Slip-line fields for explaining the mechanics of polishing and related processes

Two-dimensional rigid cylindrical asperities are used in modelling the friction and material removal mechanisms occurring in moving contact between engineering surfaces and particularly between abrasive or polishing grits and softer work-pieces. The contact zone of the circular section of the cylinder is approximated by a single chord or by two chords, thereby permitting slip-line fields to be constructed to represent the plastic deformation of the softer material. Account is taken of lubrication conditions. The single chord model is associated with low normal loads, low coefficients of friction and no wear but plastic working of the traversed surface. As normal load is increased there is a transition to the double chord model where the coefficient of friction is higher and where wear occurs due to a cutting action in conjunction with working of the traversed surface. Under certain conditions of lubrication and high loads wear can occur by a tearing mechanism. Experimental findings are cited which confirm that there can be no wear but working of the surface with low loads and wear plus working of the surface with high loads as predicted by the theory.     

A model for the mild ratchetting wear of metals

A mechanism of metallic wear is proposed in which laminar wear debris is generated by a process of plastic ratchetting brought about by repeated pummelling of the softer wearing surface by the asperities on a harder mating surface. Wear rate is found to be approximately proportional to (load) and an increasing function of a single non-dimensional parameter termed the plasticity index for repeated sliding which relates the roughness of the hard surface to the limiting elastic strain of the softer wearing surface. For small values of this parameter the wear rate becomes negligibly small and a shakedown state obtains in which the deformation of the surface is entirely elastic and ratchetting effectively stops. The hardness of the wearing surface and the coefficient of friction at the interface influence the wear rate through their influence on the value of the plasticity index.     

Influence of surface texture and roughness parameters on friction and transfer layer formation during sliding of aluminium pin on steel plate

Surface texture of harder mating surfaces plays an important role during sliding against softer materials and hence the importance of characterizing the surfaces in terms of roughness parameters. In the present investigation, basic studies were conducted using inclined pin-on-plate sliding tester to understand the surface texture effect of hard surfaces on coefficient of friction and transfer layer formation. A tribological couple made of a super purity aluminium pin against steel plate was used in the tests. Two surface parameters of steel plates, namely roughness and texture, were varied in the tests. It was observed that the transfer layer formation and the coefficient of friction along with its two components, namely, the adhesion and plowing, are controlled by the surface texture and are independent of surface roughness (R_a). Among the various surface roughness parameters, the average or the mean slope of the profile was found to explain the variations best. Under lubricated conditions, stick–slip phenomena was observed, the amplitude of which depends on the plowing component of friction. The presence of stick–slip motion under lubricated conditions could be attributed to the molecular deformation of the lubricant component confined between asperities.     

Study on the Boundary-Lubricated Sliding Contact with Subsurface Plastic Deformation

In this study, low-velocity oblique plastic impact-testing experiments were conducted at different angles of incidence to investigate the consequences of the short-distance sliding interaction between a very hard (En31) ball and a relatively softer (mild steel) metal specimen. The purpose was to understand the mechanism of boundary lubrication in the metalworking processes. The specimen was mounted on a specially designed inclined-plane-type fixture so that its surface could be oriented at any desired angle against the free-falling hard ball from a predetermined height. The experimental setup included sufficient details of instrumentation to record the post-impact travel distance and time from which the average coefficient of friction was calculated using a simple methodology. The specimen surfaces were studied using the SEM for different cases of sliding experiments with and without lubricants and two different additives in the lubricants. Marked difference was observed in the nature of surfaces produced in different cases. The oblique impact process was modeled using the equations of motion of the ball and its interaction with plastically deforming specimen material. A fourth-order Runge-Kutta method was used and variations of shear and normal forces during the sliding contact were estimated. The friction behavior showed by this model is in conformance with the experimental results. In addition to that, it has been shown by this model that the coefficient of friction cannot exceed the value of one in sliding. A finite element model has been prepared to estimate the plastic deformation component of friction. Considering the soft asperities of the workpiece deforming as a wave in front of hard asperities, the steady-state Galerkin finite-element model enabled estimation of friction. The trend of the results of the FEM model seems to substantiate the experimental results.     

The influence of surface roughness on abrasive wear

Analyses are given of the mechanism of friction and abrasive wear and of the effect of surface roughness on them. Theoretical expressions are derived for ploughing, adhesion and the total friction coefficient of hard conical asperities ploughing a soft metal surface, with the assumption that the asperities of the hard metal are cones with randomly distributed slopes, the mean value of which varies with surface roughness. Simple expressions for the abrasive wear rate and the mean wear particle size are also derived on the basis of a ploughing mechanism of the hard conical asperities on the soft metal surface.A comparison of calculated values based on these theories with experimental data of single-pass wear tests for various soft metals such as copper, cadmium, lead and zinc sliding on low carbon steel plates shows good agreement. The effects of surface roughness on the tangential forces under unlubricated and lubricated conditions as well as the mean wear particle size are theoretically discussed and the theoretical results are compared with experimental data.     

Deformation and wear behaviour of the junction in quasi-scratch friction

The initial scratching of soft metals by relatively hard metallic asperities involves considerable plastic deformation and wear of the harder metal. Thus the penetration effect on friction is reduced successively as sliding proceeds, leading to the shearing type of friction. Such a transition state of sliding can be defined as a quasi-scratch friction process because ploughing precedes the steady sliding condition.The deformation and wear behaviour at a friction junction was investigated using model experiments between a mild steel conical rider and a flat copper surface. Changes in geometry of the rider and pile-up of the flat metal were examined metallographically and with a microscope. It was found that a stable value of the friction force is determined from the geometric shape of the junction attained after the completion of transient sliding and the effect of initial asperity shape on the friction force becomes insignificant.     

Explaining the mechanics of metallic sliding friction and wear in terms of slipline field models of asperity deformation

It is shown that the force which opposes the sliding of a hard relatively smooth surface over a softer surface can be explained as the force needed to push waves of plastically deformed material along the soft surface ahead of asperities on the hard surface. For rougher surfaces and/or poorer lubrication it is shown how the wave can be torn off or material removed by a chip formation process and wear particles formed. Coefficients of friction predicted from the corresponding asperity deformation models are shown to give good agreement with experimental results. For smooth well lubricated surfaces the wear of the softer surface is shown to occur as a result of the progressive damage to this surface brought about by the repeated passage of waves across it. Equations for predicting wear are derived from the asperity deformation models and a comparison made between predicted and experimental wear results. The paper ends by considering possible future trends in research into the mechanics of friction and wear.     

Contributions of adhesion and hysteresis to coefficient of friction between shoe and floor surfaces: effects of floor roughness and sliding speed

Abstract

Improving shoe–floor friction in order to reduce slip and fall accidents requires thorough understanding of the factors that contribute to friction. The friction between a sliding viscoelastic material (shoe) and a hard surface (floor) has two major components: adhesion and hysteresis. This study aimed to quantify the effects of floor roughness and sliding speed on adhesion and hysteresis to determine how each component contributes to the coefficient of friction. Experiments were conducted on a pin on disc tribometer using ceramic tiles with three levels of roughness, six sliding speeds, two common shoe materials and four liquid lubricants. Hysteresis was measured using a lubricant that minimised adhesion. Dry and lubricated adhesion was measured by subtracting hysteresis from the coefficient of friction. Analysis of variance regression models were used to determine the contributions of hysteresis, dry adhesion, sliding speed and fluid to lubricated coefficient of friction. Increased floor roughness led to increased hysteresis, while increased sliding speed reduced both adhesion and hysteresis. These findings are consistent with theory that states that larger asperities increase hysteretic deformation and that sliding speed affects deformation and real area of contact between a viscoelastic material and a hard surface. The model correctly predicted 83% of variation in coefficient of friction based on dry adhesion, hysteresis and fluid dependent constants. The sensitivity of hysteresis friction to shoe material and floor roughness indicates that optimising these parameters may be effective at reducing slip accidents on oily floor surfaces.     

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。     

粗糙表面微凸体对液黏传动的影响

为研究液黏传动过程中粗糙表面的承载特性,将分形理论引入到两粗糙表面摩擦过程之中,分析传动过程中混合摩擦和边界摩擦两阶段的微凸体承载过程,考虑微凸体弹塑性变形,对M-B模型进行修正,建立修正的微凸体承载模型。建立基于修正M-B模型的微凸体承载模型。通过数值仿真得到有效面积系数、分形参数对液黏调速离合器传动过程的影响规律;对修正的微凸体承载模型的计算结果与M-B模型的计算结果进行对比分析。结果表明:微凸体接触载荷和传递转矩随着面积比的增大而增大,当有效面积系数与尺度系数增大时,接触载荷与传递转矩均有所增大;分形维数为1.5时,微凸体接触载荷与传递转矩最小且随面积比的变化最为缓慢;在整个接触区域内,弹性变形区域的面积、接触载荷以及传递转矩最大,其次是弹塑性变形区域,塑性变形区域最小;考虑弹塑性变形时,微凸体接触载荷与传递转矩均有所下降;修正M-B模型和M-B模型间的修正系数范围在25%以内,修正系数随着有效面积系数、尺度系数的增大而增大,随着分形维数的增大而减小。     

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.     

An explanation of the different regimes of friction and wear using asperity deformation models

A slip-line field analysis is given for the deformation of a soft asperity by a hard one and equations are derived for the corresponding coefficients of friction and wear rates. Three main models are proposed. For smooth surfaces the first model gives low coefficients of friction and shows how plastic deformation of the asperity can occur without removal of material. The second model shows how wear and high coefficients of friction can occur for such surfaces. For rougher surfaces a cutting model applies with a chip (wear particle) being produced. In this way an explanation is offered of why “lubrication” is observed to inhibit wear for smooth surfaces and to encourage it for rougher surfaces. A possible explanation is also given of why the actual wear for engineering surfaces under normal working conditions is many orders of magnitude less than that calculated by assuming that all of the plastically deformed material is removed.     

Studies on friction and transfer layer: role of surface texture

Friction influences the nature of transfer layer formed at the interface between tool and metal during sliding. In the present investigation, experiments were conducted using “Inclined Scratch Tester” to understand the effect of surface texture of hard surfaces on coefficient of friction and transfer layer formation. EN8 steel flats were ground to attain surfaces of different textures with different roughness. Then super purity aluminium pins were scratched against the prepared steel flats. Scanning electron micrographs of the contact surfaces of pins and flats were used to reveal the morphology of transfer layer. It was observed that the coefficient of friction and the formation of transfer layer depend primarily on the texture of hard surfaces, but independent of surface roughness of hard surfaces. It was observed that on surfaces that promote plane strain conditions near the surface, the transfer of material takes place due to the plowing action of the asperities. But, on a surface that promotes plane stress conditions the transfer layer was more due to the adhesion component of friction. It was observed that the adhesion component increases for surfaces that have random texture but was constant for the other surfaces.     

Prediction of Archard's wear coefficient for metallic sliding friction assuming a low cycle fatigue wear mechanism

A recently developed model for sliding friction, in which the frictional force is assumed to result from the pushing of waves of plastically deformed material in the soft surface ahead of asperities on the hard surface, is used to calculate the magnitude of the resulting plastic strain increments which progressively deform the soft surface. On the assumption that a low cycle fatigue mechanism eventually results in detachment of wear particles from the soft surface as a result of this cyclic working of the surface, the calculated strain increments (the magnitudes of which vary with the roughness of the hard surface and the boundary lubrication conditions) are used to estimate wear rates. The results are expressed in terms of Archard's wear coefficient and, for very smooth surfaces and good lubrication, this is predicted to have extremely low values as observed in wear tests for such conditions. For rougher surfaces and less efficient lubrication it is shown that the wear coefficient can increase dramatically.     

Surface topography and integrity effects on sliding wear

The effect of surface roughness and integrity on the sliding wear of metals was investigated experimentally. The results are consistent with the delamination theory of wear. The initial wear rate was influenced by the surface roughness and the applied load but the steady state wear rate was independent of the initial roughness. Under low applied loads delamination of smooth surfaces commences soon after sliding is initiated, whereas the delamination of rough surfaces is delayed until the original asperities are worn. Consequently, under low loads the initial wear rate of a smooth surface is higher than that of a rougher surface. The opposite is found under high loads since original asperities are removed immediately. It is also shown that machining damage to the surface or the subsurface (in the form of deformation, voids and cracks) accelerates the initial wear rate of the machined surface.     

Analysis of the influence of loading and the plasticity index on variations in surface roughness between two flat surfaces

Contact between two highly loaded flat surfaces is examined. In these experiments, a polished, hard metal surface was pressed against a rough aluminium alloy surface. The goal of the experiments was to flatten the peaks on the rough surface by plastic deformation. The experiments elucidated the relation between the normal load and the plasticity index, ψ, and the plastic deformation of the surface roughness peaks in the softer material. The results showed a significant reduction in surface roughness. Increasing the load caused a gradual reduction in the surface peaks. However, based on the values of the plasticity index ψ, it can be concluded that the peaks of the softer material underwent plastic deformation, regardless of the load.     

Analytical determination of friction resistance as a function of normal load and geometry of surface irregularities

A mathematical modeling and simulation of friction during steady state sliding of metals, based on the upper-bound approach, is demonstrated. The existence of wedge-shaped protrusions on the tool surface is assumed. Pressing these protrusions onto the workpiece and sliding the tool along the workpiece produces asperities on the surface of the workpiece. These asperities move in a wave-like motion along the surface layer and cause plastic deformation through a specified depth under the surface. This plastic deformation combines with local friction between the tool and the workpiece along the asperity interface to produce resistance to sliding. The relation between the normal pressure and the sliding resistance is established for the entire range of pressure levels from zero to infinity. The apparent Coulomb coefficient of friction for lower levels of normal pressure and the constant friction factor for excessive load levels are determined. The transition region from Coulomb coefficient of friction to constant friction factor also becomes clear. A mathematical determination is obtained by means of a force equilibrium considering the concept of a contact surface friction ratio. The force of resistance to sliding is related both to the geometry of the asperity of the surface of the tool and to the constant friction factor, which is used for measuring a local frictional force along the interface of each asperity.     

Influence of surface roughness and work-hardened layers on the contact between a rough and a flat surface

The validity of a theory which was derived considering the distribution of the surface slopes of conical asperities and the variation of the flow pressure of each contact due to the work-hardened layer of the softer surface was checked by comparing the theoretical and experimental results. The number, the real area and the distribution of the radii of contact points produced by impressing hard and rough surfaces into soft and flat surfaces with work-hardened layers were measured. The distribution of the surface slopes of contact asperities and the variation of the flow pressure with increasing penetration of the hard asperities were also obtained experimentally.     

Plastic flattening of a sinusoidal metal surface: A discrete dislocation plasticity study

The plastic flattening of a sinusoidal metal surface is studied by performing plane strain dislocation dynamics simulations. Plasticity arises from the collective motion of discrete dislocations of edge character. Their dynamics is incorporated through constitutive rules for nucleation, glide, pinning and annihilation. By analyzing surfaces with constant amplitude we found that the mean contact pressure is inversely proportional to the wavelength. For small wavelengths, due to interaction between plastic zones of neighboring contacts, the mean contact pressure can reach values that are about 1/10 of the theoretical strength of the material, thus significantly higher than what is predicted by simulations that do not account for size dependent plasticity. Surfaces with the same amplitude to period ratio have a size dependent response, such that if we interpret each period of the sinusoidal wave as the asperity of a rough surface, smaller asperities are harder to be flattened than large ones. The difference between the limiting situations of sticking and frictionless contacts is found to be negligible.     

Numerical experiments on the influence of material and other variables on plane strain continuous chip formation in metal machining

Finite element simulations of metal machining chip formation have been carried out with model materials that have been given a range of thermal softening and strain hardening behaviours. For materials that are approximately perfectly plastic, predictions of slip-line field theory regarding the dependence of chip/tool normal contact stress distribution on the combination of shear plane angle, friction angle and tool rake angle are reproduced. But it has not proved possible to generate the full range of non-unique fields predicted by slip-line theory. The introduction of strain hardening causes chips to thicken but with deviations at high hardening rates from the behaviour proposed by Oxley. These observations are generally in agreement with previously published physical test data. A study of the effect of increasing the cutting edge radius confirms the important effect of that, particularly on tool thrust forces. By continually comparing the results to expectations from more simple modelling, and asking the question ‘Is that expected?’, a general problem of creating a friction law applicable to both plastically flowing high stress conditions and to more lightly loaded elastic conditions has been recognised and is the subject of continuing work.