Plastic deformation in rough surface line contacts—a finite element study

The paper describes an elastic-plastic finite element (EPFE) analysis of line contact between a cylinder and rigid plane using commercial software. The range of loading demonstrates the transition from purely elastic to fully plastic contact behaviour, revealing the residual deformations and stress fields upon unloading. A multiple contact configuration was analysed in the form of sinusoidal roughness. Results obtained under elastic conditions were validated by comparison with theoretical solutions. This model was extended by replacing the sinusoidal surface with a real roughness profile. Modelling multiple contacts indicates the influence of adjacent surface “asperities” on contact pressure and residual stress distributions.     

工作参数对接触式机械密封端面接触特性的影响

为研究和掌握接触式机械密封端面接触特性,通过模拟计算分析了工作参数对其特性的影响.结果表明,在密封端面间真实接触面积中,弹性变形微凸体接触面积所占比例最大,塑性变形微凸体接触面积所占比例最小;随着弹簧比压的增大,弹性接触面积比近似呈线性增大,弹塑性接触面积比和塑性接触面积比近似呈线性减小;随着密封介质压力的增大,弹性接...     

Validation of a simplified numerical contact model

Surface roughness tends to have a significant effect on how loads are transmitted at the contact interface between solid bodies. Most numerical contact models for analyzing rough surface contacts are computational demanding and more computationally efficient contact models are required. Depending on the purpose of the simulation, simplified and less accurate models can be preferable to more accurate, but also more complex, models. This paper discusses a simplified contact model called the elastic foundation model and its applicability to rough surfaces. The advantage of the model is that it is fast to evaluate, but its disadvantage is that it only gives an approximate solution to the contact problem. It is studied how surface roughness influences the errors in the elastic foundation solution in terms of predicted pressure distribution, real contact area, and normal and tangential contact stiffness. The results can be used to estimate the extent of error in the elastic foundation model, depending on the degree of surface roughness. The conclusion is that the elastic foundation model is not accurate enough to give a correct prediction of the actual contact stresses and contact areas, but it might be good enough for simulations where contact stiffness are of interest.     

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.     

渗氮钢粗糙表面的弹塑性接触研究

利用弹塑性有限元和单纯形法求解弹塑性接触模型，分别模拟了屈服强度呈梯度变化的渗氮钢、未经处理的匀质材料和硬涂层材料粗糙表面的弹塑性接触行为。与未经处理的匀质材料相比，渗氮钢可承受更大接触载荷。在相同载荷作用下，渗氮钢表面粗糙峰接触面积较小，平均间距较大，接触体内材料不易发生屈服，从而显著提高接触性能。和硬涂层材料相比，渗氮钢接触体内等效von Mises应力分布平缓，没有应力突变。最后讨论了渗氮层和硬涂层的厚度对粗糙表面接触特性的影响。     

Photoelastic visualization of contact phenomena between real tribological surfaces, with and without sliding

The design, construction and operation of a machine for visualizing real contact interfaces and testing sliding wear is described. The bodies that form the interface are both opaque—the slider is a carbon graphite sample (National Electrical Carbon Company brush grade 634) and the rotor surface is copper. The visualization technique uses contact indentation stresses and photoelasticity to generate optical fringes (shadows) directly beneath the contact interface. The resultant fringes indicate the size and location of the islands of real contact that exist within the apparent contact region. Resolution is sufficient to distinguish two neighbouring millimetre-sized contacts. For calibration and comparison purposes, photoelastic pictures of sharp graphite pencil points and hard plastic spheres of various diameter indenting the copper slip ring surface are presented. Photographs of photoelastic images of contact interfaces between an opaque carbon sample sliding against an opaque copper slip ring are also presented. Photographs are presented that show the formation of concentrated contact (and possible evolution to thermal mounding) on the carbon slider surface. Collective data from other photographs measures the relative occurrence of concentrated contact and suggests operating and surface conditions that can discourage concentrated contact and formation of thermal mounds.     

A novel test rig for in situ and real time optical measurement of the contact area evolution during pre-sliding of a spherical contact

An experimental test rig was developed in order to investigate elastic–plastic single micro-spherical contact under combined normal and tangential loading. This novel apparatus allows in situ and real time direct optical measurement of the real contact area (RCA) evolution in pre-sliding. It also allows relative displacement measurements under very low rates of tangential loading (down to 0.01 N/s) to capture accurately the fine details at sliding inception. This is achieved by piezoelectric actuation in closed loop feedback control in addition to synchronization with data and image acquisition to obtain real time measurement. The RCA measurement is realized by direct optical observation technique, whereas two different image processing algorithms were implemented for the elastic and the elastic–plastic contact regimes. The various features and capabilities of the test rig are presented along with some preliminary experimental results of RCA and friction behavior to assess its performance.     

Temperature Analysis in Lubricated Simple Sliding Rough Contacts

A temperature analysis of dry sliding fully plastic contact is extended to calculate the asperity temperatures between a sliding lubricated rigid smooth plane and a stationary elastic rough surface. First, surface roughness is generated numerically to have a Gaussian height distribution and a bilinear autocorrelation function. Lai and Cheng's elastic rough contact computer program is then used to determine the asperity contact loads and geometries of real contact areas. Assuming different frictional coefficients for shearing the lubricant film at the noncontact areas, shearing the surface film at the asperity contacts and shearing the oxide film as the asperity temperature exceeds a critical temperature, asperity temperature distributions can be calculated. Eight cases in Durkee and Cheng's scuffing tests of lubricated simple sliding rough contacts are simulated by using 20 computer-generated rough surfaces. The results show that scuffing is correlated to high-temperature asperities which are above the material-softening temperature.     

基于分形理论的滑动摩擦表面接触力学模型

依据分形理论,考虑微凸体变形特征及摩擦作用的影响建立滑动摩擦表面接触力学模型。采用一个三次多项式来表达弹塑性变形微凸体的接触压力与接触面积的关系,从而满足在变形状态转变临界点处的微凸体接触面积与接触压力转化皆是连续和光滑的条件。推导出滑动摩擦表面临界弹性变形微接触面积、临界塑性变形微接触面积、量纲一真实接触面积的数学表达式。理论计算结果表明,表面形貌一定时,真实接触面积随着载荷的增大而增大;载荷一定时,真实接触面积随着特征尺度系数的增大而减小,随着分形维数的增大先增大后减小;当表面较粗糙时,摩擦因数对真实接触面积的影响很小;随着表面光滑程度的增大,摩擦因数对真实接触面积的影响增大,真实接触面积随着摩擦因数的增大而增大,特别是当摩擦因数较大时,真实接触面积增大的幅度也较大。接触力学模型的建立,为研究滑动摩擦表面间的摩擦磨损性能提供了依据。     

Multi-phase materials and their surface contact behaviour with reference to friction and wear

The recent advances in the development of composite surface coatings and the increasing tribological application of multi-phase materials in engineering require a more rigorous treatment of the problem of the contact of surfaces of such materials. This paper considers the surface contact behaviour of materials having contrasting physical properties and the results presented quantitatively identify the boundaries of three contact regimes, purely elastic, elastic/plastic and predominantly plastic. The treatment also offers a method for determining the real areas of contact and corresponding supported loads associated with the modes of deformation of each phase. This is particularly important for predicting the friction and wear characteristics of multi-phase materials.     

Analysis of friction contact between wavy surfaces

The objective of the present work is to study the tribological behaviour of two contact bodies coated with solid lubricant films. The suggested model relaxes two restrictions of the classical Hertz theory by introducing the friction effect and the elastic-plastic behaviour as irreversible effects.The analysis is based on the automated direct procedure developed by Mahmoud and Salamon and an extension of that model to deal with plastic flow and Coulomb friction between contact surfaces. The proposed model is applied to a typical example of a wavy surface pressed against a flat strata. Both the wavy surface and the flat strata are coated with a hard lubricant film. The history of the advancing contact and the initiation of the plastic flow are determined through the procedure of the model.     

Development of plastic zones and residual stress in elasto-plastic contact problems with stress singularities in elastic range

Stress singularities appear in such elastic contact problems as a plane indenter compressing a semi-infinite body, or the axisymmetric case of a turbine disc shrunk onto a shaft. The stress is infinite at the edge of the corner of the indenter and the disc as well as in neighbouring areas of the semi-infinite body and the shaft.In this paper the complex investigation of the distributions of plastic zones, deformations, pressure and residual stress has been presented for plane indenters of different shapes being in elasto-plastic contact with semi-infinite bodies. Different strain-hardening characteristics of the material, different yield criteria and states of stress/strain have been considered.The aim of the investigation is to find an answer to the question, what happens to the stress singularity, which appears in the elastic solution? The considered problem is of interest from the cognitive point of view and is of real importance in engineering practice.     

Shear deformation of voids with contact modelled by internal pressure

The behaviour of voids in a ductile material subject to simple shear or to a shear-dominated stress state is analyzed numerically. Here the stress triaxiality is so low that instead of void volume growth to coalescence there is void closure leading to micro-cracks that rotate in the shear field. At some stage of the deformation, the void surfaces will come in contact so that sliding with or without friction will start to occur. To avoid problems with strong mesh distortion in the large strain field around the deforming void and with mesh resolution at the tip of the crack, an internal pressure is applied as an approximate representation of void surfaces pressed together in frictionless sliding, and also remeshing is applied. This micromechanical model for a strain hardening elastic–plastic material shows that a maximum overall shear stress is reached, at which localization of plastic flow occurs, leading to final failure in the material.     

Modeling of fretting wear evolution in rough circular contacts in partial slip

This paper presents a numerical model that maps the evolution of contact pressure and surface profile of Hertzian rough contacting bodies in fretting wear under partial slip conditions. The model was used to determine the sliding distance of the contacting surface asperities for one cycle of tangential load. The contact pressure and sliding distance were used with Archard's wear law to determine local wear at each surface asperity. Subsequently, the contact surface profile was updated due to wear. The approach developed in this study allows for implementation of simulated and/or measured real rough surfaces and study the effects of various statistical surface properties on fretting wear. The results from this investigation indicate that an elastic–perfectly plastic material model is superior to a completely elastic material model. Surface roughness of even small magnitudes is a major factor in wear calculations and cannot be neglected.     

The behavior of an elastic-perfectly plastic sinusoidal surface under contact loading

The goal of this paper is to provide the foundation for an analysis of contact between elastic-plastic solids, whose surface roughness is idealized with a Weierstrass profile. To this end, we conduct a parametric study of the plastic deformation and residual stress developed by the two-dimensional contact between a flat, rigid platen and an elastic-perfectly plastic solid with a sinusoidal surface. Our analysis shows that the general characteristics of the deformation can be characterized approximately by two parameters: α = a/λ, where a is the half-width of the contact and λ is the period of the surface waviness; ψ = E^*g/σ_Yλ, where E^* and σ_Y are the effective modulus and yield stress of the substrate, respectively, and g is the amplitude of the surface roughness. Depending on the values of these parameters, we identify eight general types of behavior for the asperity contacts: (a) elastic, elastic-plastic or fully plastic isolated Hertz type contacts; (b) elastic, or elastic-plastic non-Hertzian isolated contacts; and (c) elastic, elastic-plastic or fully plastic, interacting contacts. Relationships between contact pressure, contact size, effective indentation depth and residual stress are explored in detail in each regime of behavior. Implications on rough surface contacts are discussed.     

Micro-contact analysis for the initial contact in nanoindentation tests

The force-depth behavior of initial contact between a Berkovich indenter and S45C steel specimens has been examined. The indenter is considered as a rigid sphere with a radius of 300 nm since the blunt tip is dominant under initial contact. The S45C steel specimens were prepared to have different surface characteristics. The specimen surface profile was decomposed by Fourier cosine series; then the statistical evaluation for force and area of micro-contact was proposed. The influence of surface roughness on the real contact area and thus the contact pressure arising in the indentation test can be investigated from the proposed analyses. The force-depth responses obtained by the proposed method revealed good agreement with the experimental results for the prepared specimens with their different surface characteristics. The evaluated results of the force fractions in the elastic, elastoplastic, and plastic deformation regions showed that the S45C steel specimens had fully plastic deformation under the initial contact load of 5 μN. The average values of real contact pressure evaluated by the current method rapidly reached the hardness value. Through the proposed method, the dominant radii of summits were evaluated and their relation to the indentation depth was demonstrated.     

Mechanics of discrete contact

An approach based on the method of averaging is proposed to solve the discrete contact problems for bodies with given macro- and microgeometry. It divides the problem analysis into two scales of sizes. In macroscale the nominal (continuous) contact region is considered, and the integral equation to determine the nominal contact pressure is reduced. This equation includes the additional displacement function which depends on the nominal contact pressure and the microgeometry parameters at the fixed point of the nominal contact region. This function can be determined from the consideration of the discrete contact problem in the microscale for the particular models of surface microgeometry. The periodic contact problem for an elastic half-space has been solved to find the additional displacement function taken into account the interaction between contact spots. The analysis of the system of equations obtained for the periodic problem makes it possible to state the principle of localization which is used to solve the problems in micro- and in macroscale. The influence of the microgeometry parameters on the real and nominal contact characteristics is analyzed.     

Contact and thermal analysis of transfer film covered real composite-steel surfaces in sliding contact

For composite-steel surfaces in sliding contact an anisotropic numerical contact algorithm has been developed to study the ‘layer type’ problems. An FE contact analysis was applied to evaluate the contact parameters (real contact area, contact pressure distribution and normal approach). The contact temperature rise was determined by using both a numerical thermal algorithm for stationary and a FE transient thermal technique for ‘fast sliding’ problems.The effect of a continuous transfer film layer (TFL), that had built up during wear of the PEEK matrix material on the steel counterpart, was considered. Its thickness was assumed to be t=1 μm, and its material properties were that of PEEK at room temperature or, in the case of frictional heating, at a temperature of 150°C (i.e. above the glass transition temperature of the polymer matrix).Results are presented for a spherical steel asperity, with/without TFL, sliding over composite surfaces of different fibre orientation, and in addition, for real composite-steel surfaces (based on measured surface roughness data) in sliding contact. The TFL has an effect on the contact parameters especially at higher operating temperatures (i.e. 150°C); it results in the production of a larger contact area and a lower contact pressure distribution. The contact temperature rise is clearly higher if a TFL is present. Due to the low thermal conductivity of PEEK, the TFL is close to the melting state or it even gets molten within a small vicinity of the contact area.     

A study of the effect of radial clearance,contact angle and contact pressure on the wear of boundary-lubricated bearing bronze

In the course of work directed towards the development of an international standard on the measurement of the tribological properties of bearing materials, the influence of radial clearance, contact angle and contact pressure on the wear of boundary-lubricated bearing bronze Cu5Sn5Pb5Zn in contact with plain carbon steel rings was studied. It was found that under all experimental conditions wear proceeds via the build-up of a thin transferred layer of bronze on the mating steel surface. Neither wear rate nor process surface roughness depend on radial clearance or contact angle. However, the friction-time diagram is found to react to a change in test conditions. From such diagrams the time necessary to attain equilibrium friction can be found. It is shown that this time bears no relation at all to the time needed to adapt the stationary bronze specimen to the radius of the mating steel ring. It is also concluded that the contact pressure does not influence the wear process.     

Elastic and elastic-perfectly plastic analysis of an axisymmetric sinusoidal surface asperity contact

ABSTRACT

Closed-form finite-element empirical models are available for elastic and elastic–plastic spherical and sinusoidal contact. However, some of these models do not consider the effect of interaction with adjacent asperities or require extensive numerical resources because they employ a full 3-D model. Therefore this work has analysed and quantified the behaviour of an elastic and elastic- perfectly plastic axisymmetric sinusoidal surface in contact with a rigid flat for a wide range of material properties and different values of the amplitude to wavelength ratio from initial to complete contact (high load). The numerical results agreed well with the Hertz model and the Jackson–Green elastic–plastic spherical contact model at low loads. Empirical equations for elastic and also elastic-perfectly plastic cases are formulated for the contact pressure, contact area and surface separation. From the current analysis, it is found that it is not any single parameter, but different combinations of material properties and surface roughness that govern the whole contact behaviour. The critical value of the amplitude of the sinusoidal asperity below which it will deform completely elastically from initial to complete contact is established. At low values of amplitude normalized by the critical amplitude, it was found that the contact behaved similar to a spherical contact, with the average pressure (hardness) always remaining lower than three times the yield strength. However, at higher values the average pressure increased toward a value as high as six times the yield strength at complete contact. All of these equations should be useful in rough surface contact modelling, lubrication analysis, electrical contact modelling and in many other applications.