Finite element analysis of the effect of interfacial roughness and adhesion strength on the local delamination of hard coating under sliding contact

The interfacial roughness and the adhesion strength are very important for making a high-quality coating for friction and wear applications. In order to obtain a quantitative understanding concerning the effect of the two factors on the local delamination of hard coatings, finite element analyses concerning the maximum shear stress in a hard coating with various kinds of interfacial roughness and adhesion strength were made under low and high frictional conditions. As a result, local delamination maps for the identification of the local delamination of hard coatings were obtained as a function of the shear strength ratio of coating to substrate and the ratio of coating thickness to half-contact width. Also, the critical contact pressure required to produce local delamination of hard coatings is given.     

单层涂层最佳厚度的有限元分析

采用有限元数值计算的方法对TiN、TiC、Si3 N4及SiC四种材料的硬涂层体系表面下的应力分布进行了模拟分析。结果表明 ,对于TiN材料 ,当涂层厚度与接触半宽之比t/a <0 .3时 ,表面下的最大剪应力分布对提高轴承疲劳寿命较为有利 ;t/a =0 .5时 ,涂层系统的摩擦力学性能最差。涂层厚度较薄时 ,位于赫兹接触中心附近的涂层表层上的最大剪应力要远大于基体内的最大静态剪应力 ;当t/a >0 .1时 ,涂层表面上的最大剪应力对提高轴承疲劳寿命较为有利 ;涂层材料与基体材料的弹性模量之比小于 2 .0时 ,有利于提高涂层系统的疲劳寿命     

Finite element modelling of brittle fracture of thick coatings under normal and tangential loading

This paper addresses coating fracture in hard brittle coatings subjected to combined normal and tangential loads through a finite element based methodology. The coating is modelled as an elastic layer perfectly bonded to an elastic substrate with a pre-microcrack, assumed to initiate at the contact trailing edge due to high tensile stress. The predicted results are consistent with previously published coating fracture results. The model predicts a significant effect of coating thickness on crack propagation for coatings with large elastic mismatch and the final propagated crack profile is predicted to depend on friction coefficient, coating fracture toughness and sliding displacement.     

ANALYSIS ON THERMAL ELASTO-PLASTIC ASPERITY CONTACTS OF LAYERED MEDIA

A thermal elasto-plastic asperity contact model is investigated, which takes into account the steady-state heat transfer and the asperity distortion due to thermal elasto-plastic deformations. A hard coating and a soft coating are applied to study the correlations between contact area and contact pressure, average gap and contact pressure, coating thickness and contours of the contact stress distribution, etc. The effects of material properties, coating thickness, frictional coefficient, and the heat input combinations on the stress distribution are investigated and discussed. The frictional heat input increases the maximum value of yon Mises stress. Finally, the appropriate thickness of the hard coating is also discussed. To protect the substrate, one can choose hard coating and the thickness of that is suggested that can be hc=70 Rm.     

Sliding wear behavior of Fe-Al and Fe-Al/WC coatings prepared by high velocity arc spraying

A comparative study was carried out to investigate the microstructure and tribological behavior of Fe-Al and Fe-Al/WC iron aluminide based coatings against Si₃N₄ under dry sliding at room temperature using a pin-on-disc tribotester. The coatings were prepared by high velocity arc spraying (HVAS) and cored wires. The effect of normal load on friction coefficient and wear rate of the coatings was studied. The microstructure and the worn surfaces of the coatings were analysed by X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersion spectroscope (EDS). The results showed that, the main phases in both coatings were iron aluminide (Fe₃Al and FeAl) and α. WC/W₂C particles were embedded in the matrix of the composite coating. With adding WC hard particles, the Fe-Al/WC composite coating exhibited higher wear-resistance than Fe-Al coating. But the friction coefficient of both coatings showed little difference. As the load increased, the friction coefficient decreases slightly due to a rise of friction contact temperature and larger areas of oxide film formation on the worn surface, which act as a solid lubricant. Increasing load causes the maximum shear stress occurring at the deeper position below the surface, thereby aggravating the wear. The coating surface is subjected to alternately tensile stress and compression stress during sliding, and the predominant wear mechanism of the coatings appears to be delamination.     

Surface stresses in coated steel surfaces—influence of a bond layer on surface fracture

Thin hard coatings in the thickness range of only a few micrometers deposited by physical vapour deposition (PVD) on components or tools can improve the friction and wear properties by several orders of magnitude. A 2 μm thick TiN (E=300 GPa) coating on a high-speed steel substrate with a bond layer at the interface between the coating and the substrate was modelled by micro-level three-dimensional finite-element method (3D FEM) in order to optimise a coated surface with regard to coating fracture. Both compliant low modulus (E=100 GPa) and stiff high modulus (E=500 GPa) bond layers at the coating/substrate interface of 200 and 500 nm thickness were investigated. First principal stresses were simulated for scratch test geometry in the load range of 7.5-15 N. Very high stress concentrations of above 5700 MPa tensile stresses were observed in the bond layer just behind the contact zone for the stiffer bond layer. The stiff bond layer generated 5 times higher tensile stress maxima compared to the compliant bond layer. There was approximately 3.5 times larger strain in the compliant bond layer compared to the stiff bond layer. The general coating design advice based on this exercise is that when a bond layer is used e.g. for coating/substrate adhesion improvement should the bond layer be less stiff than the coating not to generate high and critical tensile stresses. The thickness of the bond layer may vary and is not critical with respect to generated stresses in the surface.     

The effect of substrate properties on tribological behaviour of composite DLC coatings

The unique features of DLC coatings in providing low friction and low wear and, at the same time, causing low wear to the counterface make them very attractive in industrial applications, in improving tribological performance of mechanical components on various substrates. In this study, composite DLC coatings have been deposited on sintered ferrous alloy, M42 tool steel, 2618 aluminium alloy, and 6063 aluminium extrusion substrates using the combined CFUBMS–PACVD technique. The effect of mechanical properties of substrate materials on tribological behaviour of the composite DLC coatings has been investigated at various loads on a ball-on-disk wear machine in dry air. A transition load was usually observed for coatings on the various substrates except for the aluminium extrusion; above the transition load the coating was completely destroyed via some spallation/fragmentation process after 2 h sliding, and the wear rate increased dramatically with further increase in load. The coating system on sintered ferrous alloy substrate exhibited the highest transition load among the four types of substrates studied. This is considered to have resulted from the combined effects of the lower elastic modulus of the porous sintered ferrous alloy substrate, which decreases the stress concentrations in the contact region, and the surface roughness and porosity, which enhance the bonding strength between the coating and the substrate under multi-contact conditions. The high elastic modulus of the tool steel substrate leads to tensile stress conditions in the sliding contact region and therefore makes coatings deposited on such a substrate more prone to breakdown/fragmentation, resulting in a transition load close to that for coatings on the soft 2618 aluminium alloy substrate. For coatings on the 6063 aluminium extrusion substrate, significant plastic deformation occurred in the substrate at loads above 1.5 N. However, despite the heavy deformation in the substrate, coatings on this substrate were not scraped off, as were coatings on the 2618 aluminium alloy substrate, even at a load as high as 20 N. The specific wear rate increased continuously with load, no apparent transition load being explicitly identifiable. This study shows that hard DLC coatings can be applied on both hard and soft substrates for improvement of the tribological behaviour of mechanical components.     

Method and surface roughness aspects for the design of DLC coatings

The design of coatings for highly loaded component contacts, such as bearings, gears and valve train components involves several important factors, including load, friction, lubrication, surface characteristics and material parameters. This paper presents an investigation of the influence of the material, coating thickness and surface roughness on tensional stress levels for coatings that are more compliant than the substrate material. Specifically the effect of multiple asperity contact is studied in three dimensions. The simulation is based on a finite element model where the load is applied as several interacting Hertzian pressure distributions.The results show that the surface structure, in combination with the elastic properties of the coating, has a large influence on the tensional stress level in the coating. The highest tensional stress level in the coating occurs when contact spots almost overlap neighbouring cells and at the same time the size of the contact spots is in the same order of magnitude as the coating thickness.     

Two-dimensional contact problem for a coating-graded layer-substrate structure under a rigid cylindrical punch

The two-dimensional frictionless contact problem of a coating structure consisting of a surface coating, a functionally graded layer and a substrate under a rigid cylindrical punch is investigated in this paper. The coating and substrate are homogeneous materials with distinct physical properties, while the intermediate layer is inhomogeneous with its shear modulus changing arbitrarily along the thickness direction. To approximate the through-thickness variation, a piecewise linear multi-layer model is used and the graded layer is divided into a number of sub-layers whose shear modulus is assumed to vary linearly. Poisson's ratio, however, is taken as a constant within the structure for simplicity. By using the transfer matrix method and Fourier integral transform technique, the governing equations are reduced to a Cauchy singular integral equation which is numerically solved to determine the normal contact pressure, contact region, the through-thickness stress fields and longitudinal stress distributions at interfaces. A parametric study is conducted, showing that both normal contact pressure and stress fields in the structure are significantly influenced by the shear modulus ratio and the thickness ratio of the exponentially graded layer but are less sensitive to the gradient index of the graded layer whose shear modulus follows a power law variation.     

薄膜粗糙表面有摩擦接触问题的数值计算研究

采用ANSYS的APDL语言编程通过参数化变量方式实现了薄膜粗糙表面有摩擦接触问题的整个建模与分析过程,其中包括参数化生成满足高斯分布的随机粗糙表面与计及摩擦因数和薄膜/基体弹性模量比变化情况下的自动有限元分析过程。计算结果表明:当摩擦因数一定时,随着薄膜/基体弹性模量比的增大,应力分布逐渐向基体深处扩展,粗糙表面上各点接触压力一致减小,接触压力峰值减小的最大幅度为9.0%;当弹性模量比一定时,摩擦因数的变化对基体部分应力分布的影响不大,然而随着摩擦因数的增加,粗糙表面上各点接触压力增大,接触压力峰值增加的最大幅度为13.2%,可见摩擦因数和弹性模量比对薄膜粗糙表面的接触应力有明显影响。     

Stress analysis of cushion form bearings for total hip replacements.

Cushion form bearings comprise a thin layer of low elastic modulus material on the articulating surface of the bearing, which can deform to help preserve a film of lubricant between the bearing surfaces and therefore reduce friction and wear. The long-term function of this type of bearing is dependent on the strength and durability of this compliant layer. Finite difference and finite element methods have been used to analyse the stress distribution in the compliant layer of cushion form bearing for artificial hip joints under physiological loading conditions. A good agreement between finite difference and finite element methods was found. Under normal loading, the highest value of the maximum shear stress was found to be at the interface between the compliant layer and the more rigid substrate close to the edge of the contact. The values of maximum shear stress in the centre of the contact close to the articulating surface were lower than in the equivalent Hertzian contact. A friction force acting at the surface had little effect on the stress distribution for coefficients of friction less than 0.05. However, for higher values of friction coefficient (larger than 0.2), corresponding to inadequate lubrication, the maximum shear stress increased by a factor of four and was found to be located at the surface. The analysis predicts that the mode of failure will be at the interface with the substrate under fluid film or mixed lubrication conditions and at the articulating surface when the bearing runs dry with higher levels of friction. Both failure modes have been observed experimentally under the conditions specified.     

Finite element analysis of coating adhesion failure in pre-existing crack field

Abstract

The influence of a pre-existing crack field on coating adhesion failure in a steel surface coated with a 2 μm thick titanium nitride (TiN) coating was investigated by finite element method modelling and simulation. The stress and strain fields were determined in contact conditions with a spherical diamond tip sliding over the coated surface at a loading of 8 N. One crack in or at the coating increased the maximum tensile stresses with six times from 82 to 540 MPa when the crack was vertical through the coating or L shaped and with nine times when the crack was horizontal at the coating/substrate interface. A simulated multicrack pattern relaxed the tensile stresses compared to single cracks. The results indicate that a cracked coated surface needs to have about five to nine times higher adhesive and cohesive bonds to resist the same loading without crack growth compared to a crack free surface. For optimal coated surface design, the strength of the adhesive bonds between the coating and the substrate in the vertical direction needs to be 50% higher than the cohesive bonds within the coating and the substrate in the horizontal direction. The first crack is prone to start at the top of the coating and grows vertically down to coating/substrate interface, and there it stops due to the bigger cohesion within the steel material. After this, there are two effects influencing that the crack will grow in the lateral direction. One is that steel cohesion is normally bigger than the coating/interface adhesion, and the second is that there are higher tensile stresses in the horizontal than in the vertical cracks. Several vertical cracks can stop the horizontal crack growth due to stress relaxation.     

Critical Load Analysis for a Layered Half-Space under Sliding Indentation

Analyses are presented for cracking or delaminating problems of thin coatings on dissimilar thick substrate materials under a normal and a tangential force. Based on the energy principle associated with the consideration of substrate deformation, an analytical expression has been proposed to predict the critical load of an adherent stiff thin coating on a compliant substrate. The critical load has been shown to depend on the hardness, the coating thickness, the surface energy of adhesion, the coefficient of friction, contact areas of a scratch track, and elastic moduli of coatings and substrates. Experimental observations of microscratch testing on a CrN coating deposited on a soft coating, labeled as SC-I, over a Cu/Zn alloy substrate have shown that buckling and cracking in a semicircular arc ahead of an indenter are the predominant failure modes, thereby confirming the assumption of the theoretical calculation. Using Beuth's solution, a simple fracture model describing the cracking of thin coatings has been developed over a range of practical elastic mismatches and applied to solve cracking problems of compliant coatings in this work. Microscratch results from another soft coating, labeled as SC-II, on a Cu/Zn alloy substrate have revealed that cracks first occur along the edge of the circular contact area in the rear of the indenter due to the tensile stress. The stress formulae of Hamilton and Bower and Fleck are therefore introduced into this model to compute the critical load required to initiate a crack in the coating and the stress intensity factor of the coating.

     

Wear stability of polymer nanocomposite coatings with trilayer architecture

A polymer trilayer (sandwiched) film with a thickness of 20–30 nm has been designed to serve as a wear resistant nanoscale coating for silicon surfaces. These surface structures are formed by a multiple grafting technique applied to self-assembled monolayers (SAM) and functionalized tri-block copolymer, followed by the photopolymerization of a topmost polymer layer. The unique design of this layer includes a hard-soft-hard nanoscale architecture with a compliant rubber interlayer mediating localized stresses transferred through the topmost hard layer. This architecture provides a non-linear mechanical response under a normal compression stress and allows additional dissipation of mechanical energy via the highly elastic rubber interlayer. At modest loads, this coating shows friction coefficient against hard steel below 0.06, which is lower than that for a classic molecular lubricant, alkylsilane SAM. At the highest pressure tested in this work, 1.2 GPa, the sandwiched coating possesses four times higher wear resistance than the SAM coating. The wear mechanism for this coating is stress and temperature induced oxidation in the contact area followed by severe plowing wear.     

The effect of gross sliding fretting wear on stress distributions in thin W-DLC coating systems

The effect of fretting wear on stress evolution in a thin, hard diamond-like carbon coating deposited on a high strength steel is simulated using a finite element (FE) based method under gross sliding conditions. The effects of coating stiffness, thickness, and coefficient of friction are studied. The trailing edge tensile stress and the leading edge compressive stress are generally predicted to reduce with wear, while the shear stress at the interface is predicted to increase. An extrapolation procedure for predicting coating wear life is shown to provide accurate and slightly conservative estimates compared with explicit modelling to complete coating wear.     

A Mixed Lubrication Model for Journal Bearings with a Thin Soft Coating—Part I: Contact and Lubrication Analysis

Soft coatings are used extensively in industry for contact friction reduction, particularly during the running-in period. A numerical model is developed for contact and lubrication analysis of some soft coating coated bearings in mixed fluid lubrication. The model is applied to determine oil film thickness, contact pressure, and the friction coefficient of the coated bearings in contact with a hard journal surface. The contact of tin-coated 339 Al-Si alloy bearings with case hardened steel is analyzed using the developed model.     

Tribological analysis of fracture conditions in thin surface coatings by 3D FEM modelling and stress simulations

A tribological analysis of deformations and stresses generated and their influence on crack generation and surface fracture in a coated surface loaded by a sliding sphere in dry conditions is presented. A three-dimensional finite element method (3D FEM) model has been developed for calculating the first principal stress distribution in the scratch tester contact of a diamond spherical tip with 200 μm radius sliding with increasing load on a 2 μm thick titanium nitride coated steel surface. The model is comprehensive in that sense that it considers elastic, plastic and fracture behaviour of the surfaces. The hard coating will be stretched and accumulates high tensile stresses. At the same time, it is carrying part of the load and thus reducing the compressional stresses in the substrate under the sliding tip. The first crack is initiated at the top of the coating from bending and pulling actions and it grows down through the coating. The fracture toughness of the coating is calculated by identifying from a scratch test experiment the location of the first cracks and the crack density and using this as input data.     

Contact of surface asperities in wear

Stresses have been examined under the elliptical Hertzian contact area, which appear during a real contact between two asperities in the process of sliding friction. The stresses are found according to the Mises-Hencky criterion and characterize the ability of the material to change its shape. Relationships have been found of such a maximum stress under the surface of the contact area depending on the geometric parameters of the contact area, on the friction coefficient and the maximum pressure in the centre of contact area. The processing of the calculation data was conducted according to a special program on a computer and yielded an approximate relationship to calculate the maximum reduced stress. The distribution of dangerous stresses under the contact surface has been shown. The most critical points may be both within the surface layer of the material and on the contact area itself.     

Development of a friction energy capacity approach to predict the surface coating endurance under complex oscillating sliding conditions

In the case of surface coatings application it is crucial to establish when the substrate is reached to prevent catastrophic consequences. In this study, a model based on local dissipated energy is developed and related to the friction process. Indeed, the friction dissipated energy is a unique parameter that takes into account the major loading variables which are the pressure, sliding distance and the friction coefficient. To illustrate the approach a sphere/plane (Alumina/TiC) contact is studied under gross slip fretting regime. Considering the contact area extension, the wear depth evolution can be predicted from the cumulated dissipated energy density. Nevertheless, some difference is observed between the predicted and detected surface coating endurance. This has been explained by a coating spalling phenomenon observed below a critical residual coating thickness. Introducing an effective wear coating parameter, the coating endurance is better quantified and finally an effective energy density threshold, associated to a friction energy capacity approach, is introduced to rationalize the coating endurance prediction. The surface treatment lifetime is then simply deduced from an energy ratio between this specific energy capacity and a mean energy density dissipated per fretting cycle. The stability of this approach has been validated under constant and variable sliding conditions and illustrated through an Energy Density–Coating Endurance chart.     

A study of stresses in alumina universal heads of femoral prostheses

Three-dimensional, frozen-stress photoelasticity was used to study the best shape for a proposed alumina universal head loaded on to a Vitallium cone taper spigot with a 30 degrees inclined force, as in vivo. Typical cone taper friction values were reproduced in the photoelastic models. The location of the highest tensile stresses in the Mark I shape with a flat crown was found to be on the inner surface of the crown. Changing to a torispherical surface in the Mark II shape reduced this magnitude. However, the Mark III shape with a hemispherical inner crown surface gave even lower stress there, equal to the maximum value of the hoop stress at the taper, which was measured to be fairly uniform both around and along the taper except at the ends where contact pressure concentrations were found to occur and it became reduced. Lamé axisymmetric cylinder stress predictions were found to be useful approximations to measured values and were generally overestimates of the tensile hoop stress at the head taper surface.