Contact analysis of three-dimensional rough surfaces under frictionless and frictional contact

A methodology for surface and sub-surface stress calculation of nominally flat on flat rough surface contact has been developed. This methodology is applicable for both large area contact (Hertzian contact) and small area of asperity contact (point load contact) with and without surface friction. A total of nine rough surfaces are generated by the computer with specified standard deviation of surface heights, σ, of 0.3, 1.0 and 3.0 nm, and correlation length, β^*, of 0.1, 0.5 and 0.9 μm. Under the typical applied load at the magnetic head slider-disk interface, small numbers of contact points are obtained and the deformation is purely elastic. Since these contact points are scattered and isolated, asperity contact behaves like point load contact. As β^* becomes larger, more adjacent points will be in contact at a certain contact spot and this is especially true at small σ. All the cases of flat on flat rough surface contact yield maximum von Mises stress on and near the surface at both frictionless and frictional contacts; no local maximum occurs in the sub-surface. In general, the friction effect in the vicinity of contact point is to increase the stress magnitude, while outside this region it also alters the stress distribution. For a surface of small β^* and large σ at high load of 1000 times of the nominal pressure at the head-disk interface, the contact pressure reaches the hardness at a few contact points and plastic deformation takes place in the near surface.     

The elastic contact of a rough surface

The elastic contact of an isotropically rough surface with a plane is treated by approximating the summits of a random process model by paraboloids with the same principal curvatures and applying the classical Hertzian solution for their deformation. The errors in this approximation are computed in terms of the separation and of a bandwidth parameter α. Load and real contact area are derived as functions of separation. For large separation the fractional area of real contact is found to be half the bearing area fraction and the separation may be eliminated to give direct porportionality between load and area. For all separations the load is approximately proportional to the contact area. The constant of proportionality depends only on the Hertzian elastic modulus and the profile absolute mean slope. Experimental measurements of the latter and of α for a variety of surfaces show little variation in either, and the measured values of α are within the range of applicability of the model. The theory is critically compared with existing theories.     

Effect of fluid lubricant on the contact characteristics of rough elastic bodies in compression

The contact problem of the compression of an elastic half-space and a periodic indenter, which models the microirregularity of the mated bodies, when the immediate contact-free space between the periodically repeated projections of the indenter is filled with a compressible liquid (lubricant) has been considered. The general solution of the problem, clearly formulated for the case of a plane deformation, has been obtained. A periodic sinusoidal profile of the irregularity has been considered in detail and final solution formulae for this profile have been derived: these formulae were used to carry out calculations for and to analyse various elastic half-space materials and lubricants. Considerations have been expounded which allow this problem to be considered in the special case when the microirregularities on the rough surface can be modelled by for example ellipsoids or spheres.     

粗糙表面滑动摩擦接触模型研究的进展

对近年来国内外粗糙表面模型的进展进行了概述,根据粗糙表面模型类型的不同,分为粗糙表面和平面接触模型以及双粗糙表面接触模型,在各自模型中按照静载和滑动接触类型的研究进展进行表述,并提出了一些目前研究中遇到的热力耦合的问题以及将来双粗糙分形表面模型的发展.     

Contact of elastic bodies with complex frictional surfaces

A general method is outlined for determining the stress and strain in the contact of bodies with surfaces of variable curvature. A simplified solution is presented for the contact of parallel noncircular cylinders. The results are compared with experimental data and known results for circular cylinders.     

工程粗糙表面接触摩擦热力学研究进展

对近年国内外工程粗糙表面微观热力学的数值模拟的进展作了综述,介绍了工程粗糙表面的表征、接触模型、表面温升的计算模型与方法的研究现状,并提出了当前相关研究中所遇到的问题及今后研究发展方向.     

Metal transfer in the frictional contact of a rough hard surface

The frictional behaviour between a hard rough surface and a soft smooth surface was examined under lubricated and unlubricated conditions. Transfer of soft metal to hard asperities in contact with it caused significant changes in the shape, size and height distributions of the asperities. Thus metal transfer reduced the effect of the initial surface roughness of the hard metal on friction.     

The contact behavior of elastic/plastic non-Gaussian rough surfaces

A three-dimensional contact analysis was conducted to investigate the contact behavior of elastic--perfectly plastic solids with non-Gaussian rough surfaces. The effect of skewness, kurtosis and hardness on contact statistics and the effect of skewness and kurtosis on subsurface stress are studied. Non-Gaussian rough surfaces are generated by the computer with skewness, Sk, of −0.3, 0.0 and 0.3, and kurtosis, K, of 2.0, 3.0 and 4.0. Contact pressures and subsurface stresses are obtained by contact analysis of a semi-infinite solid based on the use of influence functions and patch solutions. Variation of fractional elastic/plastic contact area, maximum contact pressure and interplanar separation as a function of applied load were studied at different values of skewness and kurtosis. Contact pressure profiles, von Mises stresses, tensile and shear stress contours as a function of friction coefficient were also calculated for surfaces with different skewness and kurtosis. In this study, it is observed that surfaces with Sk = 0.3 and K = 4 in the six surfaces considered have a minimum contact area and maximum interplanar separation, which may provide low friction and stiction. The critical material hardness is defined as the hardness at which severe level of plastic asperity deformation corresponding to the Greenwood and Williamson’s cut-off A _plastic/A _real = 0.02 occurs for a given surface and load condition. The critical material hardness of surfaces with Sk = 0.3 and K = 4 is higher than that of other surfaces considered.     

On frictional effects at inelastic contact between spherical bodies

Normal inelastic contact between spherical bodies is examined theoretically and numerically. The analysis is focused on viscoplastic material behaviour. In particular the effect of Coulomb friction is analysed in some detail, both regarding global and field variables. It is shown that the solution to the problem of contact between two deformable spherical bodies is provided by the solution of the fundamental problem of indentation of a viscoplastic half-space by a rigid sphere. The indentation analysis is based on self-similarity and cumulative superposition of intermediate flat die solutions as outlined in detail in a previous study by Storåkers et al. (International Journal of Solids and Structures 1997;34:3061–83). The results show that frictional effects, when global properties such as the contact area and the mean contact pressure are at issue, will only be of importance at close to perfectly plastic material behaviour. Even in such circumstances the difference between values given by the solutions for frictionless and for full adhesive contact is no more than approximately 10%. Accordingly, it can be concluded that frictional effects are essentially negligible, when, for example, material characterization of viscoplastic solids by Brinell indentation is of interest. The situation is, however, quite different when field variables are at issue. In this case, stress and strain fields can be substantially influenced by friction with possible implications for features such as crack initiation and crack growth.     

Models of adhesive contact between rough elastic solids

Adhesion of rough elastic solids is considered. Roughness is simulated by the Winkler–Fuss nonlinear elastic layer, which can be stretched. Mechanical properties of the layer are determined by statistical theories of adhesive contact between nominally flat rough surfaces. The contact of solids is described by the nonlinear boundary integral equations with non-monotonic operators, whose solutions determine reduction of effective thickness of the rough layer, nominal contact stresses, nominal contact regions and relation between applied force and approach of solids. The theoretical background and numerical implementation of the models are given. Both a full model and its simplified version are analyzed.     

Mechanisms of elastic contact and friction between rough surfaces

The mechanisms of elastic contact and friction between two rough surfaces were analysed, assuming that the surface asperities were spherical, at least near their summits, and that they contacted elastically. It was found that the real contact area and the number of contact spots are approximately proportional to the load, whereas the mean area of contact spots and the mean pressure at the contact areas are almost independent of load. The frictional force F is almost equal to sA_r, where s is the shearing strength at the contact area and A_r is the real contact area. The experimental results using Pyrex glass specimens agreed within experimental limits with the theoretical results.     

Contact deformation of finite bodies initially in linear contact

A method is developed for determining the total contact deformation of two elastic bodies that are initially in linear contact. The example considered is the interaction of a roller and plate subject to a distributed force.     

On the elastic solution of frictional contact problems using variational inequalities

This article is devoted to the development and implementation of a variational inequalities approach to treat the general frictional contact problem. Unlike earlier studies which adopt penalty methods for the solution of the corresponding variational inequalities, the current investigation uses quadratic programming and Lagrange's multipliers to solve the frictional contact problem and identify the candidate contact surface. The proposed method avoids the use of user-defined penalty parameters, which ultimately govern the convergence and accuracy of the solution. To establish the validity of the method, a number of test cases are examined and compared with existing solutions where penalty methods are employed.     

An elastic approach to rough contact with asperity interactions

A simple static elastic contact model is developed to verify and to extend the generalization proposed in an earlier study. A direct comparison is also given with a recent mathematical model devised by Kalker: this method is seminumerical and requires discretization of the domain as our problem is solved using an integral formulation of the plane theory of elasticity. The contact zones are dependent, so interaction between neighbouring asperities is possible.     

Static contact under load between nominally flat surfaces in which deformation is purely elastic

In considering the contact between two rough surfaces, an asperity-based model has been obtained by applying the most general Hertzian equations for elastic deformation to the random surface model of Longuet-Higgins. For a given separation, general formulae for the expectations and variances of the load and real contact area and for the mean number of contacts are given, whilst for the variance of the number of contacts an upper bound has been derived. The formulae, involving analytically intractable integrals, have been evaluated in a special case by Monte Carlo techniques.     

Limits of applicability of elastic contact models of rough surfaces

Recent stochastic models for analyzing the contact of rough surfaces assume that the asperities are microhertzian, i.e. that they can be approximated as second-order surfaces in the vicinity of contact points, and that the asperities deform elastically. Using a plane strain solution from the literature for a sinusoidally corrugated half-space, the range of validity of these assumptions is shown to be related to the mean square surface slope and the macrocontact pressure. By extension to random surfaces characterized by a one-dimensional spectral density function an interval on the surface spatial frequency is found over which the asperities deform elastically but without completely flattening. A numerical example is given.     

Mechanics of contact approach of elastic bodies in Hertz problem

A method for determining the approach of elastic bodies with initial line contact on the basis of Hertz theory is proposed, and formulas for finding the approach are obtained. A theoretical proof of the fact that, if the materials of the bodies are the same, the value of plates’ approach does not depend on the radius of a roller clamped between them is given. It is shown that the approach depends on the thickness of the plate. The result is in satisfactory agreement with experimental data presented in the literature. A problem on deformation of cylinders with parallel axes is solved by the Belyaev method.     

An elastic–plastic contact model of ellipsoid bodies

A theoretical model for the elastic–plastic contact of ellipsoid bodies is presented in this paper. Relation of the contact parameters, such as the mean contact pressure, the contact area and the contact load as a function of the contact interference are modeled in the three different contact regimes: elastic, elastic–plastic and fully plastic. The model is verified by experimental results and is compared with published theoretical models. Very good agreement between the present model and the experimental results are found compared to the prediction of the other contact models.     

Analysis of static and dynamic frictional contact of deformable bodies including large rotations of the contact surfaces

The numerical techniques are presented to solve the static and dynamic contact problems of deformable bodies having large rotations of the contact surfaces. The contact conditions on the possible contact surfaces are enforced by using the contact error vector, and an iterative scheme similar to augmented Lagrange multiplier method is employed to reduce the contact error vector monotonically. For dynamic contact problems using implicit time integration, a contact error vector is also defined by combining the displacement, velocity, and acceleration on the contact surface. The suggested iterative technique is implemented toABAQUS by using theUEL subroutineUEL. In this work, after the computing procedures to solve the frictional contact problems are explained, the numerical examples are presented to compare the present solutions with those obtained byABAQUS.     

Asperity micro-contact models as applied to the deformation of rough line contact

Different statistical micro-contact models including Greenwood–Williamson (GW), Chang–Etsion–Bogy (CEB), Zhou–Maietta–Chang (ZMC), Kogut–Etsion (KE) and Jackson–Green (JG) are employed together with the bulk deformation of the bounding solids to predict dry rough line-contact characteristics such as the apparent pressure profile, contact width and real area of contact. The approach involves solving the micro-contact models and separation formulas simultaneously. Comparison of different contact models reveals that the use of elastic–plastic micro-contact models predicts a lower maximum normal pressure and a greater contact width and real contact area compared to the GW model. Further, based on the results of numerical simulations, useful relationships are provided for the prediction of the maximum contact pressure, contact width, real area of contact and pressure distribution.