A unified treatment of axisymmetric adhesive contact problems using the harmonic potential function method

Zhou, S.-S.; Gao, X.-L.; He, Qi‐Chang

doi:10.1016/j.jmps.2010.11.006

Cited by 24 publications

(5 citation statements)

References 41 publications

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“…To mitigate this issue, in the present work, the average normal stress and correspondingly the contact radius and deformation are also calculated numerically by solving a general contact mechanics model proposed by Zhou et al 35 for the adhesive contact of arbitrarily shaped axisymmetric punches. All of the classic contact mechanics models, including Sneddon's and Boussinesq's solutions, are special cases of the proposed solution.…”

Section: Resultsmentioning

confidence: 99%

“…All of the classic contact mechanics models, including Sneddon’s and Boussinesq’s solutions, are special cases of the proposed solution. Equations 34, 35a, and 35b of ref are used for this purpose. In these equations, the term p ( t ), the adhesive interaction force function, is set to zero because of the fact that there is not a straightforward way to accurately determine the adhesive function for the AFM tips.…”

Section: Resultsmentioning

confidence: 99%

“…As the AFM tip apexes are not simple smooth paraboloids, it is important to consider the difference between the stress calculated by simply fitting a paraboloid to the tip apex and the stress calculated using a line fit to the actual tip profile. As mentioned earlier, we use the solution presented by Zhou et al 35 for an axisymmetric arbitrary punch shape. It is important to determine the point in the profile estimated to be the point of initial contact with the sample and the profile's correct orientation with respect to the sample.…”

Section: Methodsmentioning

confidence: 99%

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Mechanics of Interaction and Atomic-Scale Wear of Amplitude Modulation Atomic Force Microscopy Probes

et al. 2013

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Wear is one of the main factors that hinders the performance of probes for atomic force microscopy (AFM), including for the widely used amplitude modulation (AM-AFM) mode. Unfortunately, a comprehensive scientific understanding of nanoscale wear is lacking. We have developed a protocol for conducting consistent and quantitative AM-AFM wear experiments. The protocol involves controlling the tip-sample interaction regime during AM-AFM scanning, determining the tip-sample contact geometry, calculating the peak repulsive force and normal stress over the course of the wear test, and quantifying the wear volume using high-resolution transmission electron microscopy imaging. The peak repulsive tip-sample interaction force is estimated from a closed-form equation accompanied by an effective tip radius measurement procedure, which combines transmission electron microscopy and blind tip reconstruction. The contact stress is estimated by applying Derjaguin-Müller-Toporov contact mechanics model and also numerically solving a general contact mechanics model recently developed for the adhesive contact of arbitrary axisymmetric punch shapes. We discuss the important role that the assumed tip shape geometry plays in calculating both the interaction forces and the contact stresses. Contact stresses are significantly affected by the tip geometry while the peak repulsive force is mainly determined by experimentally controlled parameters, specifically, the free oscillation amplitude and amplitude ratio. The applicability of this protocol is demonstrated experimentally by assessing the performance of diamond-like carbon-coated and silicon-nitride-coated silicon probes scanned over ultrananocrystalline diamond substrates in repulsive mode AM-AFM. There is no sign of fracture or plastic deformation in the case of diamond-like carbon; wear could be characterized as a gradual atom-by-atom process. In contrast, silicon nitride wears through removal of the cluster of atoms and plastic deformation.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Mechanics of Interaction and Atomic-Scale Wear of Amplitude Modulation Atomic Force Microscopy Probes

et al. 2013

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“…Equations (2.25) and (2.26) constitute the generalized JKR model of adhesive contact, and they have been previously derived in a number of papers [14,53,54] by different approaches.…”

Section: Theorymentioning

confidence: 99%

Controlling the adhesive pull-off force via the change of contact geometry

Argatov

2021

Phil. Trans. R. Soc. A.

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A first-order asymptotic analysis of the Griffith energy balance in the Johnson–Kendall–Roberts model of adhesive contact under non-symmetric perturbation of the contact geometry is presented. The pull-off force is evaluated in explicit form. A particular case of adhesive contact between a relatively stiff sphere and an elastic half-space is considered under the assumption that the sphere geometry is changed by the application of an arbitrary lateral normal surface loading. The effect of the sphere Poisson’s ratio on controlling the adhesive pull-off force is considered. This article is part of a discussion meeting issue ‘A cracking approach to inventing new tough materials: fracture stranger than friction’.

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“…The Papkovich-Neuber formalism and the Galin solution were used in application to mechanics of adhesive contact. In particular, Zheng and Yu (2007) and Zhou et al (2011) considered the JKR and Maugis-Dugdale contact problems for power-law shaped solids. As Zheng and Yu (2007) noted, their solution to the JKR problem for power-law shaped solids coincides with the solution by Borodich and Galanov (2004).…”

Section: Sneddon 1965 Borodich and Keer 2004b)mentioning

confidence: 99%

The JKR-type adhesive contact problems for power-law shaped axisymmetric punches

Borodich

Galanov

Suarez-Alvarez

2014

Journal of the Mechanics and Physics of Solids

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The JKR (Johnson, Kendall, and Roberts) and Boussinesq-Kendall models describe adhesive frictionless contact between two isotropic elastic spheres, and between a flat-ended axisymmetric punch and an elastic half-space respectively. However, the shapes of contacting solids may be more general than spherical or flat ones. In addition, the derivation of the main formulae of these models is based on the assumption that the material points within the contact region can move along the punch surface without any friction. However, it is more natural to assume that a material point that came to contact with the punch sticks to its surface, i.e. to assume that the non-slipping boundary conditions are valid. It is shown that the frictionless JKR model may be generalized to arbitrary convex, blunt axisymmetric body, in particular to the case of the punch shape being described by monomial (power-law) punches of an arbitrary degree d ≥ 1. The JKR and Boussinesq-Kendall models are particular cases of the problems for monomial punches, when the degree of the punch d is equal to two or it goes to infinity respectively. The generalized problems for monomial punches are studied under both frictionless and non-slipping (or no-slip) boundary conditions. It is shown that regardless of the boundary conditions, the solution to the problems is reduced to the same dimensionless relations between the actual force, displacements and contact radius. The explicit expressions are derived for the values of the pull-off force and for the corresponding critical contact radius. Connections of the results obtained to problems of nanoindentation in the case of the indenter shape near the tip has some deviation from its nominal shape and the shape function can be approximated by a monomial function of radius, are discussed.

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A unified treatment of axisymmetric adhesive contact problems using the harmonic potential function method

Cited by 24 publications

References 41 publications

Mechanics of Interaction and Atomic-Scale Wear of Amplitude Modulation Atomic Force Microscopy Probes

Mechanics of Interaction and Atomic-Scale Wear of Amplitude Modulation Atomic Force Microscopy Probes

Controlling the adhesive pull-off force via the change of contact geometry

The JKR-type adhesive contact problems for power-law shaped axisymmetric punches

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