Contact Mechanics Analysis Research Articles

Analysis of contact mechanics in McKee–Farrar metal-on-metal hip implants

Analysis of contact mechanics in McKee–Farrar metal-on-metal hip implants

Analysis of Contact Mechanics for Rotor-Bristle Interference of Brush Seal

Brush seals have proven to be an attractive alternative to labyrinth seals for turbomachinery applications. This innovation in seal technology utilizes both the high temperature capability of special-alloy wire and the flexural adaptability of fibers to accommodate a wide range of operating conditions that are encountered during service. The effectiveness of the seal is principally derived from the bristles ability to endure forces imparted by both the fluid and shaft, and yet maintain contact between the filament tips and the surface of the rotor. Consequently, contact forces generated along the interface of the fiber tip and rotor are an important consideration for both the design and performance of the rotor-seal assembly. This paper focuses on evaluating brush seal forces that arise along the surface of the rotor due to the dimensional disparity or interference between the rotor-fiber. Filament tip contact forces are computed on the basis of an in-plane, large deformation mechanics analysis of a cantilever beam, and validation of the model is assessed by using an electronic balance for measuring the shear and normal force exerted by a bristle tip onto a flat, hardened surface. Formulation of the mechanics problem is briefly reviewed, and includes the effect of Coulombic friction at the interface of the fiber tip and rotor. Filament contact force is used as a basis for computing bearing stress along the fiber-rotor interface. Results are reported for a range of brush seal design parameters in order to provide a better understanding of the role that seal geometry, friction, and bristle flexural rigidity play in generating rotor contact force.

Analysis of contact mechanics in ceramic-on-ceramic hip joint replacements.

The contact mechanics in ceramic-on-ceramic hip implants has been analysed in this study using the finite element method. Only the ideal conditions where the contact occurs within the acetabular cup were considered. It has been shown that the contact pressure distribution and the contact area at the main articulating bearing surfaces depend largely on design parameters such as the radial clearance between the femoral head and the acetabular cup, as well as the thickness of the ceramic insert. For the ceramic-on-ceramic hip implants used in clinics today, with a minimum 5-mm-thick ceramic insert, it has been shown that the radius of the contact area between the femoral head and the acetabular cup is relatively small compared with that of the femoral head and the ceramic insert thickness. Consequently, Hertz contact theory can be used to estimate the contact parameters such as the maximum contact pressure and the contact area.

Parametric quadratic programming method for elastic contact fracture analysis

A solution procedure for elastic contact fracture mechanics has been proposed in this paper. The procedure is based on the quadratic programming and finite element method (FEM). In this paper, parametric quadratic programming method for two-dimensional contact mechanics analysis is applied to the crack problems involving the crack surfaces in frictional contact. Based on a linear complementary contact condition, the parametric variational principle and FEM, a linear complementary method is extended to analyze contact fracture mechanics. The near-tip fields are properly modeled in the analysis using special crack tip elements with quarter-point nodes. Stress intensity factor solutions are presented for some frictional contact fracture problems and are compared with known results where available.

Analysis of Contact Mechanics and Lubrication in Ceramic-on-Ceramic Hip Joint Replacements

Analysis of Contact Mechanics and Lubrication in Ceramic-on-Ceramic Hip Joint Replacements

How two- and three-dimensional surface metrology data are being used to improve the tribological performance and life of some common machine elements

The use of two-dimensional (2D) and three-dimensional (3D) topography data in assessing the functional significance of manufactured surfaces has formed a useful tool to production and design engineers for many years. However, over recent years, the development of numerical contact analysis methods has allowed much more quantitative analysis of both 2D and 3D topography data to be performed. Some examples of how this has led to real improvements in the performance and life of common engineering components such as rolling element bearings and gears are presented to demonstrate the potential of such methods. At present numerical contact mechanics analysis is simply a research tool, but programs are now reaching a level of sophistication and potential to be of general use as production and design tools. It is likely that, in the near future, they will form a further, and very useful, analysis option available on future surface metrology instrument data-analysis packages.

Dynamic Contacts on Viscoelastic Films: Work of Adhesion

Dynamic mechanical contacts with nanometer to millimeter dimensions are important in scanned probe microscopy, contact mechanics analysis, ultralow load indentation, microelectromechanical systems, compact disks, biological systems, pressure sensitive adhesives, and so forth. The response of these contacts is poorly understood if they involve adhesive viscoelastic materials. We have used indentation to study contacts to styrene−butadiene latex films with a range of glass transition temperatures. Contact times were in the range 0.01−200 s and loads were in the micronewton to millinewton range. Diamond probes with Berkovich and spherical end shapes were used. Load versus displacement data showed substantial adhesion hysteresis between the loading and unloading portions. The hysteresis is at least partially due to creep as indicated by the continued increase in penetration after the start of unloading. We show that an extended Johnson−Kendall−Roberts (JKR) model due to Johnson provides a robust way to extrac...

Contact mechanics analysis of measured wheel-rail profiles using the finite element method

A tool has been developed for contact mechanics analysis of the wheel-rail contact. Using measurements of wheel and rail profiles as input, the tool is based on the finite element (FE) code ANSYS. Traditionally, two methods have been used to investigate the rail-wheel contact, namely Hertz's analytical method and Kalker's software program Contact. Both are based on the half-space assumption as well as on a linear-elastic material model. The half-space assumption puts geometrical limitations on the contact. This means that the significant dimensions of the contact area must be small compared with the relative radii of the curvature of each body. Especially in the gauge corner of the rail profile, the half-space assumption is questionable since the contact radius here can be as small as 10 mm. By using the FE method (FEM) the user is not limited by these two assumptions. The profile measurement system Miniprof was used to measure the wheel and rail profiles that were used as input when generating the FE mesh. As a test case, a sharp curve (303 m radius) in a unidirectional commuter train track used by X1 and X10 trains was chosen. The results of two contact cases were compared with the results of the Hertz analytical method and the program Contact. In the first contact case the wheel was in contact with the rail gauge corner. In the second case the wheel was in contact with the rail head. In both contact cases Hertz and Contact presented very similar results for the maximum contact pressure. For the first contact case, a significant difference was found between the FE method and the Hertz method and the program Contact in all of output data. The Hertz and Contact methods both presented a maximum contact pressure that was three times larger (around 3 GPa) than the FE solution. Here, the difference was probably due to the combination of both the half-space assumption and the elastic-plastic material model. For the second contact case, there was no significant difference between the maximum contact pressure results of the three different contact mechanics methods employed.

A Contact-Mechanics Based Model for Dishing and Erosion in Chemical-Mechanical Polishing

ABSTRACTWe present a new model for dishing and erosion during chemical-mechanical planarization. According to this model, dishing and erosion is controlled by the local pressure distribution between features on the wafer and the polishing pad. The model uses a contact mechanics analysis based on the work by Greenwood to evaluate the pressure distribution taking into account the compliance of the pad as well as its roughness. Using the model, the effects of pattern density, line width, applied down-force, selectivity, pad properties, etc. on both dishing and erosion can be readily evaluated. The model may be applied to CMP used for oxide planarization, metal damascene or shallow trench isolation.The model is implemented as an algorithm that quickly calculates the evolution of the profile of a set of features on the wafer during the polishing process. With proper calibration of the process parameters, it can be used as a tool in optimizing the CMP process and implementing CMP design rules.

Contact Mechanics Studies with the Quartz Crystal Microbalance

A quartz crystal microbalance (QCM) is used to measure the contact area between a gold-coated quartz crystal and a low-modulus elastic solid. When combined with an appropriate contact mechanics analysis, such as the well-known method of Johnson, Kendall, and Roberts, quantitative information about the adhesion of the elastic solid to the electrode surface of the quartz crystal can be obtained. We use a hemispherical, elastic gel to demonstrate that the QCM can be used to acquire contact area information directly, without visually monitoring the area of contact between the gel and the electrode surface. Provided that the area of contact is confined to the central portions of the gold electrode, a linear relationship is observed between the crystal's resonant frequency and the gel/electrode contact area. The coefficient describing this linear relationship depends on the viscoelastic properties of the gel. A simple expression for this coefficient is derived.

The effect of substrate surface roughness on the wear of DLC coatings

The effect of substrate surface roughness on the wear behaviour of diamond-like carbon (DLC) coatings deposited on M42 tool steel substrate with composite interlayers has been investigated on a ball-on-disk wear rig in dry air. After deposition, the surface roughness of the coating was approximately half of the original substrate surface roughness. While the frictional behaviour was not apparently affected, the wear rate of the coatings increased significantly with increase in the substrate surface roughness. Wear rate increased rapidly when the substrate surface roughness exceeded R a 0.93 μm. Above this substrate roughness, the dominant wear mechanism also changed from adhesion to chip/flake formation and fragmentation of the coatings. Chipping/flaking of the coatings initially occurred mainly at the tops of asperities of the surface texture. The Archard specific wear rate increased with increase in total load for coatings on the rough substrate surfaces; however, this was almost invariant with increase in load for coatings on the smoother substrate surfaces, nominally following the Archard's wear law. Contact pressure distributions over the real area of contact between the ball and the rough coating surfaces have been analysed by applying the elastic foundation model of contact mechanics. It has been shown that the contact pressures increase significantly with increase in surface roughness of the coatings. Plastic yielding is highly possible in the coatings deposited on rough substrate surfaces above R a 0.93 μm. The observed apparent effect of surface roughness on wear and wear mechanism transitions of the DLC coatings can be explained according to the contact mechanics analysis results.

Linear elastic contact of the Weierstrass profile

A contact problem is considered in which an elastic half–plane is pressed against a rigid fractally rough surface, whose profile is defined by a Weierstrass series. It is shown that no applied mean pressure is sufficiently large to ensure full contact and indeed there are not even any contact areas of finite dimension — the contact area consists of a set of fractal character for all values of the geometric and loading parameters. A solution for the partial contact of a sinusoidal surface is used to develop a relation between the contact pressure distribution at scale n − 1 and that at scale n . Recursive numerical integration of this relation yields the contact area as a function of scale. An analytical solution to the same problem appropriate at large n is constructed following a technique due to Archard. This is found to give a very good approximation to the numerical results even at small n , except for cases where the dimensionless applied load is large. The contact area is found to decrease continuously with n , tending to a power–law behaviour at large n which corresponds to a limiting fractal dimension of (2 − D ), where D is the fractal dimension of the surface profile. However, it is not a ‘simple’ fractal, in the sense that it deviates from the power–law form at low n , at which there is also a dependence on the applied load. Contact segment lengths become smaller at small scales, but an appropriately normalized size distribution tends to a limiting function at large n . † The authors dedicate this paper to the memory of Dr J. F. Archard, 1918–1989.

Investigations Into Asperity Persistence in Heavily Loaded Contacts

Experimental results are presented along the lines of the early work of Moore (1948) where a hard smooth roller is pressed into a softer rough surface to study the resulting real to apparent areas of contact and their associated local contact pressures. Results are presented for a hard steel roller deforming mild-steel and aluminum-alloy rough surface specimens. An analysis of the local contact mechanics is performed before and after indentation using a recently developed numerical elastic contact simulation method which allows local asperity contact pressures and areas to be studied in detail. The method is shown to reveal the level and distribution of pressures and asperity contact areas prevalent during the indentation process, and therefore allows the contribution of elastic and plastic load support to be quantified. The persistence of asperities during such indentation tests is discussed in terms of the pressures the asperities can support in relation to reported mechanisms of persistence. Results of subsequent sub-surface stresses are also presented and discussed in terms of how the method might be used to create an elastic-plasticdeformation model that can account for asperity persistence in future numerical contact simulation models.

Analysis of Contact Mechanics for a Circular Filamentary Brush/Workpart System

This paper addresses the contact problem associated with the filament/workpart interaction that arises during brushing processes. A discretized model of a filament within the brushing tool is developed by employing Lagrange’s equations in conjunction with special constraint equations that are appropriate for the impact and impending large displacement of a flexible fiber whose tip traverses a flat, rigid surface. This formulation leads to the identification of five nondimensional parameters which fully characterize the filament/workpart contact problem. A damping mechanism is also included which can be used for modeling complex filament interactions that arise during the actual brushing operation. Special consideration is given to examining the initial filament/workpart impact and the subsequent forces that are generated along the contact region. Initial velocity of the filament is determined by employing an inelastic impact mechanics analysis. Time-varying transient response of the filament is then obtained by employing a predictor-corrector technique in conjunction with a finite difference method. Overall brush force is computed by a superposition of filament contact forces exerted onto the workpart surface. Numerical results are reported and compared with experimentally obtained data for an actual brush/workpart system.

Contact analysis of elastic-plastic fractal surfaces

Rough surfaces are characterized by fractal geometry using a modified two-variable Weierstrass–Mandelbrot function. The developed algorithm yields three-dimensional fractal surface topographies representative of engineering rough surfaces. This surface model is incorporated into an elastic-plastic contact mechanics analysis of two approaching rough surfaces. Closed form solutions for the elastic and plastic components of the total normal force and real contact area are derived in terms of fractal parameters, material properties, and mean surface separation distance. The effects of surface topography parameters and material properties on the total deformation force are investigated by comparing results from two- and three-dimensional contact analyses and elastic and elastic-perfectly plastic material behaviors. For normal contact of elastic-perfectly plastic silica surfaces and range of surface interference examined, the interfacial force is predominantly elastic and the real contact area is approximately one percent of the apparent contact area or less, depending on the mean interfacial distance. The analysis can be easily modified to account for anisotropic fractal surfaces and different material behaviors.

Three-Dimensional Elastic-Plastic Fractal Analysis of Surface Adhesion in Microelectromechanical Systems

High adhesion is often encountered at contact interfaces of miniaturized devices, known as microelectromechanical systems, due to the development of capillary, electrostatic, and van der Waals attractive forces. In addition, deformation of contacting asperities on opposing surfaces produces a repulsive interfacial force. Permanent surface adhesion (referred to as stiction) occurs when the total interfacial force is attractive and exceeds the micromachine restoring force. In the present study, a three-dimensional fractal topography description is incorporated into an elastic-plastic contact mechanics analysis of asperity deformation. Simulation results revealing the contribution of capillary, electrostatic, van der Waals, and asperity deformation forces to the total interfacial force are presented for silicon/silicon and aluminum/aluminum material systems and different mean surface separation distances. Results demonstrate a pronounced effect of surface roughness on the micromachine critical stiffness required to overcome interfacial adhesion.

Aspects of equivalence between contact mechanics and fracture mechanics: theoretical connections and a life-prediction methodology for fretting-fatigue

We identify aspects of quantitative equivalence between contact mechanics and fracture mechanics via asymptotic matching. An analogy is invoked between the geometry of the near-tip regions of cracked specimens and that of the sharp-edged contact region between two contacting surfaces. We then demonstrate that the asymptotic elastic stress and strain fields around the rim of the contact region, as derived from classical contact mechanics analyses, are identical to those extracted from linear-elastic fracture mechanics solutions for analogous geometries. Conditions of validity of this model for contact mechanics are established by recourse to the singular fields and small-scale-yielding concepts of fracture mechanics. With this method, the geometry of the contact-pad/substrate system naturally introduces a fictitious crack length, thereby providing a physical basis to analyze contact-fatigue fracture initiation and growth. Possible extensions of this crack analogue model are then suggested, for situations where static or cyclic mechanical loads are superimposed parallel to the direction of interfacial friction, using the two-parameter fracture characterization that involves the stress intensity factor K and the non-singular T-stress, or alternatively, the J integral and the triaxiality parameter, Q. The predictions of the crack analogue model are then compared with fretting-fatigue experiments and are shown to be in agreement with a variety of independent experimental observations. A new life-prediction methodology for fretting fatigue is also proposed on the basis of the present approach.

Analysis of contact mechanics for composite cushion knee joint replacements.

Recent research in the area of cushion form bearings for total joint replacements has primarily used thin, soft, elastomeric layers with similar elastic modulus to articular cartilage, bonded to rigid substrates. These are designed to promote the body's natural lubricants to separate the articulating surfaces and prevent wear. Applications to joint replacements have revealed that the abrupt change in stiffness between the soft layer and the rigid substrate and the relatively low strength of the interface resulted in high shear stresses and debonding of the soft layer from the substrate. The approach adopted in this study is to use components with a graded modulus or composite construction. The composite construction consists of a soft compliant layer of polyurethane and a second stiffer polyurethane layer thought to be rigid enough to mechanically interlock to a metallic tibial tray. In this composite structure the deformation of the more rigid polyurethane underlay may generally influence the stress distribution and deformation in the softer upper layer and at the interface between the two materials. A simple analysis technique is presented in the present study where the composite double layer was approximated as an equivalent modulus single layer. Single layer theory, which is readily available in the literature, can then be used to determine the contact parameters, including the maximum contact pressure and the contact radius, for the composite structure. By varying the layer thicknesses and material properties of both the soft surface layer and the stiffer structural support layer, the magnitudes and locations of stresses can be controlled. Results of a parametric stress analysis are presented to assist in the selection of the most appropriate composite layers for cushion knee designs. A 4 mm thick surface layer with an elastic modulus of 20 MPa and a 4 mm thick structural support layer with an elastic modulus of 1000 MPa were considered suitable for this application.

THREE-DIMENSIONAL THERMOELASTIC CONTACT BETWEEN TWO PLATES WITH BOLTED JOINTS

This paper presents a three-dimensional finite element procedure for the thermoelastic contact problem of two plates with bolted joints. The thermal contact conductance at the interface between two plates, which is a known function of contact traction, is considered in heat transfer analysis. A rigorous and efficient contact mechanics analysis between two plates and bolted joints is also achieved. A bolted lap joint in two 6061-T6 aluminum alloy plates subjected to a heat transfer, where on one side of a joint heat is generated and the other side acts as a heat sink, is selected as the research problem. The distribution of temperature and contact traction between the two-plate interface is also shown. The results computed by the present approach show a good agreement with the referenced experimental data. The present work should aid the design of many mechanical systems.

Contact Mechanics of Ultrahigh-Molecular-Weight Polyethylene for Artificial Knee Joint

To investigate the wear mechanism of an ultrahigh-molecular-weight polyethylene (UHMWPE) for an artificial knee joint, the pin-on-disk-type wear test and the numerical analysis of contact mechanics of the UHMWPE were performed. In this analysis, to calculate the cyclic deformation of the UHMWPE, a constitutive equation for cyclic plasticity was used. In the initial stage of deformation, the UHMWPE was deformed only plastically ; beyond this stage, however, wear of the UHMWPE progressed rapidly with weight loss. In this initial stage, shear stress and equivalent plastic strain were accumulated by cyclic loading on the contact surface of the UHMWPE and it was expected that the microcracks that create wear particles would be generated on the surface.