dimensional adhesive problem involving a multi-layered elastic solid loaded normally by a rigid indenter. The subsurface stress field is determined using a semi-analytic solution and the footprint using a fast converging iterative algorithm. The solid to be indented consists of a graded elasticity coating with exponential increase of decay of its shear modulus bonded on a homogeneously elastic substrate. By applying the Fourier Transform to the governing boundary value problem, we formulate expressions for the stresses and displacements induced by the application of line forces acting both normally and tangentially at the origin. The superposition principle is then used to generalize these expressions to the case of distributed normal pressure acting on the solid surface. A pair of coupled integral equations are further derived for the parabolic stamp problem which are easily solved using collocation methods.Copyright

Computing the Stresses Induced Within Multi-Layered Elastic Media That Result From Sliding Contact With a Rigid Punch

This paper is concerned with the solution of the contact problem that results when a rigid punch is pressed into the surface of an inhomogeneously elastic solid comprising three distinct layers. The upper and lower layers of the solid are assumed to be homogeneous and are joined together by a functionally graded interlayer whose material properties progressively change from those of the coating to those of the substrate.By applying the Fourier transform to the governing boundary value problem (BVP), we may write the stresses and displacements within the solid in terms of indefinite integrals. In particular, the expressions for the horizontal and vertical displacements of the solid surface are used to formulate a coupled pair of integral equations which may be solved numerically to approximate the solution of the stamp problem. A selection of numerical results are then presented which illustrate the effects of friction on the contact problem and it is found that the presence of friction within the contact increases the magnitude of the maximum principal stress and changes its location. These observations indicate that material failure is much more likely to occur when friction is present within the contact as expected.Copyright

A Fast-Solving Semi-Analytical Solution Method for Contact Problems Involving Multi-Layered Inhomogeneously Elastic Solids

This work is concerned with the derivation of an iterative solver which allows the accurate estimation of both the contact half-width and contact pressure when an inhomogeneouly elastic solid comprising a homogeneous coating and substrate joined by a graded layer is indented by a rigid punch. A selection of numerical results are then presented illustrating the accuracy of this model.Copyright

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

The current paper proposes a semi-analytical solution method which predicts both the sub-surface stress fields and pressures that result from adhesive contact between a multi-layered functionally graded material (FGM) and a rigid punch. The FGM is deemed to consist of a homogeneously elastic coating and substrate joined together by a transition layer whose shear modulus depends on the depth coordinate in some predetermined way. It is further assumed that the FGM is in a state of plane strain so that we may perform a two-dimensional analysis.We present analytical solutions for the horizontal and vertical displacements within the solid which hold when the applied surface pressure is known and then discuss how we may use these solutions to solve the contact problem. A selection of numerical results are then presented using this model and it is found that the algorithm proposed in this work is both accurate and computationally cheap to use.Copyright

Adhesive contacts for graded-elastic coatings using fourier series decomposition

We propose a semi-analytic solution technique to determine the subsurface stresses and local deflections resulting in an adhesive contact of graded elastic layers. Identical pressure distributions, typical for a Maugis parameter λ = 1, were applied to a range of graded elastic coatings. The principal stresses and surface deflection in both regions (graded elastic layer and substrate) are computed in terms of Fourier series. This control case has the advantage that the response of different coatings can be easily monitored and compared.Copyright