粗糙表面接触力学问题的重新分析

为了克服基于统计学参数的接触模型的尺度依赖性以及现有接触分形模型推导过程中初始轮廓表征受控于接触面积或取样长度的不足,基于粗糙表面轮廓分形维数$D$、尺度系数$G$ 和最大微凸体轮廓基底尺寸$l$,建立了新的粗糙表面接触分形模型,探讨了微凸体变形机制、粗糙表面的真实接触面积和接触载荷的关系,揭示了接触界面的孔隙率和真实接触面积随端面形貌、表面接触压力等参数变化的规律,给出了不同形貌界面被压实的最大变形量. 结果表明:微凸体变形从弹性变形开始,并随着平均接触压力$p_{\rm m}$ 的增大逐步向弹塑性变形和完全塑性变形转变;接触界面的初始孔隙率$\phi_{0}$ 随$D$ 的增大而增大,压实孔隙所需要的最大变形量$\delta $ 也随之增大;接触压力$p_{\rm c}$ 增大,孔隙率$\phi$ 减小,并随着$D$ 的增大和$G$ 减小,$\phi$ 快速减小,直至填实,变为零;$D$ 较小时,$G$ 的增大对真实接触面积的增大影响较小;$D$ 较大时,$G$ 的增大对真实接触面积的增大作用明显. 研究成果为端面摩擦副的润滑与密封设计提供了理论基础.      

Dynamic analysis of single and cyclic indentation of an elastic-plastic multi-layered medium by a rigid fractal surface

Dynamic indentation of an elastic-plastic multi-layered medium by a rigid rough surface that exhibits fractal behavior was analyzed with the finite element method. A sufficiently large mesh was used to avoid the effects of the faster propagating dilatation waves after they were reflected from the artificial mesh boundaries. Single-indentation results illustrate the significance of the thickness of the surface layer and the indentation speed on the contact pressure distribution and subsurface stresses and strains. The initiation of yielding and the development of plasticity are interpreted in the context of results for the von Mises equivalent stress and equivalent plastic strain obtained during the loading and unloading phases of an indentation cycle. Cumulative plasticity and elastic shakedown are discussed in light of results revealing the evolution of deformation in the multi-layered medium due to cyclic indentation. The analysis provides insight into the importance of indentation speed, layer thickness, surface topography, and indentation cycle on the mechanical response of a multi-layered medium in dynamic contact with a rough surface exhibiting multi-scale (fractal) roughness.     

考虑弹塑性变形阶段的干气密封接触模型

为探究干气密封摩擦界面在变形全阶段的接触特性,基于分形接触理论及微观接触力学理论,充分考虑微凸体变形的3个阶段,通过余弦函数构建干气密封全阶段接触模型,并分别与GW模型、KE模型和ZMC模型三种经典接触模型及相关文献的试验数据作对比,验证本文中接触模型的合理性与正确性.最后对干气密封摩擦界面接触特性的主要影响因素进行探究.模型研究结果表明：干气密封摩擦界面的接触特性与分形维数、特征尺度及两表面的真实接触面积有关.接触特性与分形维数和两表面真实接触面积呈正相关,与特征尺度呈负相关.分形维数越大,接触载荷与接触刚度的数量级就越大,且接触载荷变化范围相对较大.当特征尺度每次以1个数量级递增时,接触载荷与接触刚度的变化范围较小,都在1个数量级内.     

An adhesive wear model of fractal surfaces in normal contact

A generalized adhesive wear analysis that takes into account the effect of interfacial adhesion on the total load was developed for three-dimensional fractal surfaces in normal contact. A wear criterion based on the critical contact area for fully-plastic deformation of the asperity contacts was used to model the removal of material from the contact interface. The fraction of fully-plastic asperity contacts, wear rate, and wear coefficient are expressed in terms of the total normal load (global interference), fractal (topography) parameters, elastic–plastic material properties, surface energy, material compatibility, and interfacial adhesion characteristics controlled by the environment of the interacting surfaces. Numerical results are presented for representative ceramic–ceramic, ceramic–metallic, and metal–metal contact systems to illustrate the dependence of asperity plastic deformation, wear rate, and wear coefficient on global interference, surface roughness, material properties, and work of adhesion (affected by the material compatibility and the environment of the contacting surfaces). The analysis yields insight into the effects of surface material properties and interfacial adhesion on the adhesive wear of rough surfaces in normal contact.     

Adhesion in the contact of a spherical indenter with a layered elastic half-space

With the emergence of micro- and nano-technology, the contact mechanics of MEMS and NEMS devices and components is becoming more important. Thus it is important to gain a better understanding of the role of coatings and thin films on micro- and nano-scale contact phenomena, and to understand the interactions of measurement devices, such as an atomic force microscope (AFM), with layered media.More specifically, in this work the frictionless contact, with adhesion, between a spherical indenter and an elastic-layered medium is investigated. This configuration can be viewed as either a single contact model or as a building block of a multi-asperity rough surface contact model. As the scale decreases to the nano level, adhesion becomes an important issue. The presence of adhesion affects the relationships among the applied force, the penetration of the indenter, and the size of the contact area. This axisymmetric problem includes the effect of adhesion using a Maugis type of adhesion model. This model spans the range of the Tabor parameter between the JKR and DMT regions. The key parameters in this analysis are the elastic moduli ratio of the layer and the substrate, the dimensionless layer thickness, and the Maugis adhesion parameter. The results can be applied to a rigid or to an elastic indenter.     

Delamination of an elastic film from an elastic–plastic substrate during adhesive contact loading and unloading

Adhesive contact between a rigid sphere and an elastic film on an elastic–perfectly plastic substrate was examined in the context of finite element simulation results. Surface adhesion was modeled by nonlinear springs obeying a force-displacement relationship governed by the Lennard–Jones potential. A bilinear cohesive zone law with prescribed cohesive strength and work of adhesion was used to simulate crack initiation and growth at the film/substrate interface. It is shown that the unloading response consists of five sequential stages: elastic recovery, interface damage (crack) initiation, damage evolution (delamination), film elastic bending, and abrupt surface separation (jump-out), with plastic deformation in the substrate occurring only during damage initiation. Substrate plasticity produces partial closure of the cohesive zone upon full unloading (jump-out), residual tensile stresses at the front of the crack tip, and irreversible downward bending of the elastic film. Finite element simulations illustrate the effects of minimum surface separation (i.e., maximum compressive surface force), work of adhesion and cohesive strength of the film/substrate interface, substrate yield strength, and initial crack size on the evolution of the surface force, residual deflection of the elastic film, film-substrate separation (debonding), crack-tip opening displacement, and contact instabilities (jump-in and jump-out) during a full load–unload cycle. The results of this study provide insight into the interdependence of contact instabilities and interfacial damage (cracking) encountered in layered media during adhesive contact loading and unloading.     

Hydrodynamic lubrication in fully plastic asperity contacts

A line contact inlet zone analysis is carried out for the hydrodynamic lubrication in a fully plastic asperity contact. A governing equation of the central film thickness i.e. the film thickness in the fully plastic contact area is derived. An equation predicting this film thickness is also derived. It is found that for the fully plastic contact, under relatively light loads the prediction accuracy for the central film thickness is good, while at the load heavy enough the prediction equation greatly overestimates the central film thickness and the central film thickness solved from the analytical governing equation is significantly low showing the asperity in boundary layer lubrication. For the fully plastic contact, the central film thickness is nearly half of that obtained based on the elastic contact assumption for relatively light loads or even lower for heavier loads. The hydrodynamic lubrication is found difficult to form in the fully plastic asperity contact for the carried load heavy enough or the significantly low sliding speed between the asperities. To achieve a high hydrodynamic lubrication film thickness in the fully plastic asperity contact it is recommended to employ a high sliding speed or a high fluid viscosity. However, in the fully plastic asperity contact, the potential hydrodynamic load-carrying capacity is limited and much smaller than that based on the elastic contact assumption or predicted by conventional line contact elasto-hydrodynamic lubrication theory.     

Interfacial slip and creep in rolling contact incorporating a cylinder with an elastic layer

A systematic approach for investigating the interfacial behaviour of tyred systems is proposed. A two-dimensional contact model of an elastic strip, shrink-fitted onto a wheel, and subjected to different rolling contact conditions, has been adopted to illustrate the method. The model combines existing techniques to explore individual elastic contact problems and it enables us to characterise the behaviour at the strip/substrate interface caused by loads induced by a quasi-static application of stationary and moving loads on the surface of the layer. The solution is compared to the stationary load case and regimes of local slip, full stick, separation and frictional creep are identified and collated for a variety of loading conditions, materials and geometries. Further, this article presents an investigation of frictional shakedown for layered systems subjected to periodic contact loading. The term shakedown is here referred to as the possibility of developing interfacial residual stresses at the layer/substrate interface such that frictional slip, originally activated by the applied external contact load, ceases after a few loading cycles. The possible applicability of the Melan’s theorem for elastic frictional system is investigated and preliminary results presented.     

A slip-line plasticity analysis of sliding friction of rough surfaces exhibiting self-affine (fractal) behavior

A plasticity analysis of sliding friction of rough (fractal) surfaces sliding against smooth surfaces was developed based on a slip-line model of a rigid spherical asperity (wear particle) plowing and cutting through a soft semi-infinite medium. Solutions of the fraction of fully plastic asperity microcontacts responsible for the evolution of friction and energy dissipation were obtained in terms of the total normal load (global interference), interfacial adhesion characteristics, topography (fractal) parameters of the hard surface, and elastic–plastic material properties of the soft surface. This was accomplished by incorporating the slip-line model of a single microcontact into a friction analysis of sliding surfaces demonstrating multi-scale roughness. Numerical results provide insight into the effects of global interference (normal load), fractal parameters (surface roughness) of the hard surface, interfacial shear strength (adhesion), and material properties of the soft surface on plastic deformation at the microcontact level, global coefficient of friction, and frictional energy dissipated during sliding.     

Cohesive failure analysis of an array of IC chips bonded to a stretched substrate

The paper presents a mechanical model for predicting the cohesive failure of a periodic array of integrated circuit (IC) chips adhesively bonded to a stretched substrate. A unit cell of the layered structure consisting of the IC chips, adhesive layer, and substrate is modeled as an assembly of two elastic Timoshenko beams, representing the chip and substrate, connected by an elastic interface, representing the adhesive. Accordingly, the stresses and energy release rate (ERR) in the adhesive layer – responsible for the premature cracking of the adhesive and debonding of the IC chips – are identified with the corresponding quantities computed for the elastic interface. Expressions for the adhesive stresses and ERR are given in terms of geometrical dimensions and material properties, combined with integration constants obtained numerically via the multi-segment analysis method. For comparison, the stresses in the adhesive are also computed based on a finite element model, and the ERR is evaluated using the virtual crack-closure technique (VCCT). The analytical predictions and numerical results match fairly well, considering the effects of key factors, such as the distance between adjacent chips, the chip size, the material properties of adhesive and substrate. The interaction between the chips is shown to have relevant effects on the adhesive stresses. In particular, only the mode II contributes to the ERR which increases with the ratio of the chip size to the distance between the chips and with the compliance of the adhesive and substrate layers.     

Finite element analysis of large contact deformation of an elastic–plastic sinusoidal asperity and a rigid flat

Normal contact deformation of an asperity and a rigid flat is studied within an axisymmetric finite element model. The asperity features a sinusoidal profile and is elastic–plastic with linear strain hardening. Influences of geometrical (asperity height and width) and loading (the maximum interference) parameters on frictionless contact responses are explored for both loading and unloading. Dimensionless expressions for contact size and pressures covering a large range of interference and asperity ratio values are obtained in power-law forms. Results show the mean contact pressure after fully-plastic contact reaches a plateau only for small asperity ratios, while it continues increasing for large asperity ratios. The residual depth is found to be associated with plastically dissipated energy.     

Surface electro-elastic shear horizontal waves in a layered structure with a piezoelectric substrate and a hard dielectric layer

The existence and behaviour of surface electro-elastic shear horizontal waves in a layered structure consisting of a piezoelectric substrate of crystal class 6, 4, 6mm, or 4mm mechanically bonded at its upper surface to an elastic dielectric layer and bounded by an adjacent dielectric medium is considered when the shear bulk wave velocity in the elastic layer is greater than or equal to that in the substrate. The dispersion equation for the existence of the surface electro-elastic SH waves with respect to the phase velocity is obtained which includes all the above crystal classes i.e. the surface wave problems related to all these classes are presented in a single mathematical model. The investigation of the solutions of the dispersion equation is carried out and all the possible cases of the behaviour of the surface electro-elastic SH wave depending on the electro-mechanical coefficients of the layered structure are revealed.     

Analysis of the adhesive contact of confined layers by using a Green's function approach

The authors develop a numerical procedure to analyze the adhesive contact between a soft elastic layer and a rough rigid substrate. The solution of the problem, which belongs to the class of the free boundary problems, is obtained by calculating the Green's function which links the pressure distribution to the normal displacements at the interface. The problem is then formulated in the form of a Fredholm integral equation of the first kind with a logarithmic kernel, and the boundaries of the contact area are calculated by requiring that the energy of the system is stationary. The methodology is relatively simple and easy to implement in a numerical code. It has been utilized to analyze the adhesive properties of a confined layer in contact with a wavy rigid substrate as a function of thickness, applied stress or penetration. It is shown that reducing the thickness of the slab reduces the effective energy of adhesion, i.e. the work needed to separate the bodies, but nevertheless increases the adherence force between the slab and the substrate. However, thinning the slab also increases the confinement of the system and therefore increases the negative hydrostatic pressure in the layer. This, in turn, may produce cavitation. When this happens the rupture of the adhesive bond does not occur through interfacial crack propagation but, by the growth of new interfacial voids or cavities.     

粗糙薄层弹性体接触刚度分析

薄层弹性体功能结构表面在工程领域有着广泛的应用前景,薄层弹性体的接触特性分析对功能结构表面设计与应用非常重要.采用随机粗糙表面模拟生成技术和有限元分析技术建立了粗糙薄层弹性体表面的接触刚度确定性分析模型,研究了薄层弹性体的接触特性,对基于半数值确定性分析方法的粗糙层-基体层串联模型用于粗糙薄层弹性体接触刚度计算的适用性进行了讨论,进一步分析了粗糙薄层弹性体串联模型接触刚度的误差来源.研究结果表明:当薄层弹性体的基体层厚度小于10倍表面均方根粗糙度时,由传统粗糙层-基体层串联模型分析获得的粗糙薄层弹性体刚度误差将超过15%,误差主要来源于粗糙峰的大变形和基体层的局部变形不均匀的共同作用.     

A slip-line plasticity analysis of abrasive wear of a smooth and soft surface sliding against a rough (fractal) and hard surface

Abrasive wear of a soft and smooth surface sliding against a rough (fractal) and hard surface was analyzed by the slip-line theory of plasticity. The analysis is based on a slip-line model of a rigid spherical asperity (wear particle) plowing through a soft surface and removing material by microcutting. Integration of this single-contact model into a three-dimensional contact mechanics analysis of an abrasive surface exhibiting multi-scale roughness described by fractal geometry yielded relationships of the abrasive wear rate and wear coefficient in terms of the interfacial shear strength (adhesion), topography (fractal) parameters of the hard/rough surface, elastic–plastic material properties of the soft/smooth surface, and total normal load. Analytical results from the single-contact analysis provide insight into the deformation of a perfectly plastic material caused by the abrasive action of a rigid asperity/wear particle under different normal load and interfacial friction (adhesion) conditions. The dependence of the abrasive wear rate and wear coefficient on normal load (global interference), roughness of the abrasive surface, elastic–plastic material properties of the abraded surface, and interfacial shear strength (lubrication effect) is interpreted in the context of numerical results obtained for representative ceramic/ceramic, ceramic/metallic, and metal/metal sliding systems.     

考虑摩擦系数和微凸体相互作用的粗糙表面接触热导分形模型

基于三维分形理论,建立了考虑摩擦系数和微凸体相互作用的粗糙表面接触热导分形模型,并且考虑了微凸体的弹性变形、弹塑性变形和完全塑性变形. 通过该模型,分析了摩擦系数、分形维数、分形粗糙度和接触载荷对热接触热导的影响. 研究结果表明:接触热导随着摩擦系数和分形粗糙度的增大而减小,随着分形维数和接触载荷的增大而增大. 该研究为开展接合面的热传递提供了一定的理论基础.      

Fracture analysis on a piezoelectric sensor with a viscoelastic interface

Fracture analysis is performed on a layered piezoelectric sensor possessing a Kelvin-type viscoelastic interface. An electrically permeable anti-plane crack is situated in the piezoelectric layer and perpendicular to the interface. The crack problem is solved by the methods of integral transform and Cauchy singular integral equation. The variations of the dynamic stress intensity factor (DSIF) vs. physical and geometrical parameters are investigated. At the beginning of creep and relaxation, larger viscosity coefficient always induces smaller DSIF. With time elapsing, the effect of viscosity coefficient becomes weaker and weaker. When time approaches infinity, the viscous effect disappears, and the DSIF converges to a value corresponding to the case of an elastic interface. The effect of the viscoelastic interface on the fracture behavior of the piezoelectric layer also depends on the substrate thickness. To some extent, thicker substrate may intensify the effect of the interface.     

关联表面分形特性的润滑模型

在分配有面粗糙度与材料表面分形特性关系的基础上，将分形特性引入润滑方程，提出了关联表面分形特性的润滑模型，并分析了润滑模型中压力流量因子和剪切流量因子与表面分形维数之间关系。计算结果表明：在相同分形维数（D）下，随着微突体纵横比v的增大，压力流量因子和剪切流量因子相应增大，且其随分形维数D的变化同随油膜粗糙度比H的变化相比呈现出更强的不规则特性，出现局部最大和最小值，并且分辨率较高。     

Adhesive elastic contact between a symmetric indenter and an elastic film

This paper examines the frictionless adhesive elastic contact problem of a rigid sphere indenting a thin film deposited on a substrate. The result is then used to model the elastic phase of micro-nanoscale indentation tests performed to determine the mechanical properties of coatings and films. We investigate the elastic response including the effects of adhesion, which, as the scale decreases to the nano level, become an important issue. In this paper, we extend the Johnson–Kendall–Roberts, Derjaguin–Muller–Toporov, and Maugis–Dugdale half-space adhesion models to the case of a finite thickness elastic film coated on an elastic substrate. We propose a simplified model based on the assumption that the pressure distribution is that of the corresponding half-space models; in doing so, we investigate the contact radius/film thickness ratio in a range where it is usually assumed the half-space model. We obtain an analytical solution for the elastic response that is useful for evaluating the effects of the film-thickness, the interface film–substrate conditions, and the adhesion forces. This study provides a guideline for selecting the appropriate film thickness and substrate to determine the elastic constants of film in the indentation tests.     

基于三维各向异性分形理论的固定机械结合面法向接触刚度建模研究

将结合面接触点拓展为椭圆形,基于KE有限元模型,类比球形微凸体在弹塑性接触变形阶段法向载荷、接触面积以及变形量之间的关系,采用代入法得到了表征椭圆抛物面形微凸体弹塑性接触变形机制的对应关系式.假设结合面接触点离心率分布与接触点面积分布相互独立,根据概率论以及接触点的面积大小分布函数,获得了关于结合面接触点面积与离心率的...