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.     

Contact Mechanics of Laser-Textured Surfaces

We study numerically the contact mechanics of a flat and a curved solid. Each solid bears laser-induced, periodic grooves on its rubbing surface. Our surface topographies produce a similar load and resolution dependence of the true contact area as nominally flat, but randomly rough, self-affine surfaces. However, the contact area of laser-textured solids depends on their relative orientation. The estimated true contact areas correlate with kinetic friction measurements.     

Effects of Interfacial Strength and Roughness on the Static Friction Coefficient

A finite element model is used to simulate sliding inception of a rigid flat on a deformable sphere under combined normal and tangential loading. Sliding inception is treated as the loss of tangential contact stiffness under combined effects of plasticity, crack propagation and interfacial slip. Energy dissipation distribution is used to quantify the relative contribution of these mechanisms on the increased compliance during tangential loading. Materials with different strength and toughness properties, and varying local interface conditions ranging from fully adhered to finite friction, are studied to relate variations in plastic deformations, crack and slip to the sliding inception. For fully adhered contact condition, crack and fracture toughness have no effect on sliding inception, with plasticity, the dominant failure mechanism. A measure of recoverable strain (yield strength to Young’s modulus ratio) is found to be the most influential parameter in sliding inception. Interfacial slip is expectedly the dominant mechanism for sliding inception for lower coefficient of friction, modeling lubricated contacts. Interplay of plasticity and interfacial slip is found to govern the onset of sliding for higher local friction coefficients. Furthermore, the single asperity results are incorporated in a statistical model for nominally flat contacting rough surfaces under combined normal and tangential loading to investigate the stochastic effects due to surface roughness and material property uncertainties. The results show that the static coefficient of friction strongly depends on the normal load, material properties, local interfacial strength and roughness parameters.     

A statistical model of elasto-plastic asperity contact between rough surfaces

This work models statistically elasto-plastic contact between two rough surfaces using the results of a previous finite element analysis of an elasto-plastic sphere in contact with a rigid flat. The individual asperity contact model used accounts for a varying geometrical hardness effect that has recently been documented in previous works (where geometrical hardness is defined as the uniform pressure found during fully plastic contact). The contact between real surfaces with known material and surface properties, such as the elastic modulus, yield strength, and roughness are modeled. The asperity is modeled as an elastic-perfectly plastic material. The model produces predictions for contact area, contact force, and surface separation. The results of this model are compared to other existing models of asperity contact. Agreement exists in some cases and in other cases it corrects flaws, especially at large deformations. The model developed by Chang, Etsion and Bogy is also shown to have serious flaws when compared to the others. This work also identifies significant limitations of the statistical models (including that of Greenwood and Williamson).     

用于缺陷检测的指尖型大面积光学式触觉传感器设计与性能研究

对各种具有复杂曲面及平面的材料进行缺陷检测的过程中,传统触觉传感器存在探测面积小、探测效率低等缺点。针对这些问题设计并制备了一种指尖型大面积光学式触觉传感器,并将该传感器应用于多种材料的表面缺陷探测中。所设计的传感器外形类似人类手指尖端,同时具备指型曲面和平面双接触面,可满足各种复杂接触面的探测需求。传感器中设计了微型传动装置用于带动摄像头转动以提高成像质量,并通过转动采集多张图像使用APAP图像拼接算法对其进行拼接,增大单次探测有效面积。通过模拟多种材料表面缺陷并制作触觉图像数据集,采用DeepLabv3模型对其进行训练。实验结果表明,在单次采集的情况下,有效探测面积达到16.3 cm²,模型通过训练MIoU达到91.2%,可实现多种材料复杂曲面和平面的缺陷探测。     

Application of spherical indentation mechanics to reversible and irreversible contact between rough surfaces

A probabilistic model for the deformation mechanics of the interface between randomly rough metal surfaces, which is geometrically and mechanically more realistic than previous models, is derived and numerically evaluated. The model is based on the premise that the contact of two nominally plane engineering surfaces is in general equivalent to loading their sum against a smooth plane. The “sum surface” is assumed to be Gaussian and isotropic; thus the height and curvature of its peaks are correlated random variables. By using an idealized peak shape which is paraboloidal only at its vertex, the surface height distribution of the population of peaks is also made Gaussian. The upper load limit of the model is estimated, beyond which the microcontacts can no longer be assumed to be geometrically discrete and mechanically independent. Each microcontact is assumed to grow by mutual spherical indentation, thus enabling the entire deformation range, from Hertzian elastic to fully plastic, to be described by previously determined empirical functions. A two-stage linear/power law stress-strain curve is assumed. By summing over all microcontacts the total contact area and load are obtained as functions of the separation of the mean surfaces. For elastic deformation both normal loading and sliding friction are treated. For plastic flow two cases are considered: (1) identical materials; (2) one surface remains elastic. The mechanics of unloading are also investigated. After enough microcontacts have yielded to cause significant deviation from totally elastic behavior, the contact mechanics depend principally on the strain hardening exponent, the ratio of the yield stress to the Young's modulus, and the measurable ratio of the mean peak radius to the r.m.s. height of the sum surface.     

On the Validity of the Method of Reduction of Dimensionality: Area of Contact, Average Interfacial Separation and Contact Stiffness

It has recently been suggested that many contact mechanics problems between solids can be accurately studied by mapping the problem on an effective one-dimensional (1D) elastic foundation model. Using this 1D mapping, we calculate the contact area and the average interfacial separation between elastic solids with nominally flat but randomly rough surfaces. We show, by comparison to exact numerical results, that the 1D mapping method fails even qualitatively. We also calculate the normal interfacial stiffness K and compare it with the result of an analytic study. We attribute the failure of the elastic foundation model to the incorrect treatment of the long-range elastic coupling between the asperity contact regions.     

Analysis of plane and rough contacts, subject to a shearing force

We analyse the surface traction conditions induced in plane contact between two bodies whose surfaces are rough. It is assumed that the roughness may be idealised by a surface of regularly spaced cylindrical “bumps”, and the overall geometry may be in the form of a cylinder, flat ended punch or wedge. The stick-slip regime experienced by each individual asperity contact is found, and hence it is shown how the applied shearing force produces concentrated regions of surface damage. Conditions for crack initiation are then discussed, and compared with equivalent results found for nominally smooth contacts.     

On the Relation of Load to Average Gap in the Contact Between Surfaces with Longitudinal Roughness

A computer simulation model for the contact between longitudinally-oriented rough surfaces has been formulated. This model closely duplicates the actual surf ace contact deformation behavior by taking into account the elastic interactions between the asperities. There were no assumptions made about the shapes, or any deformation behavior of the asperities, except for their obeying the laws of elasticity. The plastic deformations on the high asperity peaks were taken into account by setting a ceiling on their contact pressures at the material hardness value. The simulations used real surface profiles which were digitized from unworn circumferentially ground steel surfaces. Each pair of these profiles was mathematically combined to form an equivalent rough profile pressing against an infinitely rigid flat and having the appropriately adjusted elastic modulus. A total of 28 different pairs of profiles were used in the simulations. Each contacting pair was subjected to 30 different load levels and the local contact pressures and deformations were calculated. The contact simulations yielded some important mathematical relationships between parameters, such as the real area of contact, average gap, and average asperity load through statistical curve fitting. Two analytical functions were generated to relate the average load to average gap and the real area of contact to load.     

双粗糙平面法向接触建模方法的有限元对比分析

基于统计学方法,Greenwood和Tripp(GT模型)提出双粗糙平面法向接触(双粗模型)可以等效为单粗糙平面与刚性平板之间的接触(单粗模型),但这种等效处理缺乏对接触应力场分析以及材料硬化的考虑。为进一步研究GT模型,基于高斯粗糙表面数字化表征,通过控制自相关长度和滤波方法,得到双粗糙平面及其等效单粗糙平面;借助有限元软件ABAQUS对2组模型法向接触进行建模及分析。结果表明:2组模型预测的接触刚度和接触面积符合较好,但接触压力与接触面积关系存在差异;2组模型预测的等效应力和接触压强的应力幅值以及云图的分布区域大致相近,但双粗模型由于存在大量微凸体侧接触,弱化接触状态以及材料硬化,因而应力幅值偏低。     

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.     

Fractal prediction model of thermal contact conductance of rough surfaces

The thermal contact conductance problem is an important issue in studying the heat transfer of engineering surfaces,which has been widely studied since last few decades,and for predicting which many theoretical models have been established.However,the models which have been existed are lack of objectivity due to that they are mostly studied based on the statistical methodology characterization for rough surfaces and simple partition for the deformation formats of contact asperity.In this paper,a fractal prediction model is developed for the thermal contact conductance between two rough surfaces based on the rough surface being described by three-dimensional Weierstrass and Mandelbrot fractal function and assuming that there are three kinds of asperity deformation modes:elastic,elastoplastic and fully plastic.Influences of contact load and contact area as well as fractal parameters and material properties on the thermal contact conductance are investigated by using the presented model.The investigation results show that the thermal contact conductance increases with the increasing of the contact load and contact area.The larger the fractal dimension,or the smaller the fractal roughness,the larger the thermal contact conductance is.The thermal contact conductance increases with decreasing the ratio of Young’s elastic modulus to the microhardness.The results obtained indicate that the proposed model can effectively predict the thermal contact conductance at the interface,which provide certain reference to the further study on the issue of heat transfer between contact surfaces.     

A finite element-based model of normal contact between rough surfaces

Engineering surfaces can be characterized as more or less randomly rough. Contact between engineering surfaces is thus discontinuous and the real area of contact is a small fraction of the nominal contact area. The stiffness of a rough surface layer thus influences the contact state as well as the behavior of the surrounding system. A contact model that takes the properties of engineering surfaces into account has been developed and implemented using finite element software. The results obtained with the model have been verified by comparison with results from an independent numerical method. The results show that the height distribution of the topography has a significant influence on the contact stiffness but that the curvature of the roughness is of minor importance. The contact model that was developed for determining the apparent contact area and the distribution of the mean contact pressure could thus be based on a limited set of height parameters that describe the surface topography. By operating on the calculated apparent pressure distribution with a transformation function that is based on both height and curvature parameters, the real contact area can be estimated when the apparent contact state is known. The model presented is also valid for cases with local plastic flow in the bulk material.     

A model for the liquid-mediated collapse of 2-D rough surfaces

Small-scale devices are particularly vulnerable to adverse effects of adhesion because of large surface area to volume ratios. Additionally, small gaps can be easily bridged at high humidity or when there are other contaminant liquids present. The bridging of a portion of an interface by a liquid droplet of given volume tends to pull surfaces in closer proximity due to the sub-ambient pressures that arise. In turn, the area spanned by the bridge will increase and lead to a greater adhesive force. A previous study considering a liquid bridge between two elastic half-spaces initially separated by a uniform gap demonstrated that, under certain conditions, an instability will arise whereby the surfaces come into full contact. Owing to the regularity of the geometry considered, the problem was amenable to a semi-analytical treatment and the stability condition was expressible analytically in terms of a single dimensionless group. In the present work, we develop a model to include the effects of surface roughness. The influence of asperities on the surface is treated by means of a recently developed multi-scale model that considers the full range of wavelengths comprising the surface profile. In the simulations, two nominally flat rough surfaces are brought together under a prescribed load and a liquid bridge of given volume is introduced in the contact, the initial areal coverage being determined by the initial mean surface separation. The interface configuration is then iterated until a configuration is found that satisfies the equations of elasticity and capillarity for the given liquid volume. As a result of the simulation, critical values are found for combinations of parameters that delineate stable and unstable conditions.     

Contact Analysis of Non-Gaussian Surfaces for Minimum Static and Kinetic Friction and Wear

Most statistical contact analyses assume that surface heights and peak (summit) height distributions follow a Gaussian distribution. However, engineering surfaces are frequently non-Gaussian with a degree of non-Gaussian character dependent upon materials and surface finishing processes used. For example, magnetic rigid disk surfaces used in magnetic storage industry are highly non Gaussian. The use of a Gaussian analysis in such cases can lead to erroneous results. This study for the first time presents a method to carry out a statistical analysis of non-Gaussian surfaces. Real area of contact, number of contacts, contact pressure and meniscus force (in wet interfaces) are calculated for probability density functions having different skewness and kurtosis. From these curves, the optimum value of skewness and kurtosis can be predicted for minimum static/kinetic friction. It is found that a range of positive skewness (between 0.3–0.7) and a high kurtosis (greater than five) significantly lower the real area of contact and meniscus contribution implying low friction and wear. Also, sensitivity of film thickness to static friction goes down for a surface with a positive skewness and a high kurtosis.     

Contact properties of a wet clutch friction material

Wet clutches are required to transmit torque and also prevent motion in automatic transmissions. Their performance is critically dependent on a friction material which comprises one of the contacting surfaces. Friction materials are usually a composite of fibres, naturally occurring minerals and particles of silicon and graphite, which are all bonded together with a resin. The material formed has very rough surfaces with much steeper slopes than normally-finished steel surfaces. When the friction material is loaded against a relatively flat counterface the real area of contact is only a small percentage of the nominal area and consists of many small, independent “contact units”. It is important to know the conditions present in the contact units (spatial dimensions and pressure) in order to understand and model wet clutch lubrication.In this study, the contact units formed between a paper based friction material and a glass counterface have been investigated under different pressures and during rubbing. A contact visualisation technique is used to directly view and capture images of the contact. The real area of contact and the number of individual units is subsequently determined by image analysis. It is found that the real area of contact increases approximately linearly with applied load, and increases rapidly with rubbing, due to wear. As the load is increased, the number of individual contact units increases up to a critical pressure, suggesting more parts of the material support the load. Above the critical pressure the contact units may be deforming elastically and/or plastically to form larger units. After rubbing, large contact units are formed by flat areas on the tops of the contacting fibres, which are formed during wear. The topography of individual fibres is studied before and after the wearing process using atomic force microscopy, and the results support the truncating wear mechanism.     

Mathematical modeling of the thermal relaxation of nominally flat surfaces in contact using fractal geometry: Maxwell type medium

This work aims at studying the stress relaxation behavior of a nominally flat (rough) surface of a viscoelastic material in contact with a rigid half space. The effect of temperature will be included through the concept of activation energy using Arrhenius's equation. A synthesized Cantor-Borodich (C_B) profile is used to construct the rough surface. C_B profile has two scaling parameters, a and b, and different heights h_i for each generation of asperities. This simple model is applicable for fractal surfaces in which a single exponent (the fractal dimension) is enough to describe their quality.The surfaces in contact are viscoelastic, and they are assumed to behave according to the linear Maxwell model. An asymptotic power law is obtained, which relates the force and the bulk temperature acted on the punch to its approach. This model is valid only when the approach between the punch and the half space is in the range of the roughness size. The proposed model admits an analytical solution for the case when the deformation is linear thermo-viscoelastic. The obtained model shows a good agreement when compared with the experimental results obtained by Handzel-Powierza et al. [Handzel-Powierza Z, Klimczak T, Polijaniuk A. On the experimental verification of the Greenwood-Williamson model for the contact of rough surfaces. Wear 1992;154:115-24].