热力耦合下微接触点塑性应变沿深度变化分析

在考虑粗糙实体弹塑性变形、热力耦合、微凸体间相互作用和摩擦热流耦合等影响下,运用有限元法数值模拟具有三维分形特性的粗糙面与刚性平面间滑动摩擦过程,分析了粗糙实体接触凸点塑性变形随深度变化情况。发现：在速度的突变和闪点温度形成时,摩擦接触表层等效塑性应变增大明显;在这一摩擦表层,过不同接触点的纵向剖面塑性应变沿深度分布不同：有的是接触表面塑性变形最大,有的是在接触微凸体表面下某一深度塑性变形最严重,而接触凸点表面的塑性应变稍小些。这与相关文献用SEM研究干摩擦后金属摩擦表层变形照片后发现的结果一致。滑动摩擦过程中,金属粗糙摩擦接触表层塑性变形的不断累积,将会导致材料表层中的夹杂或微观缺陷周围萌生微孔和裂纹源。     

An upper-bound analysis of friction in metal forming

In the analysis of metal forming processes, a knowledge of friction is important, especially when the microstructure evolution and criteria for limiting phenomena are predicted by numerical simulation. The friction wave model has been studied by several researchers. Their analyses are mainly based on the assumption that there is no plastic deformation of the bulk material. However, it is necessary to clarify the influence of bulk material deformation on the surface asperity deformation. This paper deals with the development of a friction wave model by considering the influence of bulk material on the surface asperity deformation. The situation of rough tool—smooth workpiece (RT—SW) contact during forming process has been investigated. Based on this condition, an admissible velocity field is constructed for the upper bound analysis. The relationship between the normal pressure and the sliding resistance is established over a large range of pressure. The role of surface roughness, bulk displacement and bulk strain on metal forming friction is analysed.     

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.     

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].     

A new roughness parameter to evaluate the near-surface deformation in dry rolling/sliding contact

Within this work, a two-dimensional finite element model for rolling contact of a wheel on a rail is presented that accounts for the roughness of the contact surfaces. The rail material is modeled with elastic–plastic behavior. The maximum of the plastic shear strain is concentrated close to the surface of the rail and is mainly influenced by the surface roughness. A concept is proposed that demonstrates one crucial parameter of the roughness determines surface deformation (based on results of a sinusoidal roughness model). This roughness parameter depicts the ratio between asperity height and width. Numerical validation is achieved for predicting plastic shear strains in rough surfaces. The plastic shear strain is associated with surface damage, such as cracks and wear.     

Effect of asperity interactions on rough surface elastic contact behavior: Hard film on soft substrate

An improved elastic micro-contact model of rough surfaces accounting for asperity interactions is proposed. The contact behavior of a single asperity system is composed of a stiffer hemi-spherical asperity deformation and bellowing softer substrate deformation, which is then extended to rough surface contact including asperity interactions. Using the solution of substrate deformation, normal positions of individual asperities are adjusted during quasi-static contact, from which surface interactive forces are obtained. Analytical simulations are performed using the proposed rough surface contact model, whose results are compared to Greenwood-Williamson-based models and with experimental measurements.     

A modified fractal microcontact model developed for asperity heights with variable morphology parameters

The cross-sections formed by the contact asperities of two rough surfaces at an interference are actually island-shaped, rather than having the commonly assumed circular or elliptic contour. These island-shaped contact area contours show fractal behavior with fractal dimension D_s of the two-dimensional profile. The three-dimensional surface fractal dimension for the topography of asperity heights is defined as D and the topothesy is defined as G. In Mandelbrot's study, the relationship between D and D_s was given as D = D_s + 1 if these two fractal dimensions are obtained before contact deformation. In the present study, D, G, and D_s are considered to be varying with the mean separation between two contact surfaces. The D–D_s relationships for the contacts at the elastic, elastoplastic, and fully plastic deformation regimes are derived and the inceptions of the elastoplastic and fully plastic deformation regimes are redefined using the equality of two expressions established in two different ways for the number of contact spots (N). A revised elastic–plastic contact model of a single fractal asperity is also proposed. The revised model shows that a fractal asperity behaves according to classical contact mechanics, but not those predicted by the MB model. The contact parameters, including the total force and the real contact area, were evaluated when the size distribution functions (n) for the three deformation regimes were available. The results indicate that both the D and D_s parameters in these deformation regimes increased with increasing mean separation.     

Pressure Dependence of Shear Strengths of Thin Films on Metal Surfaces Measured in Ultrahigh Vacuum

The friction coefficient is measured for systems consisting of a thin potassium chloride film deposited onto a variety of clean, flat metal substrates, namely Pb, Sn, Au, Ag, Cu, Pd, Fe, Ta, and two types of steel, which are rubbed by a tungsten carbide pin in an ultrahigh vacuum. The friction coefficients are plotted versus 1/H _S, the inverse of the substrate hardness, where two regimes are found. In the first regime, where deformation at the asperity tips is suggested to be plastic, the observed variation in friction coefficient with substrate hardness is rationalized by assuming that the shear strength S for sliding on a KCl film varies with contact pressure P as S = S ₀ + aP, yielding values for a of 0.14 ± 0.02 and S ₀ of ~60–70 MPa. In the second regime, it is proposed that the softer, film-covered Pb and Sn substrates are closer to being in conformal contact with the rough tribopin. These values of S ₀ and a, along with the measured surface asperity height distribution of the tribopin and the value of the friction coefficient for a KCl monolayer on the metal, are used to rationalize the observed increase in friction coefficient with increasing film thickness.     

基于真应力-应变关系的粗糙表面法向接触模型

提出一种粗糙表面的法向弹塑性接触分析的建模方法。基于微凸体的弹塑性有限元接触模型,分别研究了40Cr、45和Q235三种钢材料的微凸体与刚性平面的法向接触特性。有限元模型中采用三种材料的真应力-应变关系,考察了不同强化特性对微凸体接触性质的影响。建立了微凸体在弹性、弹塑性、塑性变形阶段统一的接触变量变化规律的表达式。在此基础上应用概率统计理论建立粗糙表面法向弹塑性接触模型。所建立的接触模型中微凸体接触变量的变化规律完全基于弹塑性有限元模型的计算结果,无需将微凸体的变形过程区分为不同的变形阶段,避免了接触变量在各阶段采用不同函数表达式带来的连续性和光滑性问题,以及在弹塑性阶段采用插值函数的随意性问题。通过与其他接触模型的计算结果相比较,证明了所提出接触模型的合理性。     

Elastoplastic contact mechanics model of rough surface based on fractal theory

Because the result of the MB fractal model contradicts with the classical contact mechanics, a revised elastoplastic contact model of a single asperity is developed based on fractal theory. The critical areas of a single asperity are scale dependent, with an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. In considering the size distribution function, analytic expression between the total contact load and the real contact area on the contact surface is obtained. The elastic, elastoplastic and full plastic contact load are obtained by the critical elastic contact area of the biggest asperity and maximun contact area of a single asperity. The results show that a rough surface is firstly in elastic deformation. As the load increases, elastoplastic or full plastic deformation takes place. For constant characteristic length scale G, the slope of load-area relation is proportional to fractal dimension D. For constant fractal dimension D, the slope of load-area relation is inversely proportional to G. For constant D and G, the slope of load-area relation is inversely proportional to property of the material ϕ, namely with the same load, the material of rough surface is softer, and the total contact area is larger. The contact mechanics model provides a foundation for study of the friction, wear and seal performance of rough surfaces.     

Deformation due to contact between a rough surface and a smooth ball

Theoretical and experimental results are presented to evaluate the deformation behavior of the contact between a real rough flat surface and a smooth ball. There are three deformation responses: plastic deformation of the asperities only, plastic deformation of the bulk only and combined plastic deformation of both the asperities and the bulk. The effects of the surface roughness and the Hertzian contact parameters on the effective contact pressure are presented. The experimental results confirmed the theoretical prediction very well. For a given Hertzian contact situation the surface roughness plays an important role in controlling the deformation behavior of the contacting surfaces. A criterion is presented to predict the deformation behavior of contacting engineering surfaces.     

微观随机粗糙表面接触有限元模型的构建与接触分析

基于相关文献提出粗糙表面模拟方法,通过软件工具在ANSYS中建立微观粗糙表面接触有限元模型,利用该模型分析载荷对弹塑性变形和接触面积的影响。结果表明:随着正压力的增大,粗糙表面上不断地有微凸峰与平面发生弹性接触变形,接触斑点(或接触斑点群)的数目逐渐增加,斑点中心区域的弹性变形很快达到最大,微凸峰负荷变形的同时也使斑点四周区域受到挤压;初始接触时,轮廓高度较大的微凸峰率先发生弹性变形,随着压力的增大,金属材料所受应力达到屈服极限同时粗糙表面的弹性变形和塑性变形的集中区域不断增加,真实接触面积不断增大;接触区数目的增多和接触区面积的增加都可以导致接触面上真实接触面积增加;随着压力的增大,真实接触面积的增大并不是由于接触区数目的增多,而是微观接触区面积的增大。     

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.     

Transition from elastic to plastic deformation as asperity contact size is increased

Contacts between a clean sodium chloride pyramidal shaped asperity and a plane NaCl surface have been investigated by molecular dynamics simulations. For small contacts, a few atoms across, the asperity jumped to contact and behaved elastically as normal load was applied. Then, when the force was reversed to detach the asperity, brittle failure occurred without any damage to the crystalline materials. However, as the contact size of the asperity was increased to 6 × 6 atoms in area, the mechanism of detachment was seen to alter. The jump to contact was elastic and damage free, but the separation could not be achieved elastically, but required plastic deformation, giving extensive energy dissipation and severe damage as edge defects propagated through the asperity. Above this contact size, plastic flow was dominant. However, there is clearly a further transition back to elastic fracture once the asperity becomes large enough for Griffith-type cracking to propagate above 1 μm in size, since large sodium chloride contacts are known to be brittle above the micrometre scale, depending on the presence of crack initiating defects.     

The residual stress distribution in a plastically deformed model asperity

When rough metallic surfaces come into contact, plastic deformation may occur locally, even at the lightest loads. This plastic deformation is thought to be an important element in a wide range of contact failure mechanisms, including fatigue and nearly all forms of wear.In this paper a simple model of asperity plastic deformation is presented. The model is based on slip line field theory and is used to calculate residual and full-load stress distributions at fully plastic asperity contacts for normal and moderate tangential loads.Measurements of surface residual stress were carried out using two different techniques on a range of plastic contacts of various materials and geometries. The results show agreement with the main predictions of the theory.     

Theoretical analysis of the plastic yielding of a hard asperity sliding on a soft flat surface

When a hard material slides on a soft material, wear occurs generally on the soft material surface. Wear can also occur on the harder material but the conditions for this have not yet been elucidated.As plastic deformation of contact points is an important factor in the generation of wear particles, the condition under which the plastic yielding of each material occurs simultaneously and the condition under which the hard asperity yields before the soft flat surface were analysed theoretically. The analysis indicates that there is a critical value, which depends on the hardness ratio and the shear stress on the interface, for the top angle of the asperity. If the top angle of an asperity is less than this critical value, the asperity can yield plastically despite its being harder than the mating surface.     

Elastic–plastic adhesive contact of rough surfaces based on plastic asperity concept

The paper describes an analysis of adhesive contact between rough surfaces with small-scale surface asperities using an elastic–plastic model of contact deformation based on fictitious plastic asperity concept developed by Abdo and Farhang [Int. J. Non-Linear Mech. 40 (2005) 495]. The model considers simultaneous occurrence of elastic and plastic behaviours for an asperity. The well-established elastic adhesion index and plasticity index are used to consider the different contact conditions that arise as a result of varying load and material parameters. The load-separation behaviour for different combinations of these parameters is obtained. Comparison with previous elastic–plastic model that was based on elastic-then-plastic assumption is made showing significant differences.     

An AFM study of single-contact abrasive wear: The Rabinowicz wear equation revisited

A nanoscale study of the abrasive wear behaviour of a ductile monophasic metallic alloy (the stainless steel AISI 316L) is presented. By using atomic force microscopy (AFM) based techniques, particularly a diamond tip mounted on a stiff steel cantilever, the contact of a single abrasive asperity was simulated, and it was possible to determine accurately the load threshold below which no measurable wear occurs. It was observed that, once this nanoscale threshold for wear is overcome, the worn volume increases linearly with the load, as predicted by the Rabinowicz model. However, it was found that, although this critical threshold for measurable wear is most certainly related with the yield-onset of plastic deformation, it cannot be predicted by using directly a criterion based on the bulk microhardness. Hence, the results presented in this paper strongly indicate that indentation size effects play a crucial role on the response to abrasive wear at the asperity contact level.     

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.     

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.