Some Closed-Form Results for Adhesive Rough Contacts Near Complete Contact on Loading and Unloading in the Johnson, Kendall, and Roberts Regime

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Michele Ciavarella ◽  
Yang Xu ◽  
Robert L. Jackson
Keyword(s):  
Fractal Dimension ◽  
Closed Form ◽  
Adhesive Contact ◽  
Full Contact ◽  
Loading And Unloading ◽  
Complete Contact

Recently, generalizing the solution of the adhesiveless random rough contact proposed by Xu, Jackson, and Marghitu (XJM model), the first author has obtained a model for adhesive contact near full contact, under the Johnson, Kendall, and Roberts (JKR) assumptions, which leads to quite strong effect of the fractal dimension. We extend here the results with closed-form equations, including both loading and unloading which were not previously discussed, showing that the conclusions are confirmed. A large effect of hysteresis is found, as was expected. The solution is therefore competitive with Persson's JKR solution, at least in the range of nearly full contact, with an enormous advantage in terms of simplicity. Two examples of real surfaces are discussed.

scholarly journals Adhesive contact of the Weierstrass profile

2015 ◽  
Vol 471 (2182) ◽  
pp. 20150248 ◽  
Author(s):  
L. Afferrante ◽  
M. Ciavarella ◽  
G. Demelio
Keyword(s):  
Fractal Dimension ◽  
Contact Problem ◽  
Contact Area ◽  
Finite Size ◽  
Adhesive Contact ◽  
Link Type ◽  
Full Contact ◽  
Contact Behaviour ◽  
Mean Pressure ◽  
Large Magnification

The Weierstrass series was considered in Ciavarella et al. (Ciavarella et al. 2000 Proc. R. Soc. Lond. A 456 , 387–405. ( doi:10.1098/rspa.2000.0522 )) to describe a linear contact problem between a rigid fractally rough surface and an elastic half-plane. In such cases, no applied mean pressure is sufficiently large to ensure full contact, and specifically there are not even any contact areas of finite dimension. Later, Gao & Bower (Gao & Bower 2006 Proc. R. Soc. A 462 , 319–348. ( doi:10.1098/rspa.2005.1563 )) introduced plasticity in the Weierstrass model, but concluded that the fractal limit continued to lead to what they considered unphysical predictions of the true contact size and number of contact spots, similar to the elastic case. In this paper, we deal with the contact problem between rough surfaces in the presence of adhesion with the assumption of a Johnson, Kendall and Roberts (JKR) regime. We find that, for fractal dimension D >1.5, the presence of adhesion does not qualitatively modify the contact behaviour. However, for fractal dimension D <1.5, a regularization of the contact area can be observed at a large magnification where the contact area consists of segments of finite size. Moreover, full contact can occur at all scales for D <1.5 provided the mean contact pressure is larger than a certain value. We discuss, however, the implication of our assumption of a JKR regime.

Adhesive Contact of Bodies Having an Elliptical Contact Area

2005 ◽  
Author(s):  
K. L. Johnson ◽  
J. A. Greenwood
Keyword(s):  
Closed Form ◽  
Contact Area ◽  
Adhesive Contact ◽  
Contact Radius ◽  
General Shape ◽  
Elliptical Contact ◽  
Jkr Theory ◽  
Two Bodies

The so-called JKR theory of adhesion between elastic spheres in contact (Johnson, Kendall & Roberts 1971, Sperling 1964) has been widely used in micro-tribology. In this paper the theory is extended to solids of general shape and curvature. It is assumed that the area of contact is elliptical which turns out to be approximately true, though the eccentricity is different from that for non-adhesive contact. Closed form expressions are found for the variation with load of contact radius and displacement, as a function of the ratio of principal relative curvatures of the two bodies in contact. The pull-off force is found to decrease with increasing eccentricity from its value of 3πΔγR/2 in the case of contact of spheres of radius R.

Contact and Adhesion of Elastic-Plastic Layered Microsphere

2010 ◽  
Author(s):  
H. Eid ◽  
L. Chen ◽  
N. Joshi ◽  
N. E. McGruer ◽  
G. G. Adams
Keyword(s):  
Layer Thickness ◽  
Plastic Material ◽  
Adhesive Contact ◽  
Contact Radius ◽  
Jones Potential ◽  
Elastic Plastic ◽  
High Durability ◽  
Loading And Unloading ◽  
Elastic Plastic Material ◽  
Maximum Contact

A finite element contact model of a layered hemisphere with a rigid flat, which includes the effect of adhesion, is developed. This configuration has been suggested as a design for a microswitch contact because it has the potential to achieve low adhesion, low contact resistance, and high durability. Elastic-plastic material properties were used for each of the materials comprising the layered hemisphere. Adhesion was modeled based on the Lennard-Jones potential. The effect of the layer thickness on the adhesive contact was investigated. In particular the influence of layer thickness on the pull-off force and maximum contact radius was studied. The results are presented as load vs. interference and contact radius vs. interference for loading and unloading from different values of the maximum interference.

Revisiting the Maugis–Dugdale Adhesion Model of Elastic Periodic Wavy Surfaces

2016 ◽  
Vol 83 (10) ◽  
Author(s):  
Fan Jin ◽  
Xu Guo ◽  
Qiang Wan
Keyword(s):  
Flat Surface ◽  
Adhesion Force ◽  
Adhesive Contact ◽  
Interaction Zone ◽  
Dugdale Model ◽  
Full Contact ◽  
Type Contact ◽  
Wavy Surfaces ◽  
Contact Models ◽  
Adhesion Model

The plane strain adhesive contact between a periodic wavy surface and a flat surface has been revisited based on the classical Maugis–Dugdale model. Closed-form analytical solutions derived by Hui et al. [1], which were limited to the case that the interaction zone cannot saturate at a period, have been extended to two additional cases with adhesion force acting throughout the whole period. Based on these results, a complete transition between the Westergaard and the Johnson, Kendall, and Roberts (JKR)-type contact models is captured through a dimensionless transition parameter, which is consistent with that for a single cylindrical contact. Depending on two dimensionless parameters, different transition processes between partial and full contact during loading/unloading stages are characterized by one or more jump instabilities. Rougher surfaces are found to enhance adhesion both by increasing the magnitude of the pull-off force and by inducing more energy loss due to adhesion hysteresis.

scholarly journals Effect of COVID-19 Non-Pharmaceutical Interventions and the Implications for Human Rights

2020 ◽  
Vol 18 (1) ◽  
pp. 217
Author(s):  
Seung-Hun Hong ◽  
Ha Hwang ◽  
Min-Hye Park
Keyword(s):  
Human Rights ◽  
Linear Regression ◽  
School Closure ◽  
Contact Tracing ◽  
Limited Evidence ◽  
School Closures ◽  
Human Rights Abuses ◽  
Full Contact ◽  
Complete Contact ◽  
Pharmaceutical Interventions

In response to the COVID-19 pandemic, many governments swiftly decided to order nationwide lockdowns based on limited evidence that such extreme measures were effective in containing the epidemic. A growing concern is that governments were given little time to adopt effective and proportional interventions protecting citizens’ lives while observing their freedom and rights. This paper examines the effectiveness of non-pharmaceutical interventions (NPIs) in containing COVID-19, by conducting a linear regression over 108 countries, and the implication for human rights. The regression results are supported by evidence that shows the change in 10 selected countries’ responding strategies and their effects as the confirmed cases increase. We found that school closures are effective in containing COVID-19 only when they are implemented along with complete contact tracing. Our findings imply that to contain COVID-19 effectively and minimize the risk of human rights abuses, governments should consider implementing prudently designed full contact tracing and school closure policies, among others. Minimizing the risk of human rights abuses should be a principle even when full contact tracing is implemented.

scholarly journals A JKR-Like Solution for Viscoelastic Adhesive Contacts

2021 ◽  
Vol 7 ◽  
Author(s):  
Guido Violano ◽  
Antoine Chateauminois ◽  
Luciano Afferrante
Keyword(s):  
Closed Form ◽  
Numerical Models ◽  
Closed Form Solution ◽  
Numerical Data ◽  
Adhesive Contact ◽  
Form Solution ◽  
Contact Radius ◽  
Rigid Sphere ◽  
Soft Spheres ◽  
Adhesive Contacts

A closed-form solution for the adhesive contact of soft spheres of linear elastic material is available since 1971 thanks to the work of Johnson, Kendall, and Roberts (JKR). A similar solution for viscoelastic spheres is still missing, though semi-analytical and numerical models are available today. In this note, we propose a closed-form analytical solution, based on JKR theory, for the detachment of a rigid sphere from a viscoelastic substrate. The solution returns the applied load and contact penetration as functions of the contact radius and correctly captures the velocity-dependent nature of the viscoelastic pull-off. Moreover, a simple approach is provided to estimate the stick time, i.e., the delay between the time the sphere starts raising from the substrate and the time the contact radius starts reducing. A simple formula is also suggested for the viscoelastic pull-off force. Finally, a comparison with experimental and numerical data is shown.

scholarly journals An Adhesive Wear Model Based on a Complete Contact Model for a Fractal Surface

2021 ◽  
Vol 2095 (1) ◽  
pp. 012098
Author(s):  
Xin Li ◽  
Bingbing Wang
Keyword(s):  
Fractal Dimension ◽  
Contact Area ◽  
Adhesive Wear ◽  
Contact Model ◽  
Wear Volume ◽  
Fractal Surface ◽  
Wear Model ◽  
Model Based ◽  
Complete Contact ◽  
Maximum Contact

Abstract An adhesive wear model based on a complete contact model for a fractal surface is presented in this work. A contact model which contains effect of adhesion is firstly presented based on ME model. A complete contact model is then proposed. Finally, an adhesive wear model based on this model is given. The results suggest that the maximum contact area increases firstly and then decreases as fractal dimension increases. The percentage of plastic contact area increases with increase of the fractal dimension. And the experimental results for wear volume have shown a good consistency with the results calculated by the wear model.

scholarly journals Modeling of the Loading–Unloading Contact of Two Cylindrical Rough Surfaces with Friction

2020 ◽  
Vol 10 (3) ◽  
pp. 742 ◽  
Author(s):  
Honghai Wang ◽  
Peng Jia ◽  
Liquan Wang ◽  
Feihong Yun ◽  
Gang Wang ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Contact Area ◽  
Fractal Model ◽  
Contact Load ◽  
Real Contact Area ◽  
Curvature Radius ◽  
Real Contact ◽  
Deformation Stages ◽  
Nonlinear Relation ◽  
Loading And Unloading

The first fractal model for the loading–unloading process between two cylindrical surfaces with friction is presented. The nonlinear relation between the real contact area and the contact load in different deformation stages are deduced for a load–unload cycle. The impacts of parameters in the model are discussed. The numerical results show that for a given dimensionless contact load, the dimensionless real contact area of the loading–unloading process of cylindrical contact surface with friction, as well as the differences of the dimensionless real contact area between the loading and unloading processes, increase with the increase of the loading interference and fractal dimension, decrease of the profile scaling parameter and curvature radius, or the substitution of external contact for internal contact.

Adhesive contact between a rippled elastic surface and a rigid spherical indenter: from partial to full contact

Soft Matter ◽  
2011 ◽  
Vol 7 (22) ◽  
pp. 10728 ◽  
Author(s):  
Congrui Jin ◽  
Krishnacharya Khare ◽  
Shilpi Vajpayee ◽  
Shu Yang ◽  
Anand Jagota ◽  
...  
Keyword(s):  
Adhesive Contact ◽  
Spherical Indenter ◽  
Elastic Surface ◽  
Full Contact
Sign in / Sign up

Export Citation Format

Share Document