Fractal Model of Elastic-Plastic Contact Between Rough Surfaces

1991 ◽  
Vol 113 (1) ◽  
pp. 1-11 ◽  
Author(s):  
A. Majumdar ◽  
B. Bhushan
Keyword(s):  
Size Distribution ◽  
Rough Surfaces ◽  
Surface Profile ◽  
Scanning Tunneling ◽  
Roughness Parameters ◽  
The Real ◽  
Real Area Of Contact ◽  
Fractal Roughness ◽  
Contact Spots ◽  
Real Area

Roughness measurements by optical interferometry and scanning tunneling microscopy on a magnetic thin-film rigid disk surface have shown that its surface is fractal in nature. This leads to a scale-dependence of statistical parameters such as r.m.s height, slope and curvature, which are extensively used in classical models of contact between rough surfaces. Based on the scale-independent fractal roughness parameters, a new model of contact between isotropic rough surfaces is developed. The model predicts that all contact spots of area smaller than a critical area are in plastic contact. When the load is increased, these plastically deformed spots join to form elastic spots. Using a power-law relation for the fractal size-distribution of contact spots, the model shows that for elastic deformation, the load P and the real area of contact Ar are related as P~Ar(3−D)/2, where D is the fractal dimension of a surface profile which lies between 1 and 2. This result explains the origins of the area exponent which has been the focus of a number of experimental and theoretical studies. For plastic loading, the load and area are linearly related. The size-distribution of spots also suggests that the number of contact spots contributing to a certain fraction of the real area of contact remains independent of load although the spot sizes increase with load. The model shows that the load-area relation and the fraction of the real area of contact in elastic and plastic deformation are quite sensitive to the fractal roughness parameters.

An Abbott Curve Based Rough Surface Contact Mechanics Approach

2005 ◽  
Author(s):  
Andreas Almqvist ◽  
Fredrik Sahlin ◽  
Roland Larsson
Keyword(s):  
Contact Mechanics ◽  
Small Deviation ◽  
Surface Profile ◽  
Real Surface ◽  
Machined Surface ◽  
The Real ◽  
Real Area Of Contact ◽  
Rough Surface Contact ◽  
Contact Mechanical ◽  
Real Area

The topography of a machined surface significantly influences the performance of both lubricated and unlubricated contacts. In this work the unlubricated frictionless contact of rough surfaces is the subject of study. The numerical deterministic contact mechanics model incorporates linear elastic surface material and the dry contact is simulated using classes of surface profiles randomly generated from a given Abbott curve (Abbott-Firestone bearing ratio curve). In this way all the height information of the surface profile is preserved and not only a few parameters, like Ra, Rq, Rz, Rsk, etc. The aim of this work is to investigate how classes of surfaces based on a single Abbott curve perform in terms of contact mechanical parameters like the real area of contact. The result shows that surfaces taken from a class of random surfaces generated from a specific Abbott curve behaves similar in a contact mechanics simulation. That is, the distribution of for example the real area of contact within such a class is compact, having a small deviation from its mean. This implies that it is possible to simulate classes of surfaces based on Abbott curves and to use the results to predict contact mechanical properties of real surface topographies.

Asperity persistence and the real area of contact between rough surfaces

1972 ◽  
Vol 327 (1569) ◽  
pp. 147-157 ◽  
Keyword(s):  
Rough Surfaces ◽  
Intrinsic Property ◽  
Surface Layers ◽  
The Real ◽  
Real Area Of Contact ◽  
Heavy Loads ◽  
The Individual ◽  
Hardened Surface ◽  
Hard Ball ◽  
Real Area

It is well known that even under very heavy loads the hills on rough surfaces are not completely flattened. Many workers have advanced possible reasons for this remarkable persistence of the surface asperities. The most commonly advocated mechanisms are examined, and it is demonstrated that none of them provides an adequate explanation of the phenomenon. The plastic indentation of a flat by a hard ball is then studied, and the real area of contact is measured directly using high resolution profilometry. It is concluded that asperity persistence does not depend on the particular metal in contact. Nor is it an intrinsic property of the individual hills on the surface; there is no evidence that work hardening during the crushing of asperities can form a hardened surface layer which leads to a smaller contact area, as is commonly supposed. It is shown that, for local indentations, the degree of contact, i. e. the ratio of real to nominal area, is in general independent of the load. Whenever the surface layers are harder than the bulk the degree of contact is typically between one quarter and one third. However, when the indented body has a uniform hardness the degree of contact was found to be accurately equal to one-half.

The Effect of Nanoparticles on the Real Area of Contact, Friction, and Wear

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Hamed Ghaednia ◽  
Robert L. Jackson
Keyword(s):  
Friction And Wear ◽  
Silicon Nanoparticles ◽  
Rough Surfaces ◽  
Contact Friction ◽  
Body Contact ◽  
The Real ◽  
Real Area Of Contact ◽  
The Coefficient Of Friction ◽  
Real Area ◽  
Nanoparticle Additives

Although nanoparticle additives have been the topic of multiple studies recently, very little work has attempted to explicitly model the third body contact of nanoparticles. This work presents and uses a novel methodology to model nanoparticles in contact between rough surfaces. The model uses two submodels to handle different scales of contact, namely the nano-sized particles and micrometer-sized roughness features. Silicon nanoparticles suspended in conventional lubricant are modeled in contact between steel rough surfaces. The effect of the particles on contact force and real area of contact has been modeled. The model makes predictions of the coefficient of friction and wear using fundamental models. The results suggest that particles would reduce the real area of contact and, therefore, decrease the friction force. Also, particles could induce abrasive wear by scratching the surfaces. The implications of the model are also discussed, and the arguments and results have been linked to available experimental data. This work finds that particle size and distribution are playing a key role in tribology characteristics of the nanolubricants.

Analysis of the Real Area of Contact Between a Polymeric Magnetic Medium and a Rigid Surface

1984 ◽  
Vol 106 (1) ◽  
pp. 26-34 ◽  
Author(s):  
Bharat Bhushan
Keyword(s):  
Complex Modulus ◽  
Critical Value ◽  
Computer Applications ◽  
Hard Material ◽  
Rigid Surface ◽  
Magnetic Medium ◽  
The Real ◽  
Real Area Of Contact ◽  
The Mean ◽  
Real Area

The statistical analysis of the real area of contact proposed by Greenwood and Williamson is revisited. General and simplified equations for the mean asperity real area of contact, number of contacts, total real area of contact, and mean real pressure as a function of apparent pressure for the case of elastic junctions are presented. The critical value of the mean asperity pressure at which plastic flow starts when a polymer contacts a hard material is derived. Based on this, conditions of elastic and plastic junctions for polymers are defined by a “polymer” plasticity index, Ψp which depends on the complex modulus, Poisson’s ratio, yield strength, and surface topography. Calculations show that most dynamic contacts that occur in a computer-magnetic tape are elastic, and the predictions are supported by experimental evidence. Tape wear in computer applications is small and decreases Ψp by less than 10 percent. The theory presented here can also be applied to rigid and floppy disks.

Contact Mechanics of Rough Surfaces in Tribology: Single Asperity Contact

1996 ◽  
Vol 49 (5) ◽  
pp. 275-298 ◽  
Author(s):  
Bharat Bhushan
Keyword(s):  
Friction And Wear ◽  
Rough Surfaces ◽  
Asperity Contact ◽  
Elastic Solids ◽  
Elastic Plastic ◽  
Single Asperity ◽  
Real Area Of Contact ◽  
Single Asperity Contact ◽  
Indentation Problem ◽  
Real Area

Contact modeling of two rough surfaces under normal approach and with relative motion is carried out to predict the real area of contact which affects friction and wear of an interface. The contact of two macroscopically flat bodies with microroughness is reduced to the contact at multiple asperities of arbitrary shapes. Most of deformation at the asperity contact can be either elastic or elastic-plastic. In this paper, a comprehensive review of modeling of a single asperity contact or an indentation problem is presented. Contact analyses for a spherical asperity/indenter on homogeneous and layered, elastic and elastic-plastic solids with and without tangential loading are presented. The analyses reviewed in this paper fall into two groups: (a) analytical solutions, primarily for elastic solids and (b) finite element solutions, primarily for elastic-plastic problems and layered solids. Implications of these analyses in friction and wear are discussed.

Sign in / Sign up

Export Citation Format

Share Document