Energy Loss in the Impact of Elastic Spheres on a Rigid Half-Space in Presence of Adhesion

Adhesion can cause energy losses in asperities or particles coming into dynamic contact resulting in frictional dissipation, even if the deformation occurring is purely elastic. Such losses are of special significance in impact of nanoparticles and friction between surfaces under low contact pressure to hardness ratio. The objective of this work is to study the effect of adhesion during the normal impact of elastic spheres on a rigid half-space, with an emphasis on understanding the mechanism of energy loss. We use finite element method for modeling the impact phenomenon, with the adhesion due to van der Waals force and the short-range repulsion included as body forces distributed over the volume of the sphere. This approach, in contrast with commonly used surface force approximation, helps to model the interactions in a more precise way. We find that the energy loss in impact of elastic spheres is negligible unless there are adhesion-induced instabilities. Significant energy loss through elastic stress waves occurs due to jump-to-contact and jump-out-of-contact instabilities and can even result in capture of the elastic sphere on the half-space.     

A numerical model of friction between rough surfaces

This paper describes a computational method to calculate the friction force between two rough surfaces. In the model used, friction results from forces developed during elastic deformation and shear resistance of adhesive junctions at the contact areas. Contacts occur between asperities and have arbitrary orientations with respect to the surfaces. The size and slope of each contact area depend on external loads, mechanical properties and topographies of surfaces. Contact force distribution is computed by iterating the relationship between contact parameters, external loads, and surface topographies until the sum of normal components of contact forces equals the normal load. The corresponding sum of tangential components of contact forces constitutes the friction force. To calculate elastic deformation in three dimensions, we use the method of influence coefficients and its adaptation to shear forces to account for sliding friction. Analysis presented in Appendix A gives approximate limits within which influence coefficients developed for flat elastic half-space can apply to rough surfaces. Use of the method of residual correction and a successive grid refinement helped rectify the periodicity error introduced by the FFT technique that was used to solve for asperity pressures. The proposed method, when applied to the classical problem of a sphere on a half-space as a benchmark, showed good agreement with previous results. Calculations show how friction changes with surface roughness and also demonstrate the method's efficiency.     

Micro–Macro-Shear-Displacement Behavior of Contacting Rough Solids

Interlocking asperities are shown to have a fundamental effect on the friction behavior of contacting solids through theoretically derived shear force–displacement relationship. The key aspect of this relationship is the asperity contact orientation probability distribution obtained using the random process theory in terms of measurable surface roughness parameters. Thus, the obliquity of surface asperity contact is included in the contact shear analysis in a fundamental manner. The interlocking asperities are found to result in a normal load-dependent friction coefficient for a contact. The interlocking also affects contact partial slip and the shear displacements that precede sliding. The derived relationship can be used to evaluate factors, such as asperity adhesion, plasticity, damage, normal-shear coupling and scale dependency, which are difficult to separate in experiments and atomistic simulations.     

Finite element calculations on the influence of surface roughness on friction

Two-dimensional finite element calculations are used to describe the interaction between a hard rigid asperity and an asperity with an elastic-plastic material behaviour. In the calculations the hard asperity is moved through the soft asperity while the separation of the surfaces is kept constant. The normal and shear forces and the friction coefficient are determined for different separations. The influence of adhesive friction in the contact zone and the influence of the radii of the asperities are also investigated. The finite element model is compared with an analytical model.     

A Basic Theoretical Model for Friction Process at Microasperity Level

This article presents a theoretical model for dry, low-velocity, and wear-less friction based on a single asperity interaction with arbitrary assumed adhesion forces and elastic deformations of the microasperities. Simulations of friction behavior according to the single asperity interaction, as well as the interaction of multiplied single models, are presented. The multiplied model assumes a regular distribution of the single asperities, arbitrarily chosen geometrical properties (based on harmonic function), and elastomechanical properties of the cooperating materials. In the proposed model, the adhesion as a function of asperity deformation is introduced. This enables the simulation of an expedient local coefficient of friction. The model assumes no breaking of the contact between single asperities; however, the proposed model enables detection of such a situation. The results obtained by simulation of the model show both qualitative and quantitative agreement with the known types of friction force dynamic behavior, in particular, nonlinearity of the friction coefficient. At this level of investigation, the model assumes the most important relations connected with its properties, which need further refinement and elaboration, especially according to assumed asperity properties.     

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.     

A Novel Generic Model at Asperity Level for Dry Friction Force Dynamics

This paper presents a theoretical model for (dry, low-velocity, wear-less) friction force dynamics based on asperity interaction considerations subject to the phenomenological mechanisms of creep/relaxation, adhesion and (elasto-plastic) deformation in their most generalized forms. The model simulates the interaction of a large population of idealized, randomly distributed asperities with arbitrarily chosen geometrical and elastic properties. Creep and adhesion are simulated by an expedient local coefficient of friction that increases with time of contact, while deformation effects are accounted for by rate-independent hysteresis losses occurring in the bulk of the material of an asperity that is breaking loose. An energy method is adopted to calculate the instantaneous, local friction force leading to better insight into the problem as well as higher numerical efficiency. The results obtained by this model show both qualitative and quantitative agreement with the known types and facets of friction force dynamic behaviour; in particular, pre-sliding quasi time-independent frictional hysteresis in the displacement, velocity weakening, slider “lift-up” effect and frictional lag, in addition to the influence of the various process parameters, all in a single formulation, such as no extant friction model could show before. Moreover, the model is still open for and capable of further refinement and elaboration so as to incorporate local inertia and viscous effects and thus to be extended to include velocity strengthening and lubricated rough contacts.     

A review of scuffing and running-in of lubricated surfaces, with asperities and oxides in perspective

The slow progress in the understanding of scuffing (scoring) and runningin of most lubricated surfaces is probably due to an inadequate understanding of the details of asperity deformation and oxide formation. The thickness and properties of oxides influence the stress states imposed on asperities as much as does the liquid lubricant, but the oxides are ignored in theories. Present theories also focus on adhesion as the cause of scuffing and they usually do not take account of the changing surface roughness during sliding. There may indeed be some evidence of adhesion in the later stages of damage but adhesion has not been demonstrated to be the initiating mechanism of scuffing. Plastic fatigue is the more likely explanation, and this can occur without atomic contact between the sliding surfaces.     

AFM针尖"突跳"研究

为了研究原子力显微镜（AFM）“突跳”现象的产生机理，基于经典弹性理论和Lennard-Jones势能定律建立了AFM针尖与样品纳米接触的弹性模型。给出了在AFM针尖逐渐趋近样品表面的过程中，AFM针尖与样品间的粘着力、样品表面的轮廓曲线和样品表面的变形量随AFM针尖与样品表面间距的变化规律。分析了AFM“突跳”现象的产生机理和影响因素。研究表明，AFM“突跳”现象主要是由样品表面在粘着引力的作用下产生拉伸变形并与AFM针尖“突跳”接触引起的。     

The Effect of Scale-Dependent Hardness on Elasto-Plastic Asperity Contact between Rough Surfaces

Statistical methods are used to model elasto-plastic contact between two rough surfaces using a recent finite element model of elasto-plastic hemispherical contact and also recent advances in strain gradient modeling. The elasto-plastic hemispherical contact model used to model individual asperities accounts for a varying hardness effect due to deformation of the contact geometry that has been documented by other works. The strain gradient model accounts for changes in hardness due to scaling effects. The contact between surfaces with hypothetical material and surface properties, such as the elastic modulus, yield strength, and roughness are modeled. A model is also constructed to consider a variable asperity contact radius to evaluate if the strain gradient model will affect it differently. The models produce predictions for contact area, contact force, and surface separation. The strain gradient effects decrease the real area of contact and increase the average contact load in comparison to the model without these effects. The strain gradient model seems to have a larger influence on the predictions of contact load and area than does considering a variable asperity contact radius for the cases considered in this work.     

假肢接受腔硅胶材料的力学性能研究

采用HY0580的压缩试验机,在反复压缩模式下模拟假肢接收腔/硅胶材料界面,研究了4种不同表面结构的硅胶内衬套材料的力学压缩性能。结果表明:4种不同表面结构的硅胶内衬套材料在载荷分别为0.5 N、3 N、7 N、10 N的试验工况下进行压缩试验时,都是在相同载荷(4.5 N)时出现平台期;在同等载荷的情况下,因1和4号硅胶材料正反两面均为光面,表面微凸体不高,粗糙度较小,2和3号材料与皮肤接触的反面上微凸体较高,粗糙度较大,故1号和4号材料的变形比2号和3号小,说明材料表面的各种纹路对缓解皮肤的压力有一定作用,硅胶材料反面上的粗大微凸体,增加了与皮肤的粘结性,有利于降低皮肤摩擦损伤的风险,提高残肢患者穿戴舒适性。     

ELASTIC-PLASTIC ADHESION MODEL FOR SINGLE ASPERICAL ASPERITY MICROCONTACT

The adhesion of single asperity contacting with a rigid flat is investigated. The microcontact model of the deformable asperity is established utilizing fractal geometry, which makes the resuRed adhesion model to relate with the surface characteristics that the asperity belongs to. The Dugdale approximation is utilized to consider the adhesive interaction within and outside the contact area. Then the model for solving the elastic-plastic adhesion of single asperity is presented by combing the Maugis-Dugdale（MD） model. To illustrate the necessity of considering the plastic deformation in microcontact, simulations of the relationship between the adhesive contact load and the interference of the asperity are performed. The result shows that the presented model is more suitable for the solution of the elastic-plastic microcontact of spherical asperity due to intermolecular adhesive interactions.     

Constitutive model of adhesive and ploughing friction in metal-forming processes

In metal-forming processes the tool-workpiece interaction is associated with friction forces due to cohesive bonds and ploughing of hard particles or asperities through the interface layer and also with irreversible asperity flattening. In the present work, the combined effect of adhesive and ploughing friction is accounted for by assuming two different length scales of interacting asperities of workpiece and tool. The constitutive model of friction slip is formulated by introducing the representative contact state variables and providing their evolution rules together with friction condition and the non-associated slip rule. The model parameters can be identified from micro-mechanical solutions of asperity flattening and ploughing problems. Also a purely phenomenological model is proposed. The dual asperity model is next applied to predict contact slip and friction response and in numerical analysis of two boundary value problems.     

传热界面真实接触面积计算与分析

在热流通过两相互接触材料尤其是金属材料的界面时，真实接触面积是界面传热的一个主要影响因素。当承受大应力的两接触体之间具有相对滑动或相对滑动趋势时，粗糙表面在压力和粘着力及剪切力的作用下接触粗糙峰发生弹性、弹一塑性或完全塑性变形，真实接触面积与压力之间的关系随变形机制而发生变化，在力的作用下材料的变形机制由表面微观几何形貌和力学性质决定。计算表明，单个粗糙峰接触面积与载荷的关系受变形机制的影响，粘着力对接触面积的影响可以忽略，表面相对滑动将增加真实接触面积。     

Mechanics of adhesion

The small scale contacts and very smooth surfaces associated with information storage devices result in adhesive forces playing a more significant role than in more conventional tribological applications. Taking the contact of spherical surfaces to be representative of asperity interactions, the mechanics of adhesion will be reviewed. From the point of view of mechanics adhesion is expressed in terms of the ‘work of adhesion', i.e. the work to separate unit area of the interface, whatever its physical origin; intermolecular forces, electrostatic forces or capillary action. For elastic solids the behaviour is a function of two non-dimensional parameters. One is a measure of the ratio of the adhesive force to the applied load and the other the ratio of elastic deformation to the range of surface forces. A map will be presented having these two parameters as co-ordinates. The effect of inelastic deformation (plastic and viscoelastic) will be considered and a criterion presented for the ‘brittle' or ‘ductile' separation of adhering surfaces.     

A Combined Molecular Dynamics and Finite Element Analysis of Contact and Adhesion of a Rough Sphere and a Flat Surface

A combined molecular dynamics and finite element model and simulation of contact and adhesion between a rough sphere and a flat surface has been developed. This model uses the results of molecular dynamics (MD) simulations, obtained using an embedded atom potential, of a nanoscale Ru-Ru asperity contact. A continuum finite element model of an elastic–plastic microscale Ru-Ru contact bump is then created. In this model, the surface roughness is represented by a system of nanoscale asperities, each of which is represented by a nonlinear hysteretic force vs. distance relationship. The nonlinear hysteretic character of these relations is determined from curve-fits of the MD results. Load vs. interference and contact area vs. interference are determined using this two-scale model for loading and unloading. Comparisons with a single-scale continuum model show that the effect of the nanoscale asperities is to reduce both the adhesion and the real area of contact. The choice of Ru as the material for this work is due to its relevance in microswitches.     

Analysis of rough line contacts operating under mixed elastohydrodynamic lubrication conditions

Heavily loaded machine elements, such as gears, usually operate in the mixed lubrication regime. Surface roughness has a significant effect on the pressure distribution, the subsurface stress field, and the friction coefficient. Based on the superposition of a dry rough and a fully flooded smooth contact, a mixed lubrication model has been developed. The roughness profile is assumed to be known. Surface deformation is calculated by taking into account the pressure distribution that is built up by asperity contacts, asperity interactions, and lubricant flow. Thermal and sliding effects are incorporated into the analysis. Non‐Newtonian lubricant behaviour is considered by using a power‐law rheological model. The pressure distribution, subsurface stress field, and friction coefficient were calculated from the model at several points along the contact path for an FZG type C gear pair. It was shown that a significant part of the load is carried by the contacting asperities. The position of the maximum shear stress is very close to the surface.     

Microscopic asperity contact and deformation of ultrahigh molecular weight polyethylene bearing surfaces

The effect of the roughness and topography of ultrahigh molecular weight polyethylene (UHMWPE) bearing surfaces on the microscopic contact mechanics with a metallic counterface was investigated in the present study. Both simple sinusoidal roughness forms, with a wide range of amplitudes and wavelengths, and real surface topographies, measured before and after wear testing in a simple pin-on-plate machine, were considered in the theoretical analysis. The finite difference method was used to solve the microscopic contact between the rough UHMWPE bearing surface and a smooth hard counterface. The fast Fourier transform (FFT) was used to cope with the large number of mesh points required to represent the surface topography of the UHMWPE bearing surface. It was found that only isolated asperity contacts occurred under physiological loading, and the real contact area was only a small fraction of the nominal contact area. Consequently, the average contact pressure experienced at the articulating surfaces was significantly higher than the nominal contact pressure. Furthermore, it was shown that the majority of asperities on the worn UHMWPE pin were deformed in the elastic region, and consideration of the plastic deformation only resulted in a negligible increase in the predicted asperity contact area. Microscopic asperity contact and deformation mechanisms may play an important role in the understanding of the wear mechanisms of UHMWPE bearing surfaces.     

Theoretical and Experimental Study of a Thermal Contact Conductance Model for Elastic,Elastoplastic and Plastic Deformation of Rough Surfaces

This study developed a thermal contact conductance model that takes into account surface asperities with elastic, elastoplastic and plastic deformation. The surface asperity model considers the continuity and smoothness of variables across different modes of deformation. Experiments were also conducted to measure thermal contact conductance for samples with different surface roughness when the contact pressure was increased or decreased. The trend of the test data supports the theoretical results.