On the Sensitivity of Adhesion between Rough Surfaces to Asperity Height Distribution

2018 ◽  
Vol 21 (1) ◽  
pp. 59-66 ◽  
Author(s):  
M. Ciavarella ◽  
A. Papangelo
Keyword(s):  
Rough Surfaces ◽  
Height Distribution ◽  
Asperity Height

A Method for Determining the Asperity Distribution of Contacting Rough Surfaces

2005 ◽  
Vol 127 (1) ◽  
pp. 24-29 ◽  
Author(s):  
Reese E. Jones ◽  
David A. Zeigler
Keyword(s):  
Data Reduction ◽  
Rough Surfaces ◽  
Height Distribution ◽  
Asperity Height ◽  
Inverse Technique ◽  
Alternative Method ◽  
Displacement Behavior ◽  
Load Displacement ◽  
Asperity Distribution ◽  
Topographic Measurement

The Greenwood and Williamson (1966) model is an elegant and often-cited paradigm for predicting the load-displacement behavior of contacting rough surfaces given the height distribution of the contacting asperities. By use of an inverse technique and available load-displacement data, this work provides an alternative method to determine the asperity distribution directly from topographic measurement and subsequent data reduction. This method produces distributions that are consistent with the Greenwood and Williamson representation of the load-displacement data and demonstrates how the asperity height distribution can evolve with loading.

scholarly journals Adhesion of Soft Materials to Rough Surfaces: Experimental Studies, Statistical Analysis and Modelling

Coatings ◽  
2018 ◽  
Vol 8 (10) ◽  
pp. 350 ◽  
Author(s):  
Andrey Pepelyshev ◽  
Feodor Borodich ◽  
Boris Galanov ◽  
Elena Gorb ◽  
Stanislav Gorb
Keyword(s):  
Statistical Analysis ◽  
Smooth Surface ◽  
Rough Surfaces ◽  
Experimental Studies ◽  
Soft Materials ◽  
Adhesive Contact ◽  
Theoretical Modelling ◽  
Height Distribution ◽  
Depth Sensing ◽  
Adhesive Properties

Adhesion between rough surfaces is an active field of research where both experimental studies and theoretical modelling are used. However, it is rather difficult to conduct precise experimental evaluations of adhesive properties of the so-called anti-adhesive materials. Hence, it was suggested earlier by Purtov et al. (2013) to prepare epoxy resin replicas of surfaces having different topography and conduct depth-sensing indentation of the samples using a micro-force tester with a spherical smooth probe made of the compliant polydimethylsiloxane polymer in order to compare values of the force of adhesion to the surfaces. Surprising experimental observations were obtained in which a surface having very small roughness showed the greater value of the force of adhesion than the value for a replica of smooth surface. A plausible explanation of the data was given suggesting that these rough surfaces had full adhesive contact and their true contact area is greater than the area for a smooth surface, while the surfaces with higher values of roughness do not have full contact. Here, the experimental results of surface topography measurements and the statistical analysis of the data are presented. Several modern tests of normality used showed that the height distribution of the surfaces under investigation is normal (Gaussian) and hence the classic statistical models of adhesive contact between rough surfaces may formally be used. Employing one of the Galanov (2011) models of adhesive contact between rough surfaces, the plausible explanation of the experimental observations has been confirmed and theoretically justified.

Application of Boltzmann Statistical Mechanics in the Validation of the Gaussian Summit-Height Distribution in Rough Surfaces

1997 ◽  
Vol 119 (4) ◽  
pp. 846-850 ◽  
Author(s):  
M. Leung ◽  
C. K. Hsieh ◽  
D. Y. Goswami
Keyword(s):  
Surface Roughness ◽  
Statistical Mechanics ◽  
Theoretical Basis ◽  
Rough Surfaces ◽  
Electrical Contact ◽  
Height Distribution ◽  
Probable Distribution ◽  
Theoretical Predictions ◽  
Most Probable Distribution ◽  
Roughness Measurements

In theoretical modeling of contact mechanics, a homogeneously, isotropically rough surface is usually assumed to be a flat plane covered with asperities of a Gaussian summit-height distribution. This assumption yields satisfactory results between theoretical predictions and experimental measurements of the physical characteristics, such as thermal/electrical contact conductance and friction coefficient. However, lack of theoretical basis of this assumption motivates further study in surface modeling. This paper presents a theoretical investigation by statistical mechanics to determine surface roughness in terms of the most probable distribution of surface asperities. Based upon the surface roughness measurements as statistical constraints, the Boltzmann statistical model derives a distribution equivalent to Gaussian. The Boltzmann statistical mechanics derivation in this paper provides a rigorous validation of the Gaussian summit-height assumption presently in use for study of rough surfaces.

Analysis of contact and bending stiffness for Curvic couplings considering contact angle and surface roughness

2019 ◽  
Vol 233 (6) ◽  
pp. 1257-1267 ◽  
Author(s):  
Younghun Yu ◽  
Bora Lee ◽  
Yongjoo Cho
Keyword(s):  
Surface Roughness ◽  
Contact Angle ◽  
Standard Deviation ◽  
Bending Stiffness ◽  
Height Distribution ◽  
Average Radius ◽  
Asperity Height ◽  
Surface Parameter ◽  
Tangential Stiffness ◽  
Nominal Contact Area

This paper develops a method for calculating the contact and bending stiffness of a Curvic coupling, and investigates stiffness changes according to the coupling shape and surface roughness characteristics. The surface of the on-site Curvic coupling is chosen as reference for a most accurate simulation. The three parameters representing the surface roughness characteristics—the standard deviation of the asperity height distribution, the average radius of asperities, and the density of asperity on the nominal contact area—are calculated with a profile of the coupling surface through a random process: the contact problem between rough surfaces is tackled using the Greenwood-Williamson model, the Curvic coupling is modeled assuming that it has as many teeth as possible within the machining limits depending on the contact angle, and the tangential stiffness resulting from the contact angle is calculated by dividing into the stick and slip regions, and is taken into account in terms of total stiffness. With this, results showed that using Curvic couplings reduces stiffness than using flat disc couplings because of the contact angle, and that the standard deviation of rough surface height is the most crucial surface parameter affecting stiffness.

Dynamic roughness model for large-eddy simulation of turbulent flow over multiscale, fractal-like rough surfaces

2011 ◽  
Vol 679 ◽  
pp. 288-314 ◽  
Author(s):  
W. ANDERSON ◽  
C. MENEVEAU
Keyword(s):  
Large Eddy Simulation ◽  
Turbulent Flow ◽  
Power Law ◽  
Rough Surfaces ◽  
Scale Height ◽  
Small Scale ◽  
Height Distribution ◽  
Subgrid Scale ◽  
Eddy Simulation ◽  
Large Eddy

Many flows especially in geophysics involve turbulent boundary layers forming over rough surfaces with multiscale height distribution. Such surfaces pose special challenges for large-eddy simulation (LES) when the filter scale is such that only part of the roughness elements of the surface can be resolved. Here we consider LES of flows over rough surfaces with power-law height spectra Eh(k) ~ kβs (−3 ≤ βs < −1), as often encountered in natural terrains. The surface is decomposed into resolved and subgrid-scale height contributions. The effects of the unresolved small-scale height fluctuations are modelled using a local equilibrium wall model (log-law or Monin–Obukhov similarity), but the required hydrodynamic roughness length must be specified. It is expressed as the product of the subgrid-scale root-mean-square of the height distribution and an unknown dimensionless quantity, α, the roughness parameter. Instead of specifying this parameter in an ad hoc empirical fashion, a dynamic methodology is proposed based on test-filtering the surface forces and requiring that the total drag force be independent of filter scale or resolution. This dynamic surface roughness (DSR) model is inspired by the Germano identity traditionally used to determine model parameters for closing subgrid-scale stresses in the bulk of a turbulent flow. A series of LES of fully developed flow over rough surfaces are performed, with surfaces built using random-phase Fourier modes with prescribed power-law spectra. Results show that the DSR model yields well-defined, rapidly converging, values of α. Effects of spatial resolution and spectral slopes are investigated. The accuracy of the DSR model is tested by showing that predicted mean velocity profiles are approximately independent of resolution for the dynamically computed values of α, whereas resolution-dependent results are obtained when using other, incorrect, α values. Also, strong dependence of α on βs is found, where α ranges from α ~ 0.1 for βs = −1.2 to α ~ 10−5 for βs = −3.

The Elastic—Plastic Contact of Rough Surfaces and its Relevance in the Study of Wear

1988 ◽  
Vol 202 (4) ◽  
pp. 269-274 ◽  
Author(s):  
J Halling ◽  
R D Arnell ◽  
K A Nuri
Keyword(s):  
Theoretical Model ◽  
Probability Distribution ◽  
Experimental Evidence ◽  
Rough Surfaces ◽  
Plasticity Index ◽  
Elastic Behaviour ◽  
Asperity Height ◽  
Real Contact ◽  
Nominal Pressure ◽  
Unique Relationship

In a recent paper it was shown that the limit of elastic behaviour of rough surfaces could be defined by a unique relationship between the plasticity index and the nominal pressure. Specific experimental evidence suggested that the best theoretical model was one when the asperity height probability distribution was assumed Gaussian with a truncation of 3 σ. This paper extends this argument by showing that for a given ratio of plastic-elastic area of real contact, similar unique relations exist between the plasticity index and nominal pressure. It is assumed that the maximum non-dimensional elastic deformation is given by the inverse of the square of the plasticity index, and this is supported by experimental results. It is also shown that the model proposed is in error at higher pressures, due to the interaction of the deformations of adjacent asperities.

Studies of Low-loading Micro-slip Contacts on Rough Surfaces with GW Model

2017 ◽  
Vol 09 (04) ◽  
pp. 1750049 ◽  
Author(s):  
Pin Lu ◽  
Lulu Yang ◽  
Gangfeng Wang
Keyword(s):  
Rough Surfaces ◽  
Extended Model ◽  
Interfacial Slip ◽  
Slip Model ◽  
Roughness Parameters ◽  
Asperity Height ◽  
Contact Conditions ◽  
Lateral Contact ◽  
Low Load ◽  
General Relations

Lateral loading and interfacial slip of multi-asperity (i.e., rough) elastic contacts are studied for micro-slip contact conditions. The Mindlin micro-slip model for smooth surfaces is generalized to rough surface contacts using the Greenwood–Williamson (GW) approach, and the general relations of lateral contact force and related stiffness are obtained. The method extends previous approaches by incorporating micro-slip, allowing application to rough surfaces and providing simple expressions for experimental analysis by use of the Greenwood–Williams roughness parameters. As applications, the numerical results of micro-slip contacts on rough surfaces for Gaussian and exponential asperity height distributions, respectively, are obtained based on the general relations of the extended model, and are compared and discussed for low load cases.

On the plastic contact of rough surfaces

1972 ◽  
Vol 327 (1569) ◽  
pp. 159-173 ◽  
Keyword(s):  
Flat Surface ◽  
Rough Surfaces ◽  
Material Constant ◽  
Unexpected Result ◽  
Height Distribution ◽  
Real Area Of Contact ◽  
Soft Surface ◽  
The Mean ◽  
Load Separation ◽  
Real Area

The treatment of plastic contact developed in this paper is based on three physical observations: that the total volume of metal is not changed by plastic deformation; that the mean indentation pressure is a well-defined material constant applicable to the whole range of likely asperity shapes; and that the displaced material reappears as a uniform rise in the non-contacting surface. An energy-balance argument is used to obtain dimensionless relations between the load, separation, and degree of contact, in terms of the height distribution of the surface. A fourth observation is then added: that the height distributions of many engineering surfaces are, to a good approximation, Gaussian. The relations are worked out in detail for this height distribution and compared with experimental observations. The treatment accurately predicts the behaviour up to extremely high loads; and accounts for the remarkable persistence of asperities on rough surfaces in plastic contact. The argument, and the main supporting experiments, were conceived in terms of the contact of a uniformly loaded nominally flat surface, but the extention to local indentations is quite straightforward. It is shown that for local indentations in homogeneous bodies the real area of contact is always one half of the nominal area. This unexpected result is in fact accurately confirmed by experiment. The treatment also discusses the effect of a hard or soft surface layer on the indented body, and again the predictions are supported by practical measurements.

Characterization and Modeling of Pad Asperity Response in CMP

2010 ◽  
Vol 1249 ◽  
Author(s):  
Duane Boning ◽  
Wei Fan
Keyword(s):  
Contact Area ◽  
Height Distribution ◽  
Asperity Height ◽  
Physical Measurements ◽  
Reduced Modulus ◽  
Area Percentage

AbstractA model is proposed to understand the interactions between CMP pad asperities and the wafer. Pad asperity reduced modulus and height distribution are included in the model. Physical measurements of asperity properties are performed: asperity reduced modulus is measured by nanoindentation, and pad asperity height distribution is scanned by profilometry. The measured results are used in the model to predict the contact area percentage between the pad and wafer in the CMP process.

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