R.D. Arnell

Finite element analysis of the contract stresses in an elastic coating on an elastic substrate

Abstract A finite element method has been used to investigate the contract stresses due to elastic indentation of coating/substrate systems consisting of a high modulus surface coating on a relativity low modulus substrate. Calculations have been made for two imposed pressure distribution identical to those arising during hertzian indentation of a homogeneous elastic half-space by spherical and cylindrical indenters respectively. For each distribution the stresses have been investigated in terms of the ratio of the Young moduli of the coating and substrate and the ratio of the coating thickness to the contact halfwidth. It has been shown that the stresses of both the outer surface of the coating and the coating-substrate interface are complicated functions of the two variables and that the stresses which could be responsible for coating failure cannot simultanously be minimized by appropriate choice of variables.

Finite element analysis of the contact stresses in elastic coating/substrate under normal and tangential load

Abstract This paper describes a continuation of previous work which reported a finite element analysis of the stress field in an elastic coating/substrate system due to both axisymmetric and plane strain hertzian pressure distribution. Here we report a similar analysis of the effects of combined normal and tangential tractions, to stimulate the stresses due to frictional sliding at the coated surface. The stresses have been computed for various values of the coating-to-substrate-modulus ratio, the coating-thickness- to-contact-half-width ratio and the coefficient of friction. It has been shown that the stresses at both the outer surface and the coating-substrate interface are complicated functions of the experimental variables and it is not possible to minimize simultaneously the various stresses which could lead to coating failure under sliding conditions.

Finite element comparative study of elastic stresses in single, double layer and multilayered coated systems

Abstract In this paper, a comparative study of elastic stresses in various types of coated surfaces including surfaces with single, double and multilayered coatings is described. The stresses have been computed for several coating thicknesses, one outer layer coating/substrate modulus ratio, and a wide range of friction coefficients. Stresses have been computed for normal load only and for combined normal and tangential loads. The main results of this study indicate that, for any given outer layer/substrate modulus ratio, the maximum tensile stress at the surfaces of all the coating systems considered increases with friction coefficient and decreases with coating thickness. Comparison of single layer, double layer and multilayered coating systems shows that, for a given total thickness and outer layer/substrate modulus ratio, the tensile stresses at the layer/substrate interface are progressively reduced as the number of intermediate layers in a multilayer coating is increased.

Two-dimensional finite-element analysis of elastic stresses in double-layer systems under combined surface normal and tangential loads

Abstract This paper describes a continuation of previous work [1] which reported a finite-element analysis of the stress field in an elastic double-layer system owing to normal pressure distribution. Here we report a similar two-dimensional analysis of the effects of combined surface normal and tangential tractions, to simulate the stresses due to frictional sliding at the coated surface. The stresses have been computed for various values of the coating thickness, friction coefficient and one value of modulus ratio and contact half-width. It has been shown that for double-layer coatings with a decreasing modulus from the surface to the bulk, the surface maximum tensile stress at the trailing edge of the contact zone increases with the friction coefficient and decreases with the total thickness of the double layer. In addition, at the coating/substrate interface the effect of the friction coefficient becomes negligible for thick coatings. Finally, at the surface, the maximum shear stress, which also increases with the friction coefficient, is higher than that of a homogeneous material for the same friction coefficient. Conversely, in the substrate, the same stress is lower than that of a homogeneous material for the same friction coefficient.

The effects of speed, film thickness and substrate surface roughness on the friction and wear of soft metal films in ultrahigh vacuum

Abstract Films of lead, indium and silver were applied to hardened steel substrates of various surface roughness and were rubbed against hardened steel balls in ultrahigh vacuum. The effects of film thickness, substrate roughness and sliding speed on the friction coefficients and wear rates are described, and the results from the three coating materials are compared.

Determination of coating mechanical properties using spherical indenters

Abstract In recent years, various forms of indentation testing have been increasingly used to determine the material properties of specimens. This technique, particularly the nano-indentation method, has been extended to the testing of coating systems in order to calculate the individual properties of the thin coatings and the substrates. However, the interpretation of the test data to achieve this is complex and continues to be a widely studied subject. Based on the finite element analysis (FEA) of coated surfaces indented by a spherical indenter, this paper describes methods for combining FEA and experimental indentation testing to determine coating modulus and hardness independent of substrate effects. An indentation test on a coated specimen is first carried out using a spherical indenter. The combined contact modulus of the coated surface is determined from the elastic portion of the experimental load/displacement curve. The modulus of the coating alone is then computed from a function derived by a parametric finite element analysis of indentation behaviour. The hardness of the coating alone is determined by comparing the experimentally determined mean contact pressure with parametric finite element results for the same contact geometry and known hardness ratios. Using this proposed methodology, the properties of the substrate are fully taken into consideration, hence providing a more universal and accurate measurement of coating elastic modulus and hardness.

Finite element analysis of contact stresses in elastic double-layer systems under normal load

Abstract A finite element method has been used to calculate contact stresses in elastic double-layer systems under a normal pressure distribution similar to that found in the hertzian contact between a spherical indenter and an elastic half-space. The double layer consisted of two layers of equal thickness but different modulus and stresses have been calculated for various values of the layer thickness:contact half width ratio and the outer layer:intermediate layer:substrate modulus ratios. It has been shown that double-layer coatings generally have less severe stress distributions than monolayers having the same total thickness as the double layer and the same modulus as the outer layer of the double-layer coating.

Multi-pass sub-critical load testing of titanium nitride coatings

TiN coatings deposited by closed field unbalanced magnetron sputter ion plating (CFUBMS) have been scratch tested in two modes. An initial conventional scratch test has been carried out to determine the critical load, and multiple scratches have been made over single tracks at different fractions of the critical load. It is shown that, even at very high fractions of the critical load, the coatings do not fail adhesively or cohesively; rather, they simply become progressively thinner with successive passes of the diamond. Scanning electron microscopy of the worn surfaces has revealed a previously unobserved wear mechanism that shows that the coating adhesion can be truly described as perfect.

Comparison between an elastic-perfectly plastic finite element model and a purely elastic analytical model for a spherical indenter on a layered substrate

Abstract The contact problem of an elastic sphere indenting an elastic-perfectly plastic substrate having an elastic layer is analysed using the finite element method and compared with a purely elastic analytical solution. The case of a layer stiffer and harder than the substrate is investigated and solutions for the contact pressure, subsurface stresses and strains are presented for various indentation depths. The results show good agreement until the threshold of plasticity is reached. Thereafter, as the system is subjected to higher penetrations, the two solutions diverge as plastic deformation initiates in the finite element model. The analysis also demonstrates that the influence of a deformable indenter upon the plastic solutions cannot be neglected.

Comparison between analytical and FEM calculations for the contact problem of spherical indenters on layered materials

Abstract An analytical solution and a finite element calculation have been utilised to investigate the contact stresses due to elastic spherical indentation into coating/substrate systems. Such calculated stress distributions may be used for the optimal design of layer systems as well as, together with experimental penetration-force curves, to determine quantitative measures for toughness and adhesion of the film. Both approaches were compared using various systems composed of a higher modulus surface coating on a relatively low modulus substrate. It was found that both methods agree very well and yield adequate stress distributions for various film thicknesses. Here we show the radial stress component Yγ = σ r for six different systems.