A fractal model of contact between rough surfaces for a complete loading–unloading process

2020 ◽  
Vol 234 (14) ◽  
pp. 2923-2935
Author(s):  
Yuan Yuan ◽  
Kuo Xu ◽  
Ke Zhao
Keyword(s):  
Size Distribution ◽  
Contact Area ◽  
Rough Surfaces ◽  
Contact Process ◽  
Distribution Functions ◽  
Contact Load ◽  
Elastic Behavior ◽  
Loading Process ◽  
True Contact Area ◽  
True Contact

The mechanical properties of contact between rough surfaces play an important role in the reliability of the electromechanical system. In order to improve the design accuracy of precision instruments, an elastic-plastic contact model for three-dimensional rough surfaces based on the fractal theory is developed for a complete loading–unloading process based on the Majumdar and Bhushan model. The truncation size distribution functions of asperities for different values of asperity level in the loading process are given. Relationships between true contact area and total contact load in the complete loading–unloading process are obtained according to the truncation size distribution functions of asperities. The results show the range of asperity levels has significant effects on contact mechanical behaviors of fractal rough surfaces. When the first six levels of asperities do not exceed the critical elastic level, the fractal rough surfaces exhibit elastic behavior in a complete contact process, and the load–area relationships in the loading and unloading processes are coincident approximately. When the critical elastic level is less than the minimum level of asperity, the inelastic deformation begins to appear in fractal rough surfaces and the true contact area during the unloading process is always greater than the true area during the loading process for a given total contact load. In comparison with the K-K-E model, the present model is proved to be reasonable.

scholarly journals Evolution of the True Contact Area of Laser Textured Tungsten Under Dry Sliding Conditions

2019 ◽  
Vol 5 ◽  
Author(s):  
Björn Lechthaler ◽  
Georg Ochs ◽  
Frank Mücklich ◽  
Martin Dienwiebel
Keyword(s):  
Contact Area ◽  
Dry Sliding ◽  
True Contact Area ◽  
True Contact

scholarly journals Sliding-induced adhesion of stiff polymer microfibre arrays. I. Macroscale behaviour

2008 ◽  
Vol 5 (25) ◽  
pp. 835-844 ◽  
Author(s):  
Jongho Lee ◽  
Carmel Majidi ◽  
Bryan Schubert ◽  
Ronald S Fearing
Keyword(s):  
Elastic Modulus ◽  
Contact Area ◽  
Shear Force ◽  
Contact Region ◽  
Pure Shear ◽  
Shear Loading ◽  
High Shear ◽  
Polypropylene Fibres ◽  
True Contact Area ◽  
True Contact

Gecko-inspired microfibre arrays with 42 million polypropylene fibres cm −2 (each fibre with elastic modulus 1 GPa, length 20 μm and diameter 0.6 μm) were fabricated and tested under pure shear loading conditions, after removing a preload of less than 0.1 N cm −2 . After sliding to engage fibres, 2 cm 2 patches developed up to 4 N of shear force with an estimated contact region of 0.44 cm 2 . The control unfibrillated surface had no measurable shear force. For comparison, a natural setal patch tested under the same conditions on smooth glass showed approximately seven times greater shear per unit estimated contact region. Similar to gecko fibre arrays, the synthetic patch maintains contact and increases shear force with sliding. The high shear force observed (approx. 210 nN per fibre) suggests that fibres are in side contact, providing a larger true contact area than would be obtained by tip contact. Shear force increased over the course of repeated tests for synthetic patches, suggesting deformation of fibres into more favourable conformations.

The Role of Diffusion of Polymer Chains in the Mechanism of Adhesion and Autohesion of Rubbers

1957 ◽  
Vol 30 (3) ◽  
pp. 837-846 ◽  
Author(s):  
B. V. Deryagin ◽  
S. K. Zherebkov ◽  
A. M. Medvedeva
Keyword(s):  
Mechanical Properties ◽  
Double Layer ◽  
Contact Area ◽  
Electric Double Layer ◽  
Contact Time ◽  
Diffusion Processes ◽  
The Other ◽  
Shearing Strength ◽  
True Contact Area ◽  
True Contact

Abstract 1. The researches so far published on the autohesion of polymers do not make it possible to isolate the influence of the mechanical properties of rubbers, which determine the true area of contact, from the influence of polymer chain diffusion. 2. Studies of the autohesion of thin films of rubber applied by the drain-off method to quartz threads, in relation to the film thickness and contact time, show that for films less than 3.10−5 cm. thick the adhesion force is small and varies very little with contact time. This proves, on the one hand, that in this instance the contact area is small (which is obvious) and does not increase with time, and on the other hand, that diffusion processes play no part in the autohesion of films of this thickness. 3. The effects which depend on mechanical properties and on the specific interaction (per unit area of true contact) between specimens may be separated if the measured values of adhesion between all possible combinations of pairs of rubbers are compared both with their compatibilities, and with their autohesion. 4. The measurements of the adhesional shearing strength of combinations of different pairs of polymers, carried out for this purpose, showed that the results for Butyl rubber may be interpreted on the assumption that diffusion processes do not play any appreciable role and that the adhesion strength is determined both by the true contact area, which depends on the mechanical properties of the corresponding polymer specimens, and also by the influence of forces associated with the electric double layer. 5. For the other rubbers the results may be interpreted only on the assumption that diffusion processes play a significant part. For similar polarities, T12/T11>1 and for dissimilar polarities, T12/T11<1. 6. General conclusion : autohesion and mutual adhesion of rubbers is determined both by mechanical properties, which determine the true contact area, and by diffusional properties. The latter are by no means always decisive. The electric double layer also probably influences the adhesional shearing strength in some instances. It is even more likely to play a role in some cases in measurements of the work of separation of two layers.

scholarly journals The effects of size distribution functions on contact between fractal rough surfaces

AIP Advances ◽  
2018 ◽  
Vol 8 (7) ◽  
pp. 075317 ◽  
Author(s):  
Kuo Xu ◽  
Yuan Yuan ◽  
Jianjiang Chen
Keyword(s):  
Size Distribution ◽  
Rough Surfaces ◽  
Distribution Functions

Metallic wear

1952 ◽  
Vol 212 (1111) ◽  
pp. 470-477 ◽  
Keyword(s):  
Contact Area ◽  
Large Fraction ◽  
Wear Particle ◽  
Wear Particles ◽  
Wear Model ◽  
Real Area Of Contact ◽  
Cylindrical Metal ◽  
Proportional Increase ◽  
True Contact Area ◽  
True Contact

This paper describes experiments on the wear between a cylindrical metal pin and a hardened steel disk. Under steady-state conditions at light loads it is found that the volume V of material worn away is proportional to the load W, and the length L of path traversed so that V = k'LW . Since the real area of contact A may be written as A = W/P m , where P m is a strength property of the pin, the wear equation may be rewritten V = k'LA /P m = kLA , where k is a constant for the surfaces. This relation suggests that, of the welded junctions formed at the interface and sheared during sliding a constant fraction is detached to form the wear particles. On this View an increase in load produces a proportional increase in the number of welds each of which remains approximately of constant size. This is supported by an examination of the wear particles. This mechanism would seem preferable to the atomic wear model suggested by Holm, which also yields a wear equation of the form V = kLA . At higher loads, in excess of an average pressure about one-third the hardness of the pin, a large increase in the wear rate is observed. It is suggested that this is primarily due to the fact that the true contact area has become such a large fraction of the apparent contact area which is available that a loose wear particle once formed is not able to get away without producing further particles in a self-accelerating process. These results are discussed in relation to the practical problem of running-in newly assembled machine parts.

Frictional behaviour of engineering surfaces in overall lubrication regimes of point contacts

2011 ◽  
Vol 225 (11) ◽  
pp. 1071-1080 ◽  
Author(s):  
S Wang ◽  
Y-Z Hu ◽  
Q-C Tan
Keyword(s):  
Friction Coefficient ◽  
Contact Area ◽  
Area Ratio ◽  
Mixed Lubrication ◽  
Point Contacts ◽  
Friction Behaviour ◽  
True Contact Area ◽  
Contact Area Ratio ◽  
True Contact ◽  
Frictional Behaviour

The aim of the present paper is to study experimentally and numerically the frictional behaviour of engineering surfaces within all lubrication regions of point contacts. For this reason, a numerical solution proposed elsewhere by the current authors, which can predict friction under the different lubrication modes of elastohydrodynamic, mixed, and boundary lubrications, is introduced. Based on a deterministic model of mixed lubrication, the solution was combined with the variation of the lubricating films’ physical state during the transition of lubrication modes. Results show that roughness amplitude has a great effect on the transition of friction regimes. In addition, it is also observed that variation of the friction coefficient has nearly the same trend as the true contact area ratio in the mixed lubrication state. Meanwhile, it is concluded that transverse roughness has better film-forming capacity than longitudinal roughness and thus leads to a lower magnitude of friction coefficient if the operating conditions are the same. Analysis of the mechanism of friction behaviour suggests that the true contact area ratio determines the friction behaviour of engineering surfaces in mixed lubrication. In smooth contacts, the comparison of experiment tests and simulation results suggests that friction variation results from gradual change of the liquid lubricant to solid-like matter with diminishing film thickness.

scholarly journals A Modified Approach in Modeling and Calculation of Contact Characteristics of Rough Surfaces

2005 ◽  
Vol 2 (1) ◽  
pp. 43
Author(s):  
J.A. Abdo
Keyword(s):  
Plastic Deformation ◽  
Rough Surfaces ◽  
Mathematical Formulation ◽  
Critical Depth ◽  
Actual Surface ◽  
Proposed Model ◽  
Definition Of ◽  
True Contact Area ◽  
Realistic Prediction ◽  
True Contact

A mathematical formulation for the contact of rough surfaces is presented. The derivation of the contact model is facilitated through the definition of plastic asperities that are assumed to be embedded at a critical depth within the actual surface asperities. The surface asperities are assumed to deform elastically whereas the plastic asperities experience only plastic deformation. The deformation of plastic asperities is made to obey the law of conservation of volume. It is believed that the proposed model is advantageous since (a) it provides a more accurate account of elasticplastic behavior of surfaces in contact and (b) it is applicable to model formulations that involve asperity shoulder-to shoulder contact. Comparison of numerical results for estimating true contact area and contact force using the proposed model and the earlier methods suggest that the proposed approach provides a more realistic prediction of elastic-plastic contact behavior. 

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