Contact mechanics and the wear of metals

It is commonly observed that metallic wear debris takes the form of thin platelets, leading to the term ‘delamination wear’. Modelling this phenomenon has proved a stiff challenge in Contact Mechanics since the fractures which give rise to wear particles lie parallel, or nearly so, to the surface; i.e. on planes of maximum compressive stress. Sectioning the surface layer beneath a wear track has revealed it to have acquired severe plastic strains, which suggests that the cracks are ductile fractures, driven by plastic strain rather than elastic stress intensity. The paper reviews recent research into the progressive plastic deformation of surfaces in repeated sliding: the process known as ‘ratchetting’. Included is an analysis of ‘running-in’ of rough surfaces by repeated sliding and a discussion of the criterion of rupture under cyclic plastic strain.     

Contact problems for a wedge with rounded apex

Elastic contact between a shallow elastic wedge, whose apex is blunted by a finite radius, and an elastically similar half-plane is studied. A closed-form contact law is found, and the interior stress field is then deduced using a Muskhelishvili’s solution in series form, for frictionless and sliding conditions. This geometry removes one of the principal objections to classical solutions to the wedge indentation problem—the unrealistic infinite stress concentration implied by an atomically sharp apex—and in the latter part of the paper the strength of the contact is evaluated explicitly. Further, cases of partial slip associated with the application of tangential load less than needed to cause sliding are considered.     

Contact mechanics analysis of metal-on-metal hip resurfacing prostheses

Finite-element method was employed to study the contact mechanics in metal-on-metal hip resurfacing prostheses, with particular reference to the effects of bone quality, the fixation condition between the acetabular cup and bone, and the clearance between the femoral head and the acetabular cup. Simple finite-element bone models were developed to simulate the contact between the articulating surfaces of the femoral head and the acetabular cup. The stresses within the bone structure were also studied. It was shown that a decrease in the clearance between the acetabular cup and femoral head had the largest effect on reducing the predicted contact-pressure distribution among all the factors considered in this study. It was found that as the clearance was reduced, the influence of the underlying materials, such as bone and cement, became increasingly important. Stress shielding was determined to occur in the bone tissue surrounding the hip resurfacing prosthesis considered in this study. However, the stress-shielding effects predicted were less than those observed in conventional total hip replacements. Both the effects of bone quality (reduction in elastic modulus) and the fixation condition between the cup and the bone were found to have a negligible effect on the predicted contact mechanics at the bearing surface. The loading was found to have a relatively small effect on the predicted maximum contact pressure at the bearing surface; this was attributed to an increase in contact area as the load was increased.     

Contact mechanics and tip shape in AFM-based nanomechanical measurements

Stiffness-load curves obtained in quantitative atomic force acoustic microscopy (AFAM) measurements depend on both the elastic properties of the sample and the geometry of the atomic force microscope (AFM) tip. The geometry of silicon AFM tips changes when used in contact mode, affecting measurement accuracy. To study the influence of tip geometry, we subjected ten AFM tips to the same series of AFAM measurements. Changes in tip shape were observed in the scanning electron microscope (SEM) between individual AFAM tests. Because all of the AFAM measurements were performed on the same sample, variations in AFAM stiffness-load curves were attributed to differences in tip geometry. Contact-mechanics models that assumed simple tip geometries were used to analyze the AFAM data, but the calculated values for tip dimensions did not agree with those provided by SEM images. Therefore, we used a power-law approach that allows for a nonspherical tip geometry. We found that after several AFAM measurements, the geometry of the tips at the very end is intermediate between those of a flat punch and a hemisphere. These results indicate that the nanoscale tip-sample contact cannot easily be described in terms of simple, ideal geometries.     

Contact mechanics and lubrication analyses of ceramic-on-metal total hip replacements

Ceramic-on-metal (CoM) total hip replacements have shown reduced wear and friction. Lubrication and contact mechanics analyses play an important role in providing an overall understanding for the tribological performance of CoM bearings. In the present study, the steady-state contact mechanics and elastohydrodynamic lubrication (EHL) and transient EHL of CoM bearings were analyzed. The dry and lubricated contact pressures of CoM bearings showed typical characteristics of hard-on-hard hip bearings. The effects of head radius and radial clearance on the lubrication performance were predicted. CoC and CoM bearings are more likely to benefit full fluid film lubrication than MoM bearings.     

Contact mechanics of a novel metal-on-metal total hip replacement

The contact mechanics of a novel metal-on-metal total hip replacement (THR) were investigated in this study. The metal-on-metal prosthesis considered consists of a cobalt-chrome acetabular insert connected to a titanium shell through a taper contact, articulating against a cobalt-chrome femoral head. Both the experimental measurement of the displacement of the acetabular insert and the contact area between the two bearing surfaces, and the corresponding numerical predictions using the finite element method have been conducted. Excellent agreement has been demonstrated between the experimental measurement and the finite element prediction under various loads up to 3 kN. The maximum contact pressure at the articulating surfaces has been predicted to be about 31 MPa from a simple axisymmetric finite element model, significantly lower than that of a similar cup but with a monoblock construct. This has been mainly attributed to the flexibility of the insert, leading to an increase in the conformity between the femoral head and the acetabular insert. In addition, the predicted maximum contact pressure is only slightly increased to 37 MPa, from a more realistic three-dimensional anatomical finite element model. The design features on metal-on-metal THRs have been shown to reduce contact stresses and may improve tribological performances of these hard-on-hard bearing couples.     

Contact mechanics of a flexible imprinter for photocured nanoimprint lithography

A flexible imprinter can be used to accommodate substrate or template roughness in nanoimprint lithography. The contact mechanics of a multi-layer imprinter incorporating bending and local deformation is described. With the right combination of dimensions, moduli, and viscosity, the imprinter can transfer a pattern evenly to a non-flat substrate. These concepts have been used to pattern magnetic media for high density information storage.     

Contact mechanics and friction of fractal surfaces probed by atomic force microscopy

We investigated the contact mechanics and friction forces between atomic force microscope (AFM) probes and self-affine fractal carbon films. We studied single-asperity contacts by means of conventional nanometric conical tips whilst custom-designed micrometric flat tips were adopted to form multiple junctions between the probe and the sample. By varying the externally applied load we found that the average frictional force follows a power-law behavior in the single-asperity regime and a linear behavior in the multi-asperity regime. The friction coefficient was the same for carbon specimens having different fractality. We also acquired quasi-static load-displacement curves on micrometric scale, revealing a strong dependence of the average indentation depth on the values of fractal parameters. A comparison of experimental data with contact theories for randomly rough surfaces is provided.     

Real versus synthesized fractal surfaces: Contact mechanics and transport properties

In this work, we analyze diffusion and viscous flow through the aperture field of a contact between rough surfaces pressed against each other. The purpose of our study is to validate the use of synthesized rough surfaces instead of real ones for surfaces exhibiting fractal properties. Models for mechanical deformation of asperities as well as for transport resulting from a pressure gradient or a species concentration gradient are presented. At the macroscopic scale, viscous and diffusive transports only depend on transmissivity K and diffusivity D, respectively. Both tensors K and D are intrinsic, which means that they can be entirely determined from the aperture field. Two kinds of surfaces obtained from two different machining processes—lapping and sand-blasting—are considered. The dependence of the global contact area, distribution of local contact areas, K and D upon the average contact pressure is compared for real surfaces and their analogue synthesized surfaces. The comparison over a wide range of contact pressures leads to the conclusion that a fractal representation is a robust representation for the contact mechanics as well as for transport properties for this class of surfaces. This validates the overall procedure described in this work.     

无源无线应变传感器中压电材料接触力学模型研究

针对现有无源无线传感器存在稳定性差,抗干扰能力不强,传输距离过短的问题,提出一种新型无源无线应变传感器。 该传感器由两个线圈和一个体声波传感器组成,体声波传感器包括传力结构和石英晶片,其可将被测表面的应变转化为可检测 的石英谐振频率偏移。 首先,建立了半椭圆接触模型,研究接触力、激励电压、接触元件形状对石英的影响,以提高传感器性能; 其次,设计了石英加载装置,实现石英表面微力加载研究;最后,搭建了无源无线应变传感系统,传输距离可达 5 cm,分辨率约 为 4. 2 Hz/ με,应变测量范围为 600 με,重复性实验显示 RSD 为 5. 47% 。 实验结果表明,该传感系统具有良好性能,在未来将与 无人机结合为大型结构应变测量提供有效的解决方案。     

Contact mechanics of rough surfaces in tribology: multiple asperity contact

Contact modeling of two rough surfaces under normal approach and with relative motion is carried out to predict real area of contact and surface and subsurface stresses affecting friction and wear of an interface. When two macroscopically flat bodies with microroughness come in contact, the contact occurs at multiple asperities of arbitrary shapes, and varying sizes and heights. Deformation at the asperity contacts can be either elastic and/or elastic-plastic. If a thin liquid film is present at the interface, attractive meniscus forces may affect friction and wear. Historically, statistical models have been used to predict contact parameters, and these generally require many assumptions about asperity geometry and height distributions. With the advent of computer technology, numerical contact models of 3-D rough surfaces have been developed, particularly in the past decade, which can simulate digitized rough surfaces with no assumptions concerning the roughness distribution. In this article, a comprehensive review of modeling of multiple-asperity contacts in dry and wet conditions is presented. Contact models for homogeneous and layered, elastic and elastic-plastic solids with and without tangential loading are presented. The models reviewed in this paper fall into two groups: (a) analytical solutions for surfaces with well-defined height distributions and asperity geometry and (b) numerical solutions for real surfaces with asperities of arbitrary shape and varying size and height distributions. Implications of these models in friction and wear studies are discussed. This revised version was published online in June 2006 with corrections to the Cover Date.     

Lateral crushing of thin-walled tubes between cylindrical indenters

The plastic-collapse load and post-collapse behaviour of ductile, thin-walled tubes compressed between cylindrical indenters are analyzed for a complete range of indenter radii; experiments on steel, brass and aluminium alloy tubes show the usefulness of this analysis when deflections are large. The effect of shear force is considered; shear can develop when the sides of the tube are constrained against lateral expansion. While crushing by diametrically opposed indenters results in symmetrical modes of deformation, any shear in addition to the normally applied forces results in an asymmetrical mode of deformation which is more compliant than the symmetrical mode. The asymmetrical mode of deformation is initially unstable.     

Contact mechanics of metal-on-metal hip implants employing a metallic cup with a UHMWPE backing

The contact mechanics in metal-on-metal hip implants employing a cobalt chromium acetabular cup with an ultra-high molecular weight polyethylene (UHMWPE) backing were analysed in the present study using the finite element method. A general modelling methodology was developed to examine the effects of the interfacial boundary conditions between the UHMWPE backing and a titanium shell for cementless fixation, the coefficient of friction and the loading angle on the predicted contact pressure distribution at the articulating surfaces. It was found that the contact mechanics at the bearing surfaces were significantly affected by the UHMWPE backing. Consequently, a relatively constant pressure distribution was predicted within the contact conjunction, and the maximum contact pressure occurred towards the edge of the contact. On the other hand, the interfacial boundary condition between the UHMWPE backing and the titanium shell, the coefficient of friction and the loading angle were found to have a negligible effect on the contact mechanics at the bearing surfaces. Overall, the magnitude of the contact pressure was significantly reduced, compared with a similar cup without the UHMWPE backing. The importance of the UHMWPE backing on the tribological performance of metal-on-metal hip implants is discussed.     

A study of the crushing of tubes by two indenters

The behaviour of mild steel open tubes loaded centrally by two opposed wedge-shaped indenters is examined. The 1.6 mm thick tubes have diameters ranging from 31.75 to 76.2 mm and lengths from 1.6 to 10 diameters. The load-deflection curves have been recorded and simple empirical formulae are obtained for them. The profiles of the deformed top generators for tubes of 10 diameters length are reported and they are found to collapse into a single curve in a suitable dimensionless plot. The observed profile is related to the force by means of a beam-foundation model. Similar empirical formulae are reported for tubes enclosed at both ends with “rigid” plates.     

Side-contact of sharp indenters, including the effects of friction

When a sharp-edged indenter is pressed into a half-plane material in the half-plane is displaced and ‘laps around’ the edges of the punch, possibly making contact with the side faces. This phenomenon is quantified within (coupled) half-plane theory, and applied first to an idealised indenter having the cross section of a trapezium, and then to a semi-infinite indenter. The latter allows an asymptotic form to be found which, through a generalised stress intensity factor may be collocated into the edge of any notionally sharp-edged indentation problem.     

带辅助环的楔块式超越离合器工作机理及楔紧和退楔条件的研究

带辅助环楔块式超越离合器不仅克服了常用超越离合器承械能力低、工作稳定性较差的缺陷,而且满足了大功率、高效率机械产品开发的需要.通过对其工作机理和工作过程的分析和描述,得到了其楔紧和退楔的条件,经仿真分析表明,该超越离会器具有结构简单、响应灵敏,承载能力强、稳定性高等特点.     

Investigations of new possibilities in the calibration of diamond hardness indenters geometry

The influence of Rockwell and Vickers diamond indenters geometry in hardness measurements justifies the strict specifications and tolerances in the relative standards. Many methods, and consequently dedicated instruments, have been developed to investigate the geometrical parameters in order to calibrate the diamond indenters. Most of them, using contact or contactless methods, can only investigate some profiles of the indenters; from these partial measurements the whole geometry is derived. Few other instruments can investigate the whole shape but, since they are custom-developed, costs and difficulties in the calibration of these instruments have limited their use.A new method is proposed in this paper using a commercial and not dedicated instrument: a 3D measuring confocal microscope. This type of instrument has also the advantage that the whole geometry is analysed with a consequently knowledge improvement in the indenter calibration.In the paper the measurement method, the used instrument and its calibration to assure traceability to the length and angle standards are investigated.     

Lateral crushing of square and rectangular tubes by non-orthogonally placed narrow width indenters

A study of the collapse behaviour of square or rectangular tubes subjected to transverse loading by narrow width indenters, placed in orthogonal and non-orthogonal positions is presented. Experiments were conducted on as-received aluminium tubes, wherein the tubes were compressed in an unsymmetrical and a symmetric arrangement. Typical load-compression curves and histories of the deforming specimens are presented. Based on experimental observations, an analysis which considers the energy absorbed in stationary and rolling plastic hinges is developed for typical cases of the two modes of tube collapse. Computed results of the hinge locations, deforming tube geometry and load-compression curves are presented in each case. These results show good agreement with the experimental observations.