Sliding contact problems involving inhomogeneous materials comprising a coating-transition layer-substrate and a rigid punch

This paper proposes a semi-analytical model for the two-dimensional contact problem involving a multi-layered elastic solid loaded normally and tangentially by a rigid punch. The solid is comprised of a homogeneous coating and substrate joined together by a graded elastic transition layer whose material properties exhibit an exponential dependence on the vertical coordinate. By applying the Fourier transform to the governing boundary value problem, we formulate analytic 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 generalise these expressions to the case of distributed normal and tangential tractions 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. The primary aim of this paper is to provide insight into the likely behaviour of graded materials under the combined effects of surface pressure and shear stress. In this study, the assumption of Coulomb friction is invoked and the effects of material gradation, coating/interlayer thickness and friction coefficient upon the contact footprint and sub-surface stress field are investigated in great detail. The results we obtain suggest that the thickness of the transition layer as well as the combined thickness of the coating and transition layer have a significant effect on the maximum sub-surface stress attained through contact. This indicates that small changes in the composition of the coating can lead to significant differences in material behaviour. We additionally find that an increase in the amount of friction present in the contact can cause dramatic changes in the pattern of the stress field and can give rise to a much larger maximum stress. This effect can be offset somewhat under certain conditions by changing the thickness of the transition layer. To the best of the authors belief, this work represents the first attempt made to characterise the effects of friction on the sub-surface stress field within a graded elastic material

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

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

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

This paper presents a mathematical model of sliding, adhering contact between a rigid parabolic indenter and a multi-layered elastic solid, which is assumed to comprise of a homogeneous coating bonded through a functionally-graded transitional layer to a homogeneous substrate. The adhesive forces in this investigation are modelled using Lennard-Jones potential and an iterative algorithm is proposed that solves for the contact pressure, surface displacement and sub-surface stresses resultant within the layered solid. The effects of surface adhesion and different material properties such as varying coating/transition layer thickness and coating hardness on the solution of the contact problem are subsequently investigated in detail. The numerical approach presented in this paper demonstrates the significance of having a suitable mathematical representation for the traction distribution along the sliding, adhering contact. It is found that under weakly adhering conditions, the assumption of only Coulombic traction suffices to determine the displacements and subsurface stresses within the multi-layered solid. However, it is noted that stress concentrations within the material begin to propagate through all three layers of the elastic solid with increased surface adhesion, which could potentially induce plasticity and lead to material ploughing under sliding. The proposed model allows us to further investigate and improve our understanding of the combined effects of traction and boundary adhesion in sliding contacts, which can be used to inform the design of materials needed in such conditions

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

This paper presents an iterative algorithm that solves for the displacement and sub-surface stresses induced within a layered elastic solid adhering to a rigid cylindrical indenter under lightly loaded conditions. The solid is assumed to comprise a functionally graded coating of finite thickness bonded to a homogeneous substrate of infinite extent and is assumed to be in a state of plane strain which allows a two-dimensional analysis to be performed. The Lennard–Jones potential is used to model the adhesive force acting between the indenter and solid whilst the effects of surface adhesion are characterised using Tabor’s parameter. A selection of numerical results for the adhesive contact problem are presented which indicate that the maximum pressure and induced sub-surface stresses increase dramatically as Tabor’s parameter increases. It is also found that the shear modulus and thickness of the coating have a significant effect on material behaviour with harder coatings experiencing significantly larger tensile stresses but smaller surface displacement than softer coatings. The present investigation allows us to deduce that at smaller scales, surface adhesion can be instrumental in causing wear or potential material failure if coatings are improperly designed

A solution method for the sub-surface stresses and local deflection of a semi-infinite inhomogeneous elastic medium

This paper proposes analytical Fourier series solutions (based on the Airy stress function) for the local deflection and subsurface stress field of a two-dimensional graded elastic solid loaded by a pre-determined pressure distribution. We present a selection of numerical results for a simple sinusoidal pressure which indicates how the inhomogeneity of the solid affects its behaviour. The model is then adapted and used to derive an iterative algorithm which may be used to solve for the contact half width and pressure induced from contact with a rigid punch. Finally, the contact of a rigid cylindrical stamp is studied and our results compared to those predicted by Hertzian theory. It is found that solids with a slowly varying elastic modulus produce results in good agreement with those of Hertz whilst more quickly varying elastic moduli which correspond to solids that become stiffer below the surface give rise to larger maximum pressures and stresses whilst the contact pressure is found to act over a smaller area

5-HT2 Receptor-Mediated Phosphoinositide Hydrolysis in Bovine Ciliary Epithelium

The serotonin 2 (5-HT2) receptor antagonists, MCI-9042 (Anplag®) and ketanserin, have been shown to lower intraocular pressure in rabbits (1) and humans (2). The mechanism of action of these drugs has not been determined, but it is hypothesized that 5-HT2 receptors, and possibly α-adrenergic receptors, (3) may regulate in part aqueous humor production via an intracellular signal transduction pathway in the ciliary body. We therefore examined whether 5-HT2 receptors were coupled to phosphoinositide hydrolysis in an organ culture system of isolated bovine ciliary epithelium. 5-HT stimulated [3H]inositol phosphates ([3H]InsPs) accumulation in a dose-dependent manner with a maximum increase approximately twice over the basal level. The mean EC50 value was 1.1 μM, which was calculated from four dose-response curves. The 5-HT stimulated accumulation of [3H]InsPs was inhibited by spiperone (5-HT2A/1A and dopamine 2 (D2) antagonists), M-1 (a major metabolite of MCI-9042), ketanserin (5-HT2A antagonist), SB-206553 (5- HT2B/2C antagonist), and mesulergine (5-HT2C antagonist and D2 agonist). It was not inhibited by chlorpromazine, which is a D2 receptor antagonist. Accordingly, our study demonstrates that 5-HT2 receptors are coupled to phospholipase C in bovine ciliary epithelium.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/63244/1/108076803762718114.pd