Plastic shear response of a single asperity: a discrete dislocation plasticity analysis

We investigate the plastic shear response during static friction of an asperity protruding from a large FCC single crystal. The asperity is in perfectly adhesive contact with a rigid platen and is sheared by tangentially moving the platen. Using discrete dislocation plasticity simulations, we elucidate the plastic shear behaviour of single asperities of various size and shape, in search for the length scale that controls the plastic behaviour. Since plasticity can occur also in the crystal, identification of the length scale that controls a possible size-dependent plastic behaviour is far from being trivial. It is found that scaling down the dimensions of an asperity results in a higher contact shear strength. The contact area is dominant in controlling the plastic shear response, because it determines the size of the zone, in and below the asperity, where dislocation nucleation can occur. For a specific contact area, there is still a dependence on asperity volume and shape, but this is weaker than the dependence on contact area alone.     

Contact mechanics analysis of oscillatory sliding of a rigid fractal surface against an elastic–plastic half-space

Oscillatory sliding contact between a rigid rough surface and an elastic–plastic half-space is examined in the context of numerical simulations. Stick-slip at asperity contacts is included in the analysis in the form of a modified Mindlin theory. Two friction force components are considered – adhesion (depending on the real area of contact, shear strength and interfacial adhesive strength) and plowing (accounting for the deformation resistance of the plastically deformed half-space). Multi-scale surface roughness is described by fractal geometry, whereas the interfacial adhesive strength is represented by a floating parameter that varies between zero (adhesionless surfaces) and one (perfectly adhered surfaces). The effects of surface roughness, apparent contact pressure, oscillation amplitude, elastic–plastic properties of the half-space and interfacial adhesion on contact deformation are interpreted in the light of numerical results of the energy dissipation, maximum tangential (friction) force and slip index. A non-monotonic trend of the energy dissipation and maximum tangential force is observed with increasing surface roughness, which is explained in terms of the evolution of the elastic and plastic fractions of truncated asperity contact areas. The decrease of energy dissipation with increasing apparent contact pressure is attributed to the increase of the elastic contact area fraction and the decrease of the slip index. For a half-space with fixed yield strength, a lower elastic modulus produces a higher tangential force, whereas a higher elastic modulus yields a higher slip index. These two competing effects lead to a non-monotonic dependence of the energy dissipation on the elastic modulus-to-yield strength ratio of the half-space. The effect of interfacial adhesion on the oscillatory contact behaviour is more pronounced for smoother surfaces because the majority of asperity contacts deform elastically and adhesion is the dominant friction mechanism. For rough surfaces, higher interfacial adhesion yields less energy dissipation because more asperity contacts exhibit partial slip.     

Dimension of similarity as a characteristic of the solid-surface relief

It is proposed that the dimension of similarity of the relief profile be used as an integral characteristic of solid-surface roughness. This parameter coincides with the fractal dimension of the line only in the case of the same length scales in the surface plane and in the direction that is normal to it. The interrelation between the dimension of similarity and the usually used fractal dimension of the relief profile is obtained and analyzed. The optical surface of single-crystal Ge is used as an example in order to reveal the correlation between the dimension of similarity of the relief surface and the transmission coefficient in the infrared range.     

基于多尺度模拟研究Ni/Cu薄膜压痕塑性的原子机制

基于准连续介质多尺度模拟方法研究了Ni/Cu双层薄膜初始压痕塑性的原子机制,结果主要包括:(1)当Ni晶体层厚度小于10nm时,随着Ni晶体层厚度的减少,薄膜弹性极限所对应的临界接触力逐渐降低,即Ni/Cu薄膜随Ni晶体层厚度减小而变软;(2)压头下方晶格Shockley分位错的开动、界面位错的分解、以及界面位错与晶格位错的相互作用是Ni/Cu薄膜初始塑性的微观原子机制,(3)根据模拟结果观察和位错弹性理论计算,承载初始塑性的界面位错数目变少是Ni/Cu薄膜软化的主要原子机制.本文研究结果能够为异质界面力学行为研究提供有益参考.     

Comparison of fractal and profilometric methods for surface topography characterization

In this study microstructural and roughness characterization of surface of aluminium foils used in lithographic printing process was performed by contact and non-contact profilometric methods and fractal analysis. Significant differences in roughness parameters values inferred from stylus method in respect to those inferred from the non-contact measurements were observed. The investigation of correlation between various fractal dimensions obtained from gray-scale SEM micrographs and binary images resulting from median filtering of the original SEM micrographs as well as selected relevant roughness parameters shows that there is a strong correlation between certain roughness parameters and particular fractal dimensions. This correlations permit better physical understanding of fractal characteristics and interpretation of the dynamics of surface roughness change through processing. Generally these correlations are more suitable for parameters obtained by stylus method than those inferred from the laser-based measurements.     

A Monte Carlo method for simulating fractal surfaces

A Monte Carlo method is presented for simulating rough surfaces with the fractal behavior. The simulation is based on power-law size distribution of asperity diameter and self-affine property of roughness on surfaces. A probability model based on random number for asperity sizes is developed to generate the surfaces. By iteration, this method can be used to simulate surfaces that exhibit the aforementioned properties. The results indicate that the variation of the surface topography is related to the effects of scaling constant G and the fractal dimension D of the profile of rough surface. The larger value of D or smaller value of G signifies the smoother surface topography. This method may have the potential in prediction of the transport properties (such as friction, wear, lubrication, permeability and thermal or electrical conductivity, etc.) on rough surfaces.     

Nanoadhesion between rough surfaces

A model is developed to describe the adhesion between deformable fractal surfaces over the mesoscopic realm that covers the familiar range of interest in nanotechnology from atomic dimensions to microns. This model helps us gain a quantitative understanding of the variation of adhesion with surface energy, with microstructure of rough surfaces, and with bulk deformability. The present analysis goes beyond the Gaussian distribution of asperity heights by investigating the influence of the microstructure of self-affine fractal surfaces. Our calculation reveals that orders of magnitude increase in adhesion are possible as the roughness exponent decreases.     

Nanodroplets on rough hydrophilic and hydrophobic surfaces

We present results of Molecular Dynamics (MD) calculations on the behavior of liquid nanodroplets on rough hydrophobic and hydrophilic solid surfaces. On hydrophobic surfaces, the contact angle for nanodroplets depends strongly on the root-mean-square roughness amplitude, but it is nearly independent of the fractal dimension of the surface. Since increasing the fractal dimension increases the short-wavelength roughness, while the long-wavelength roughness is almost unchanged, we conclude that for hydrophobic interactions the short-wavelength (atomistic) roughness is not very important. We show that the nanodroplet is in a Cassie-like state. For rough hydrophobic surfaces, there is no contact angle hysteresis due to strong thermal fluctuations, which occur at the liquid-solid interface on the nanoscale. On hydrophilic surfaces, however, there is strong contact angle hysteresis due to higher energy barrier. These findings may be very important for the development of artificially biomimetic superhydrophobic surfaces.     

The effect of substrate roughness on the static friction of CuO nanowires

The dependence of static friction on surface roughness was measured for copper oxide nanowires on silicon wafers coated with amorphous silicon. The surface roughness of the substrate was varied to different extent by the chemical etching of the substrates. For friction measurements, the nanowires (NWs) were pushed by an atomic-force microscope (AFM) tip at one end of the NW until complete displacement of the NW was achieved. The elastic bending profile of a NW during this manipulation process was used to calculate the ultimate static friction force. A strong dependence of static friction on surface roughness was demonstrated. The real contact area and interfacial shear strength were estimated using a multiple elastic asperity model, which is based on the Derjaguin–Muller–Toporov (DMT) contact mechanics. The model included vertical elastic flexure of NW rested on high asperities due to van der Waals force.     

用分形理论研究低温条件下Al-Al界面间的接触导热现象

界面形貌是固体界面间接触导热的最主要影响因素 ,传统的形貌表征参数与仪器的分辨率和取样长度密切相关 ,因而基于这些参数的常规接触导热模型显然是尺度相关的。分形网络模型利用粗糙表面处处连续却不可微的分形特征 ,采用与尺度无关的分形参数 ,揭示了接触导热的本质 ,为准确预测接触热导开辟了一条新的途径。实验测定了粗糙表面的分形参数和低温条件下 Al50 52 - Al50 52界面间的接触热导 ,将接触热导的实验值与分形网络模型的预测结果进行了比较 ,并就接触热导与压力、分形参数和温度之间的关系进行了分析 ,指出分形网络模型的预测精度与分形参数相关联。     

Current challenges for statistical physics in fracture and plasticity

Statistical physics has been applied in the last decades to several problems in mechanics, including fracture and plasticity. Concept drawn from percolation, fractal geometry, phase-transitions, and interface depinning have been used with varying degrees of success to understand these problems. In this colloquium, I describe recent successes and current challenging problems for statistical physics in fracture and plasticity, focusing on the roughness of cracks, fracture size effects and micron-scale plasticity.     

Rough surfaces and elasto-plastic contacts

We consider the contact between a rough surface and a smooth rigid plane. The real contact area and pressure are determined by taking into account the deformation regimes of metallic asperities. The local contact of each asperity is studied, by introducing a transitional regime between perfectly elastic and plastic extreme behaviours.     

Adhesion between an elastic body and a randomly rough hard surface

I have developed a theory of adhesion between an elastic solid and a hard randomly rough substrate. The theory takes into account that partial contact may occur between the solids on all length scales. I present numerical results for the case where the substrate surface is self-affine fractal. When the fractal dimension is close to 2, complete contact typically occurs in the macro-asperity contact areas, while when the fractal dimension is larger than 2.5, the area of (apparent) contact decreases continuously when the magnification is increased. An important result is that even when the surface roughness is so high that no adhesion can be detected in a pull-off experiment, the area of real contact (when adhesion is included) may still be several times larger than when the adhesion is neglected. Since it is the area of real contact which determines the sliding friction force, the adhesion interaction may strongly affect the friction force even when no adhesion can be detected in a pull-off experiment. Received 3 April 2002     

A Generalized Johnson Parameter for Pull-Off Decay in the Adhesion of Rough Surfaces

There is no simple theory at present to predict accurately the decay of pull-off in the adhesion of randomly rough surfaces. The asperity model of Fuller and Tabor has shown significant error in recent numerical investigations by Pastewka and Robbins of self-affine random roughness from micrometer to atomic scale which corresponds to low values of Tabor parameter. For sinusoidal contact, the Johnson parameter, originally introduced for the JKR regime (from Johnson-Kendall-Roberts) is the dominant parameter ruling the pull-off at intermediate Tabor values. Hence, we define a generalized Johnson parameter as the ratio between the adhesive energy to the elastic strain energy to flatten the surface in the case of multiscale roughness and find that it correlates very well with the data of Pastewka and Robbins spanning almost five orders of magnitude of reduction from theoretical strength, improving significantly with respect to other possible single parameter criteria. For the most important case in practice, that of low fractal dimensions, this suggests the product of amplitude and slope of the largest wavelength components of roughness dominate pull-off decay, and not small scales features like slopes and curvatures, as suggested by Pastewka and Robbins.     

粗糙表面形貌对湿润性的影响

采用自仿射分形对粗糙表面形貌进行了定量描述。基于分形粗糙表面形貌,建立了粗糙表面润湿性的理论模型并进行了数值计算,分析讨论了均方根粗糙度和表面分形维数对接触角的影响。研究结果表明,均方根粗糙度对接触角的影响较大,而粗糙表面的分形维数对润湿性的影响则并不明显。     

Indenter size effect on the reversible incipient plasticity of Al(001) surface:Quasicontinuum study

Indenter size effect on the reversible incipient plasticity of Al(001) surface is studied by quasicontinuum simulations.Results show that the incipient plasticity under small indenter, the radius of which is less than ten nanometers, is dominated by a simple planar fault defect that can be fully removed after withdrawal of the indenter; otherwise, irreversible incipient plastic deformation driven by a complex dislocation activity is preferred, and the debris of deformation twins, dislocations,and stacking fault ribbons still remain beneath the surface when the indenter has been completely retracted. Based on stress distributions calculated at an atomic level, the reason why the dislocation burst instead of a simple fault ribbon is observed under a large indenter is the release of the intensely accumulated shear stress. Finally, the critical load analysis implies that there exists a reversible-irreversible transition of incipient plasticity induced by indenter size. Our findings provide a further insight into the incipient surface plasticity of face-centered-cubic metals in nano-sized contact issues.     

粗糙表面形貌对微尺度流动换热的影响

基于分形几何定量描述了多尺度自仿射的粗糙表面形貌,建立了微通道内层流流动换热的理论模型并对表面形貌的影响进行了数值模拟.研究表明,自仿射分形维数直接反映了表面轮廓的不规则度,对于两个具有相同统计粗糙度的轮廓,可能存在不同的分形维数;与常规尺度通道不同,雷诺数、粗糙高度和粗糙表面分形维数都对微通道内层流流动换热有着重要影...     

Definition of road roughness parameters for tire vibration noise control

Road roughness plays an important role in the generation of tire vibration noise. However, it is unclear which kinds of road roughness parameters should be controlled to reduce the noise. In this paper, we define the essential road roughness parameters that govern tire tread vibration and provide information on tire/road noise abatement. The detailed effects of road roughness parameters on tire tread vibration are estimated using a tire/road contact model. The results reveal that pavement asperity height itself is not an essential parameter, but asperity height unevenness, asperity radius, and asperity spacing are important for the abatement of tire vibration noise.     

Nanotribological behavior of diamond surfaces using molecular dynamics with fractal theory and experiments

The frictional and indented behavior of a diamond asperity on a diamond plate was carried out using a molecular dynamics (MD) and experiments. The contact load, contact area, dynamic frictional force, and dynamic frictional coefficient increased as the contact interference increased at a constant loading velocity. The microcontact and frictional behavior can be evaluated between a rigid smooth hemisphere to a deformable rough flat plane by combined the deformed behavior of the asperity obtained from MD results with the fractal and statistic parameters. The comparison and the discrepancy of simulated results and nanoindentation and scratching experimental results will be discussed.     

Influence of surface roughness on superhydrophobicity

Superhydrophobic surfaces, with a liquid contact angle theta greater than 150 degrees , have important practical applications ranging from self-cleaning window glasses, paints, and fabrics to low-friction surfaces. Many biological surfaces, such as the lotus leaf, have a hierarchically structured surface roughness which is optimized for superhydrophobicity through natural selection. Here we present a molecular dynamics study of liquid droplets in contact with self-affine fractal surfaces. Our results indicate that the contact angle for nanodroplets depends strongly on the root-mean-square surface roughness amplitude but is nearly independent of the fractal dimension D(f) of the surface.