Adhesive Contact of Elastically Deformable Spheres: A Computational Study of Pull-Off Force and Contact Radius

2001 ◽  
Vol 238 (2) ◽  
pp. 318-323 ◽  
Author(s):  
James Q. Feng
Keyword(s):  
Computational Study ◽  
Adhesive Contact ◽  
Contact Radius

An Extension to a Cohesive Zone Solution for Adhesive Cylinders

2004 ◽  
Author(s):  
Clint A. Morrow ◽  
Michael R. Lovell
Keyword(s):  
Cohesive Zone ◽  
Normal Load ◽  
Adhesive Contact ◽  
Physical Contact ◽  
Contact Radius ◽  
Intimate Contact ◽  
Contact Behavior ◽  
Micro Scale ◽  
Applied Normal Load ◽  
Adhesive Forces

When adhesive forces are taken into consideration, contacting asperities can still interact after intimate contact is broken. Current theories that predict the contact behavior of adhesive cylindrical asperities fail to capture the forces in this regime. In the present investigation, prior solutions for adhesive cylindrical asperities will be extended to include the condition where the asperities are not in physical contact but are still interacting through adhesive forces. In the extended results, relationships between the adhesive contact radius and the applied normal load will be developed and discussed with respect to the design of micro-scale components.

A Unified Treatment of Axisymmetric Adhesive Contact on a Power-Law Graded Elastic Half-Space

2013 ◽  
Vol 80 (6) ◽  
Author(s):  
Fan Jin ◽  
Xu Guo ◽  
Wei Zhang
Keyword(s):  
Half Space ◽  
Power Law ◽  
Contact Region ◽  
Adhesive Contact ◽  
Elastic Half Space ◽  
Hertzian Contact ◽  
Contact Radius ◽  
Abel Transformation ◽  
Numerical Solution Methods ◽  
Special Cases

In the present paper, axisymmetric frictionless adhesive contact between a rigid punch and a power-law graded elastic half-space is analytically investigated with use of Betti's reciprocity theorem and the generalized Abel transformation, a set of general closed-form solutions are derived to the Hertzian contact and Johnson–Kendall–Roberts (JKR)-type adhesive contact problems for an arbitrary punch profile within a circular contact region. These solutions provide analytical expressions of the surface stress, deformation fields, and equilibrium relations among the applied load, indentation depth, and contact radius. Based on these results, we then examine the combined effects of material inhomogeneities and punch surface morphologies on the adhesion behaviors of the considered contact system. The analytical results obtained in this paper include the corresponding solutions for homogeneous isotropic materials and the Gibson soil as special cases and, therefore, can also serve as the benchmarks for checking the validity of the numerical solution methods.

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.

A Model of Contact With Adhesion of a Layered Elastic-Plastic Microsphere With a Rigid Flat Surface

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
H. Eid ◽  
N. Joshi ◽  
N. E. McGruer ◽  
G. G. Adams
Keyword(s):  
Contact Resistance ◽  
Layer Thickness ◽  
Plastic Material ◽  
Element Model ◽  
Adhesive Contact ◽  
Contact Radius ◽  
Elastic Plastic ◽  
High Durability ◽  
Special Procedure ◽  
Elastic Plastic Material

A finite element model of a layered hemisphere contacting a rigid flat, which includes the effect of adhesion, is developed. In this analysis elastic-plastic material properties were used for each of the materials comprising the layered hemisphere. The inclusion of the effect of adhesion, which was accomplished with the Lennard-Jones potential, required a special procedure. This configuration is of general theoretical interest in the understanding of adhesion. It has also been suggested as a possible design for a microswitch contact because, with an appropriate choice of metals, it has the potential to achieve low adhesion, low contact resistance, and high durability. The effect of the layer thickness on the adhesive contact was investigated. In particular the influences of layer thickness on the pull-off force, maximum contact radius, and contact resistance were determined. The results are presented as load versus interference and contact radius versus interference for loading and unloading from different values of the maximum interference.

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 Contact probing of stretched membranes and adhesive interactions: graphene and other two-dimensional materials

2016 ◽  
Vol 472 (2195) ◽  
pp. 20160550 ◽  
Author(s):  
Feodor M. Borodich ◽  
Boris A. Galanov
Keyword(s):  
2D Materials ◽  
Contact Problems ◽  
Adhesive Contact ◽  
Contact Radius ◽  
Elastic Membrane ◽  
Displacement Curve ◽  
Circular Membrane ◽  
Two Dimensional ◽  
Adhesive Interactions ◽  
Force Displacement

Contact probing is the preferable method for studying mechanical properties of thin two-dimensional (2D) materials. These studies are based on analysis of experimental force–displacement curves obtained by loading of a stretched membrane by a probe of an atomic force microscope or a nanoindenter. Both non-adhesive and adhesive contact interactions between such a probe and a 2D membrane are studied. As an example of the 2D materials, we consider a graphene crystal monolayer whose discrete structure is modelled as a 2D isotropic elastic membrane. Initially, for contact between a punch and the stretched circular membrane, we formulate and solve problems that are analogies to the Hertz-type and Boussinesq frictionless contact problems. A general statement for the slope of the force–displacement curve is formulated and proved. Then analogies to the JKR (Johnson, Kendall and Roberts) and the Boussinesq–Kendall contact problems in the presence of adhesive interactions are formulated. General nonlinear relations among the actual force, displacements and contact radius between a sticky membrane and an arbitrary axisymmetric indenter are derived. The dimensionless form of the equations for power-law shaped indenters has been analysed, and the explicit expressions are derived for the values of the pull-off force and corresponding critical contact radius.

scholarly journals Adhesive contact problems for a thin elastic layer: Asymptotic analysis and the JKR theory

2018 ◽  
Vol 24 (5) ◽  
pp. 1405-1424 ◽  
Author(s):  
Feodor M. Borodich ◽  
Boris A. Galanov ◽  
Nikolay V. Perepelkin ◽  
Danila A. Prikazchikov
Keyword(s):  
Elastic Foundation ◽  
Elastic Layer ◽  
Order Approximation ◽  
Contact Problems ◽  
Adhesive Contact ◽  
Contact Radius ◽  
Direct Derivation ◽  
Compressible Elastic Layer ◽  
Jkr Theory ◽  
Thin Elastic Layer

Contact problems for a thin compressible elastic layer attached to a rigid support are studied. Assuming that the thickness of the layer is much less than the characteristic dimension of the contact area, a direct derivation of asymptotic relations for displacements and stress is presented. The proposed approach is compared with other published approaches. The cases are established when the leading-order approximation to the non-adhesive contact problems is equivalent to contact problem for a Winkler–Fuss elastic foundation. For this elastic foundation, the axisymmetric adhesive contact is studied in the framework of the Johnson–Kendall–Roberts (JKR) theory. The JKR approach has been generalized to the case of the punch shape being described by an arbitrary blunt axisymmetric indenter. Connections of the results obtained to problems of nanoindentation in the case that the indenter shape near the tip has some deviation from its nominal shape are discussed. For indenters whose shape is described by power-law functions, the explicit expressions are derived for the values of the pull-off force and for the corresponding critical contact radius.

scholarly journals ADHESION BETWEEN A POWER-LAW INDENTER AND A THIN LAYER COATED ON A RIGID SUBSTRATE

2018 ◽  
Vol 16 (1) ◽  
pp. 19 ◽  
Author(s):  
Antonio Papangelo
Keyword(s):  
Thin Layer ◽  
Layer Thickness ◽  
Power Law ◽  
Contact Area ◽  
Critical Thickness ◽  
Adhesive Contact ◽  
Indentation Load ◽  
Contact Radius ◽  
Indenter Shape

In the present paper we investigate indentation of a power-law axisymmetric rigid probe in adhesive contact with a "thin layer" laying on a rigid foundation for both frictionless unbounded and bounded compressible cases. The investigation relies on the "thin layer" assumption proposed by Johnson, i.e. the layer thickness being much smaller than the radius of the contact area, and it makes use of the previous solutions proposed by Jaffar and Barber for the adhesiveless case. We give analytical predictions of the loading curves and provide indentation, load and contact radius at the pull-off. It is shown that the adhesive behavior is strongly affected by the indenter shape; nevertheless below a critical thickness of the layer (typically below 1 µm) the theoretical strength of the material is reached. This is in contrast with the Hertzian case, which has been shown to be insensitive to the layer thickness. Two cases are investigated, namely, the case of a free layer and the case of a compressible confined layer, the latter being more "efficient", as, due to Poisson effects, the same detachment force is reached with a smaller contact area. It is suggested that high sensitive micro-/nanoindentation tests may be performed using probes with different power law profiles for characterization of adhesive and elastic properties of micro-/nanolayers.

An Elastic Adhesion Model for Contacting Cylinder and Perfectly Wetted Plane in the Presence of Meniscus

2007 ◽  
Vol 129 (2) ◽  
pp. 231-234 ◽  
Author(s):  
Y. F. Peng ◽  
G. X. Li
Keyword(s):  
Relative Humidity ◽  
Normal Load ◽  
Adhesive Contact ◽  
Laplace Pressure ◽  
Contact Radius ◽  
Adhesive Interaction ◽  
Applied Normal Load ◽  
Adhesion Model ◽  
The Relationship

The present research concerns the elastic contacting adhesion of a cylinder with a perfectly wetted plane in the presence of a meniscus. The Laplace pressure due to the meniscus is simplified utilizing Maugis–Dugdale approximation. Then the Baney and Hui solution and its extension are used to solve the adhesive interaction of the cylinder and the plane. Simulations of the relationship between the adhesive contact radius and the applied normal load are performed, and the influence of the relative humidity on the relationship is also discussed.

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