scholarly journals THE “SPORT” OF ROUGH CONTACTS AND THE FRACTAL PARADOX IN WEAR LAWS

2018 ◽  
Vol 16 (1) ◽  
pp. 65 ◽  
Author(s):  
Michele Ciavarella ◽  
Antonio Papangelo
Keyword(s):  
Contact Area ◽  
Rough Surfaces ◽  
Wear Loss ◽  
Length Scale ◽  
Elastic Contact ◽  
Contact Sport ◽  
Frictional Loss ◽  
Contact Models ◽  
Large Effort ◽  
The Times

In a recent paper in Science, namely, “The Contact Sport of Rough Surfaces”, Carpick summarizes recent efforts in a “contact challenge” to predict in detail an elastic contact between the mathematically defined fractal rough surfaces under (very little) adhesion. He also suggests the next steps that are needed to “fulfill da Vinci’s dream of understanding what causes friction”. However, this is disappointing as friction has been studied since the times of Leonardo and in 500 years, no predictive model has emerged, nor any significant improvement from rough contact models. Similarly, a very large effort we have spent on the “sport” of studying rough surfaces has not made us any closer to being able to predict the coefficient of proportionality between wear loss and friction dissipation which was already observed by Reye in 1860. Recent nice simulations by Aghababaei, Warner and Molinari have confirmed the criterion for the formation of debris of a single particle, proposed in 1958 by Rabinowicz, as well as Reye’s assumption for the proportionality with frictional loss, which is very close to Archard anyway. More recent investigations under variable loads suggest that Reye’s assumption is probably much more general than Archard’s law. The attempts to obtain exact coefficients with rough surfaces models are very far from predictive, essentially because for fractals most authors fail to recognize that resolution-dependence of the contact area makes the models very ill-defined. We also suggest that in the models of wear, rough contacts should be considered “plastic” and “adhesive” and introduce a new length scale in the problem.

scholarly journals The Elastic Contact of Rough Spheres Investigated Using a Deterministic Multi-Asperity Model

2019 ◽  
Vol 10 (01) ◽  
pp. 1841002 ◽  
Author(s):  
Vladislav A. Yastrebov
Keyword(s):  
Contact Area ◽  
Rough Surfaces ◽  
Contact Problems ◽  
Hertzian Contact ◽  
Contact Radius ◽  
Geometrical Shape ◽  
Elastic Contact ◽  
Deterministic Analysis ◽  
Asperity Model ◽  
Deformation Modes

In this paper, we use a deterministic multi-asperity model to investigate the elastic contact of rough spheres. Synthetic rough surfaces with controllable spectra were used to identify individual asperities, their locations and curvatures. The deterministic analysis enables to capture both particular deformation modes of individual rough surfaces and also statistical deformation regimes, which involve averaging over a big number of roughness realizations. Two regimes of contact area growth were identified: the Hertzian regime at light loads at the scale of a single asperity, and the linear regime at higher loads involving multiple contacting asperities. The transition between the regimes occurs at the load which depends on the second and the fourth spectral moments. It is shown that at light indentation the radius of circumference delimiting the contact area is always considerably larger than Hertzian contact radius. Therefore, it suggests that there is no scale separation in contact problems at light loads. In particular, the geometrical shape cannot be considered separately from the surface roughness at least for approaching greater than one standard roughness deviation.

Strongly Anisotropic Rough Surfaces

1979 ◽  
Vol 101 (1) ◽  
pp. 15-20 ◽  
Author(s):  
A. W. Bush ◽  
R. D. Gibson ◽  
G. P. Keogh
Keyword(s):  
Random Process ◽  
Rough Surface ◽  
Contact Area ◽  
Process Model ◽  
Rough Surfaces ◽  
Plasticity Index ◽  
Real Contact Area ◽  
Elastic Contact ◽  
Elastic Plastic ◽  
Real Contact

The statistics of a strongly anisotropic rough surface are briefly described. The elastic contact of rough surfaces is treated by approximating the summits of a random process model by parabolic ellipsoids and applying the Hertzian solution for their deformation. Load and real contact area are derived as functions of the separation and for all separations the load is found to be approximately proportional to the contact area. The limits of elastic/plastic contact are discussed in terms of the plasticity index.

Numerical Analysis for the Elastic Contact of Real Rough Surfaces

1999 ◽  
Vol 42 (3) ◽  
pp. 443-452 ◽  
Author(s):  
Yuan-Zhong Hu ◽  
Gary C. Barber ◽  
Dong Zhu
Keyword(s):  
Numerical Analysis ◽  
Rough Surfaces ◽  
Elastic Contact

scholarly journals A Static Friction Model for Unlubricated Contact of Random Rough Surfaces at Micro/Nano Scale

Micromachines ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 368
Author(s):  
Shengguang Zhu ◽  
Liyong Ni
Keyword(s):  
Rough Surfaces ◽  
Static Friction ◽  
Friction Model ◽  
Elastic Contact ◽  
Nano Scale ◽  
Random Rough Surfaces ◽  
Proposed Model ◽  
Dissipation Mechanism ◽  
Rigid Plane ◽  
Contact Situation

A novel static friction model for the unlubricated contact of random rough surfaces at micro/nano scale is presented. This model is based on the energy dissipation mechanism that states that changes in the potential of the surfaces in contact lead to friction. Furthermore, it employs the statistical theory of two nominally flat rough surfaces in contact, which assumes that the contact between the equivalent rough peaks and the rigid flat plane satisfies the condition of interfacial friction. Additionally, it proposes a statistical coefficient of positional correlation that represents the contact situation between the equivalent rough surface and the rigid plane. Finally, this model is compared with the static friction model established by Kogut and Etsion (KE model). The results of the proposed model agree well with those of the KE model in the fully elastic contact zone. For the calculation of dry static friction of rough surfaces in contact, previous models have mainly been based on classical contact mechanics; however, this model introduces the potential barrier theory and statistics to address this and provides a new way to calculate unlubricated friction for rough surfaces in contact.

scholarly journals Measurement of Real Contact Area for Rough Metal Surfaces and the Distinction of Contribution From Elasticity and Plasticity

2020 ◽  
Vol 143 (7) ◽  
Author(s):  
Lei-Tao Li ◽  
Xuan-Ming Liang ◽  
Yu-Zhe Xing ◽  
Duo Yan ◽  
Gang-Feng Wang
Keyword(s):  
Contact Area ◽  
Rough Surfaces ◽  
Normal Load ◽  
Real Contact Area ◽  
The Real ◽  
Physical Mechanisms ◽  
Frustrated Total Internal Reflection ◽  
Real Contact ◽  
New Apparatus ◽  
Elastic And Plastic Deformation

Abstract The measurement of the real contact area between rough surfaces is one of the most challenging problems in contact mechanics and is of importance to understand some physical mechanisms in tribology. Based on the frustrated total internal reflection, a new apparatus is designed to measure the real contact area. For metallic samples with various surface topographies, the relation between normal load and the real contact area is measured. The unloading process is first considered to distinguish the contribution of elasticity and plasticity in contact with rough surfaces. It is found that both elasticity and plasticity are involved throughout the continuous loading process, different from some present understanding and assumptions that they play at different loading stages. A quantitative parameter is proposed to indicate the contribution of plasticity. The present work not only provides an experimental method to measure the real contact area but figures out how elastic and plastic deformation works in contact with rough surfaces.

Comparative Contact Analysis Study of Finite Element Method Based Deterministic, Simplified Multi-Asperity and Modified Statistical Contact Models

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
A. Megalingam ◽  
M. M. Mayuram
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rough Surface ◽  
Contact Area ◽  
Model Analysis ◽  
Contact Model ◽  
Contact Load ◽  
Asperity Contact ◽  
Single Asperity ◽  
Contact Models

The study of the contact stresses generated when two surfaces are in contact plays a significant role in understanding the tribology of contact pairs. Most of the present contact models are based on the statistical treatment of the single asperity contact model. For a clear understanding about the elastic-plastic behavior of two rough surfaces in contact, comparative study involving the deterministic contact model, simplified multi-asperity contact model, and modified statistical model are undertaken. In deterministic contact model analysis, a three dimensional deformable rough surface pressed against a rigid flat surface is carried out using the finite element method in steps. A simplified multi-asperity contact model is developed using actual summit radii deduced from the rough surface, applying single asperity contact model results. The resultant contact parameters like contact load, contact area, and contact pressure are compared. The asperity interaction noticed in the deterministic contact model analysis leads to wide disparity in the results. Observing the elastic-plastic transition of the summits and the sharing of contact load and contact area among the summits, modifications are employed in single asperity statistical contact model approaches in the form of a correction factor arising from asperity interaction to reduce the variations. Consequently, the modified statistical contact model and simplified multi-asperity contact model based on actual summit radius results show improved agreement with the deterministic contact model results.

scholarly journals A semi-analytical approach to the elastic loading behaviour of rough surfaces

Friction ◽  
2019 ◽  
Vol 8 (5) ◽  
pp. 970-981
Author(s):  
Xiaogang Zhang ◽  
Yali Zhang ◽  
Zhongmin Jin
Keyword(s):  
Contact Area ◽  
Rough Surfaces ◽  
Real Contact Area ◽  
Exponential Relationship ◽  
Load Range ◽  
Contact Behaviour ◽  
Elastic Loading ◽  
Moderate Load ◽  
Convergence Problems ◽  
Linear Decay

AbstractThe elastic loading behaviour of rough surfaces is derived based on the physical understanding of the contact phenomena, where the pressure distribution is analytically obtained without any negative values or convergence problems, thus the evolution of the contact behaviour is obtained in a semi-analytical manner. Numerical results obtained by the proposed approach facilitate the understanding of the contact behaviour in the following aspects: 1) the ratio of contact area to load decreases with an increase in real contact area; 2) normal approach-load relationship is approximated by an exponential decay under relatively small loads and a linear decay under relatively large loads; and 3) average gap shows an exponential relationship with load only in moderate load range.

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