A multiscale molecular dynamics approach to contact mechanics

The friction and adhesion between elastic bodies are strongly influenced by the roughness of the surfaces in contact. Here we develop a multiscale molecular dynamics approach to contact mechanics, which can be used also when the surfaces have roughness on many different length-scales, e.g., for self affine fractal surfaces. As an illustration we consider the contact between randomly rough surfaces, and show that the contact area varies linearly with the load for small load. We also analyze the contact morphology and the pressure distribution at different magnification, both with and without adhesion. The calculations are compared with analytical contact mechanics models based on continuum mechanics.     

Adhesive properties of contacts between elastic bodies with randomly rough self-affine surfaces: A simulation with the method of reduction of dimensionality

Adhesive properties (adhesion force and adhesion coefficient) of contacts between elastic bodies with rough surfaces have been investigated and adhesion maps constructed showing the dependence of adhesive properties on the roughness, rms slope of the surface, elastic modulus, surface energy and fractal dimension. Simulations have been carried out in the frame of the method of reduction of dimensionality.     

Monte Carlo simulations of catalytic CO oxidation on fractal surfaces of dimension between two and three

We present a method for generating fractal surfaces of dimension between two and three. By using the method, five fractal surfaces with dimension 2.262, 2.402, 2.524, 2.631, and 2.771 are created. For each of these surfaces, the reaction of carbon monoxide and oxygen is simulated by using a Monte Carlo method based on the ZGB model [Phys. Rev. Lett. 24 (1986) 2553]. The results show that the catalytic CO oxidation proceeds more efficiently on a surface with higher fractal dimension. It is also found that as the fractal dimension of the surface becomes higher, the first-order kinetic phase transition point (y₂) is shifted to a higher partial pressure of CO. This implies that poisoning of the catalyst surface due to CO segregation sets in at a higher CO partial pressure for surfaces with more complexity.     

Investigation of the dry normal contact between fractal rough surfaces using the reduction method,comparison to 3D simulations

The reduction method was applied to solving the elastic contact problem of fractal rough surfaces having different fractal dimensions. These surfaces are of particular interest, as contact spots influence each other on large and small scales, depending on the power spectrum. Results were compared to previous boundary-element method simulations that had been conducted with 3D surfaces, taking into account all interdependencies between contact spots. Excellent agreement in the contact stiffness was found. Even though no interactions are allowed in the reduced model, the same power-law behavior can be observed as in the 3D case, due to the transformation of the power spectrum. Theoretical considerations about the power-law for different fractal dimensions are given.     

Subcooled pool boiling heat transfer in fractal nanofluids:A novel analytical model

A novel analytical model to determine the heat flux of subcooled pool boiling in fractal nanofluids is developed. The model considers the fractal character of nanofluids in terms of the fractal dimension of nanoparticles and the fractal dimen- sion of active cavities on the heated surfaces; it also takes into account the effect of the Brownian motion of nanoparticles, which has no empirical constant but has parameters with physical meanings. The proposed model is expressed as a function of the subcooling of fluids and the wall superheat. The fractal analytical model is verified by a reasonable agreement with the experimental data and the results obtained from existing models.     

Non-contact adhesion to self-affine surfaces: A theoretical model

Strength of adhesion between materials is known to be strongly influenced by interface irregularities. In this work, I devise a perturbative approach to describe the effect of self-affine roughness on non-contact adhesive interactions. The hierarchy of the obtained analytical solutions is the following. First, analytical formulae are deduced to describe roughness corrections to the van der Waals interaction energies between a hemi-space adherend, bounded by a self-affine surface, and a point-like adherent. Second, the problem of two hemi-spaces, one of which has a planar surface, and the other is bounded by a self-affine surface, is solved analytically. In the latter case, a numerical analysis is performed to delineate the behavior of the roughness corrections as a function of the parameters, characterizing self-affine fractal surface roughness. The problem of two hemi-spaces, both bounded by self-affine fractal surfaces, is also addressed in this work. The model?s predictions are compared with previously reported theoretical results and available experimental data.     

A fractal study for nucleate pool boiling heat transfer of nanofluids

In this paper, a fractal model for nucleate pool boiling heat transfer of nanofluids is developed based on the fractal distribution of nanoparticles and nucleation sites on boiling surfaces. The model shows the dependences of the heat flux on nanoparticle size and the nanoparticle volume fraction of the suspension, the fractal dimension of the nanoparticle and nucleation site, temperature of nanofluids and properties of fluids. The fractal model predictions show that the natural convection stage continues r...     

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...     

Prediction of heat transfer of nanofluid on critical heat flux based on fractal geometry

Analytical expressions for nucleate pool boiling heat transfer of nanofluid in the critical heat flux (CHF) region are derived taking into account the effect of nanoparticles moving in liquid based on the fractal geometry theory. The proposed fractal model for the CHF of nanofluid is explicitly related to the average diameter of the nanoparticles, the volumetric nanoparticle concentration, the thermal conductivity of nanoparticles, the fractal dimension of nanoparticles, the fractal dimension of active cavities on the heated surfaces, the temperature, and the properties of the fluid. It is found that the CHF of nanofluid decreases with the increase of the average diameter of nanoparticles. Each parameter of the proposed formulas on CHF has a clear physical meaning. The model predictions are compared with the existing experimental data, and a good agreement between the model predictions and experimental data is found. The validity of the present model is thus verified. The proposed fractal model can reveal the mechanism of heat transfer in nanofluid.     

Transfer across random versus deterministic fractal interfaces

A numerical study of the transfer across random fractal surfaces shows that their responses are very close to the response of deterministic model geometries with the same fractal dimension. The simulations of several interfaces with prefractal geometries show that, within very good approximation, the flux depends only on a few characteristic features of the interface geometry: the lower and higher cutoffs and the fractal dimension. Although the active zones are different for different geometries, the electrode responses are very nearly the same. In that sense, the fractal dimension is the essential "universal" exponent which determines the net transfer.     

Formation of different surface reliefs of metallic glasses under mechanical stress

The micro- and nanoreliefs of loaded lateral surfaces and fracture surfaces of foils of the Fe₇₇Ni₁Si₉B₁₃, Fe₅₈Ni₂₀Si₉B₁₃, and Fe₇₀Cr₁₅B₁₅ amorphous alloys have been investigated using scanning tunneling and atomic force microscopy. The isotropic and anisotropic surface reliefs have been examined. The fractal dimensions of the surfaces of loaded specimens and the fracture surfaces along and across the direction of crack propagation have been estimated using the box counting method. Fractal characteristics of the surfaces, such as the Hölder exponent and the half-width of the singularity spectrum, have been calculated using the wavelet transform method. It has been found that, on the topographies with a clearly pronounced anisotropy of the relief, the surface is fractal in only one direction, and the surface is fractal in two directions on the topographies with a less pronounced anisotropy of the relief. The fractal characteristics of the lateral surfaces and the fracture surfaces with allowance made for their anisotropy have close values. It has been shown that the formation of two types of fracture surfaces is adequately described in terms of the model of a cellular automaton.     

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.     

Kinetic Simulation of Fractal Aggregation on Liquid Surfaces

A modified fractal growth model based on the deposition, diffusion, and aggregation (DDA) with cluster rotation is presented to simulate two-dimensional fractal aggregation on liquid surfaces. The mobility (including diffusion and rotation) of clusters is related to its mass, which is given by D_m=D₀ s^-γ_D and θ_m=θ₀s^-γ_θ, respectively. We concentrate on revealing the details of the influence of deposition flux F, cluster diffusion factor γ_D and cluster rotation factor γ_θ on the dynamics of fractal aggregation on liquid surfaces. It is shown that the morphologies of clusters and values of cluster density and fractal dimension depend dramatically on the deposition flux and migration factors of clusters.     

分形基底上刻蚀模型动力学标度行为的 数值模拟研究

为探讨分形基底结构对生长表面标度行为的影响, 本文采用Kinetic Monte Carlo(KMC)方法模拟了刻蚀模型(etching model)在谢尔宾斯基箭头和蟹状分形基底上刻蚀表面的动力学行为. 研究表明,在两种分形基底上的刻蚀模型都表现出很好的动力学标度行为, 并且满足Family-Vicsek标度规律. 虽然谢尔宾斯基箭头和蟹状分形基底的分形维数相同, 但模拟得到的标度指数却不同, 并且粗糙度指数 α与动力学指数z也不满足在欧几里得基底上成立的标度关系α+z=2. 由此可以看出, 标度指数不仅与基底的分形维数有关, 而且和分形基底的具体结构有关.     

断裂表面自相似与自仿射复杂分形结构的研究

 按照分形理论研究了具有自相似和自仿射分形结构的复杂表面,并研究了其在Ⅰ型+Ⅱ型和Ⅰ型+Ⅲ型混合载荷下形成的断裂表面的应用。结果指出：分维D与粗糙度指数H之间的关系（D+H=2或D×H=1）只是粗略的近似。用分维D或粗糙度指数H测量断裂表面,在双对数图上得到的是实验曲线而不是直线并不说明没有分形结构,很可能是自相似和自仿射结构的混合。     

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.     

Evolution of fractal particles in systems with conserved order parameter

Computer simulations of the evolution of fractal aggregates in systems with conserved order parameter are described in this work. The aggregates are generated by diffusion-limited aggregation. This model describes such important processes as annealing of dendrite inclusions in solids, healing of cracks in ceramics, temperature-induced transformations in composites, relaxation of rough surfaces, aging of colloid particles, etc. It is shown that the evolution in fractal media differs significantly from that occurring in initially homogeneous systems and leads to different values of the scaling exponent. A relationship between the fractal dimension, mechanism of relaxation, and scaling exponent was also derived.     

Studies of the collision frequency of ideal gas particles with the surfaces of the objects created using the ballistic deposition technique

This paper is a continuation of our studies of the collision frequency of ideal gas particles with the rough/fractal surfaces. Here, we applied a more realistic surface growth model, i.e. ballistic deposition for creation of fractal objects. We found that the collision frequency with irregular surfaces is the linear function of pressure and this frequency per unit pressure is quite a complicated function of the surface fractal dimension as well as the diameter of colliding particle. The collision frequency with rough surfaces cannot be exactly described by the analytical formula called the Langmuir-Hertz equation. However, we have stated that the deviations of the true collision frequency from the Langmuir-Hertz prediction are not huge and in typical catalytic studies the error introduced by replacing the true frequency by the Langmuir-Hertz prediction can be safely neglected. We have also studied the probability of finding on the surface an atom which has been hit a certain number of times by a gas particle. This probability reveals an interesting behaviour for small gas particles, i.e. it perfectly correlates with the number of directions from which the surface atom is accessible from the gas phase. We have also estimated the evolution of the adsorption energy distribution with the increasing fractal dimension of the surface in the ballistic deposition.     

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     

KDP晶体单点金刚石车削表面形貌分形分析

 分别使用2维和3维分形方法对单点金刚石车削加工的KDP晶体表面形貌进行了分析,并对表面的3维分形维数和3维粗糙度表征参数进行了比较,分析了二者对表面形貌表征的差异。使用2维轮廓分形方法计算了KDP晶体表面圆周各方向上的分形维数。通过分析得出：3维分形维数与表面粗糙度值成反比关系;使用单点金刚石车削方法加工KDP晶体会形成各向异性特征明显的已加工表面,在一定程度上容易形成小尺度波纹;已加工表面是否具有明显的小尺度波纹特征与表面粗糙度值并无直接关系,但与其表面轮廓分形状态分布密切相关;KDP晶体表面2维功率谱密度与其分形状态具有相近的方向性特征。