Experimental investigation of the contact mechanics of rough fractal surfaces

The nonstationary character of roughness is a widely recognized property of surface morphology and suggests modeling several solid surfaces by fractal geometry. In the field of contact mechanics, this demands novel investigations attempting to clarify the role of multiscale roughness during physical contact. Here we review the results we recently obtained in the characterization of the contact mechanics of fractal surfaces by depth-sensing indentation. One class of experiments was conducted on organic thin films, load-displacement curves being acquired by atomic force microscopy using custom-designed tips. Another class of experiments focused on well-defined crystalline and mechanically polished ceramic substrates probed by a traditional nanoindenter. We observed the first-loading cycle to be considerably affected by surface roughness. Plastic failure was found to dominate incipient contact while contact stiffness increased on decreasing fractal dimension and roughness. Our findings suggest fractal parameters to drive contact mechanics whenever the penetration depth is kept below the interface width.     

基于分形理论的两粗糙表面接触的黏滑摩擦模型EI北大核心CSCD

两粗糙表面的接触本质上是大量微凸体的接触,具有复杂的力学行为,连接界面的力学建模是重要的科学问题。从微观角度出发,对单个微凸体进行接触分析,并考虑了微凸体相互作用造成的基底面的下降,根据分形理论积分,建立了整个接触面的法向接触模型。利用该模型,可确定在给定法向预紧载荷下微接触截面积的概率密度函数;根据Mindlin模型、Masing准则和分形理论,建立了两粗糙表面接触的切向载荷与切向位移的关系,并研究了不同参数对系统能量耗散的影响。数值仿真结果表明,能量耗散随分形维数D增大而增大,随分形粗糙度参数G及法向预紧力增大而降低。     

Multi-parameter identification and shape reconstruction for unbounded fractal rough surfaces with tapered wave incidence

In this paper, we study the inverse scattering of tapered waves from sound soft surfaces or horizontally polarized electromagnetic waves from perfectly conducting surfaces. By the related Fréchet derivative with respect to a given surface of the solution of direct scattering problems, an efficient algorithm is proposed to reconstruct the parameters of unbounded rough surfaces from a set of scattered field measurements. Tapered wave is introduced to realize the asymptotic truncation for unbounded fractal rough surface. In order to improve the results of reconstruction, multi-angle and multi-frequency incidence strategy has been used. The numerical results show that the method yields satisfactory reconstructions for some rough surface profiles.     

Double-scatter cross sections for two-dimensional random rough surfaces that exhibit backscatter enhancement

Full-wave solutions are given for the single- and double-scatter radar cross sections for two-dimensional random rough surfaces. High-frequency approximations are used for the double-scatter cross sections in order to express them as numerically tractable four-dimensional integrals. The major contributions to the double-scatter cross sections are associated with the quasi-parallel and quasi-antiparallel double-scatter paths. They come from the neighborhoods of specular points. The enhancement of the backscatter cross sections, which is associated with the quasi-antiparallel double-scatter paths, is observed for both the like- and cross-polarized cross sections.     

Contact and frictional behavior of rough surfaces using molecular dynamics combined with fractal theory

The microcontact behavior of a copper asperity on a diamond plate was carried out using a molecular dynamics (MD) simulation with the parallel algorithms atom decomposition method. The results show that the dynamic frictional force had an oscillated behavior when the flat diamond plane slipped through the copper asperity. The contact load, contact area, dynamic frictional force, and dynamic frictional coefficient increased as the contact interference increased at a constant loading velocity. The dynamic frictional force and dynamic frictional coefficient increased as the sliding velocity increased. Furthermore, the microcontact behavior can be evaluated between a rigid smooth flat plane and a rigid smooth hemisphere to a deformable rough flat plane by combining the deformed behavior of the asperity obtained from MD results and the fractal and statistic parameters.     

Measurement of random processes at rough surfaces with digital speckle correlation

We present a detailed investigation of digital speckle correlation to measure small changes in the microstructure of random rough surfaces. The corresponding alterations in the scattered-light field are recorded by an electronic camera with subsequent numerical correlation. Among the classical theoretical approaches to describe the scattering at random rough surfaces, the composite-roughness model is advanced to calculate the speckle correlation in terms of parameters of the changes in surface microstructure. For an experimental verification, surfaces with similar microstructure are fabricated with a photolithographic technique. They are employed for comparative measurements with high-resolution scanning force microscopy and for correlation measurements under variation of experimental parameters. A good agreement between theoretically predicted and experimental correlation data can be observed. The results allow a quantitative whole-field monitoring of surface processes by remote optical means.     

Characterization of random rough surfaces from scattered intensities by neural networks

Abstract

Optical scatterometry, a non-invasive characterization method, is used to infer the statistical properties of random rough surfaces. The Gaussian model with rms-roughness [sgrave] and correlation length σ is considered in this paper but the employed technique is applicable to any representation of random rough surfaces. Surfaces with wide ranges of Λ and σ, up to 5 wavelengths (λ), are characterized with neural networks. Two models are used: self-organizing map (SOM) for rough classification and multi-layer perceptron (MLP) for quantitative estimation with nonlinear regression. Models infer Λ and σ from scattering, thus involving the inverse problem. The intensities are calculated with the exact electromagnetic theory, which enables a wide range of parameters. The most widely known neural network model in practise is SOM, which we use to organize samples into discrete classes with resolution ΔΛ = Δσ = 0.5λ. The more advanced MLP model is trained for optimal behaviour by providing it with known parts of input (scattering) and output (surface parameters). We show that a small amount of data is sufficient for an excellent accuracy on the order of 0.3λ and 0.15λ for estimating Λ and σ, respectively.     

Reflectometer for measuring the bidirectional reflectance of rough surfaces

A fully automatic, four-axis gonioreflectometer is described. It has an angular accuracy of 0.3 degrees and a range of 90 degrees in both the theta(i) and the theta(r) zenith angles. The gonioreflectometer is simpler than previous designs because of its use of rotating arms rather than moving carriages to mount the optical components. Where possible, commercial components have been used to reduce the cost. A novel off-axis angular encoding scheme is also described.     

Beam implementation in a nonorthogonal coordinate system: application to the scattering from random rough surfaces

The C method is known to be one of the most efficient and versatile tools established for modeling diffraction gratings. Its main advantage is the use of a coordinate system in which the boundary conditions apply naturally and are, ipso facto, greatly simplified. In the context of scattering from random rough surfaces, we propose an extension of this method in order to treat the problem of diffraction of an arbitrary incident beam from a perfectly conducting (PEC) rough surface. For that, we were led to revisit some numerical aspects that simplify the implementation and improve the resulting codes.     

Monte Carlo simulation of Stokes vectors of polarized light scattering from two-dimensional random rough surfaces

A Monte Carlo model was established to simulate polarized scattering fields of two-dimensional rough surfaces based on the Kirchhoff approximation. Based on this model, numerical studies of the hemispherical distribution of Stokes vectors of scattered light from dielectric and metal rough surfaces were carried out. These surfaces have Gaussian distributions with correlation length of 3.1?µm and standard deviation varying between 0.1 and 0.6?µm. The results reveal that the V component of metal surfaces has peaks antisymmetric with the incident plane, whereas the V component of dielectric surfaces is almost zero. We consider that this property of the V component would provide a new method which could be used to distinguish the target material.     

Velocities for moving random surfaces

For a stationary two-dimensional random field evolving in time, we derive statistical distributions of appropriately defined velocities. The results are based on a generalization of the Rice formula. We discuss importance of identifying the correct form of the distribution which accounts for the sampling bias. The theory can be applied to practical problems where evolving random fields are considered to be adequate models. Examples include changes of atmospheric pressure, variation of air pollution, or dynamical models of the sea surface elevation. We study the last application in more detail by applying the derived results to Gaussian fields representing irregular sea surfaces. In particular, we study statistical properties of velocities both for the sea surface and for the envelope field based on this surface. The latter is better fitted to study wave group velocities and is of particular interest for engineering applications. For wave and wave group velocities, numerical computations of distributions are presented and illustrated graphically.     

Pressure dependence of the thermal contact resistance for rough surfaces

The contact resistance is expressed analytically as a function of load for elastic and elastoplastic contacts by taking the rough surface as consisting of spherical projections with a normal distribution.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 19, No. 1, pp. 62–67,July, 1970.     

Force of friction between fractal rough surface and elastomer

The force of friction between a fractal rough surface and a model elastomer has been numerically simulated using the method of dimensionality reduction. For elastomers, in which the imaginary part of the complex shear modulus is much greater than the real part, the friction coefficient is proportional to the mean square gradient of the solid surface profile. The empirical value of the proportionality coefficient is close to unity.     

Remote sensing of penetrable objects buried beneath two-dimensional random rough surfaces by use of the Mueller matrix elements

The modified Mueller matrix elements for electromagnetic scattering from penetrable objects buried under two-dimensional random rough surfaces are investigated. This matrix relates the incident to the scattered waves, and it contains different combinations of the fully polarimetric scattering matrix elements. The statistical average of each Mueller matrix element is computed on the basis of the Monte Carlo simulations by exploiting the speed of the three-dimensional steepest-descent fast multipole method. The numerical results clearly show that relying only on the co-polarized or the cross-polarized intensities or both (i.e., vv, hh, vh, and hv) is not sufficient for sensing the buried objects. However, examining all 16 Mueller matrix elements significantly increases the possibility of detecting these objects. This technique can be used in remote sensing of scatterers buried beneath the rough ground.     

Friction tensor concept for textured surfaces

Directionality of grinding marks influences the coefficient of friction during sliding. Depending on the sliding direction the coefficient of friction varies between maximum and minimum for textured surfaces. For random surfaces without any texture the friction coefficient becomes independent of the sliding direction. This paper proposes the concept of a friction tensor analogous to the heat conduction tensor in anisotropic media. This implies that there exists two principal friction coefficients μ_1,2 analogous to the principal conductivities k _1,2. For symmetrically textured surfaces the principal directions are orthogonal with atleast one plane of symmetry. However, in the case of polished single crystalline solids in relative sliding motion, crystallographic texture controls the friction tensor.