Adhesion between a thin elastic plate and a hard randomly rough substrate

When two solids are squeezed together they will in general not make atomic contact everywhere within the nominal (or apparent) contact area. This fact has huge practical implications and must be considered in many technological applications. In this paper I briefly review basic theories of contact mechanics. I consider in detail a recently developed contact mechanics theory. I derive boundary conditions for the stress probability distribution function for elastic, elastoplastic and adhesive contact between solids and present numerical results illustrating some aspects of the theory. I analyze contact problems for very smooth polymer (PMMA) and Pyrex glass surfaces prepared by cooling liquids of glassy materials from above the glass transition temperature. I show that the surface roughness which results from the frozen capillary waves can have a large influence on the contact between the solids. The analysis suggest a new explanation for puzzling experimental results [L. Bureau, T. Baumberger and C. Caroli, arXiv:cond-mat/0510232] about the dependence of the frictional shear stress on the load for contact between a glassy polymer lens and flat substrates. I discuss the possibility of testing the theory using numerical methods, e.g., finite element calculations.

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“…The limiting case of a thin elastic plate can be treated using the formalism developed in Ref. [28,29].…”

Section: Elastic Contact Mechanics With Graded Elasticitymentioning

confidence: 99%

Contact mechanics for randomly rough surfaces

Persson

2006

Surface Science Reports

645

534

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“…Equations (10, 13, 14, 15, 16 and 17) can be solved to calculate the stress probability distribution P (σ, ζ) and hence the apparent contact area A (ζ) /A 0 as a function of the magnification ζ [11], [21] A (ζ)…”

Section: Persson's Theory For Anisotropic Surfacesmentioning

confidence: 99%

“…In Eq. (14) the quantity γ eff (ζ) is the apparent energy of adhesion at the interface defined as [11], [21] …”

Section: Persson's Theory For Anisotropic Surfacesmentioning

confidence: 99%

Adhesive contact of rough surfaces: Comparison between numerical calculations and analytical theories

2009

Self Cite

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The authors have employed a numerical procedure to analyze the adhesive contact between a soft elastic layer and a rough rigid substrate. The solution of the problem, which belongs to the class of the free boundary problems, is obtained by calculating the Green's function which links the pressure distribution to the normal displacements at the interface. The problem is then formulated in the form of a Fredholm integral equation of the first kind with a logarithmic kernel, and the boundaries of the contact area are calculated by requiring that the energy of the system is stationary. The methodology has been employed to study the adhesive contact between an elastic semi-infinite solid and a randomly rough rigid profile with a self-affine fractal geometry. We show that, even in presence of adhesion, the true contact area still linearly depends on the applied load. The numerical results are then critically compared with the prediction of an extended version of the Persson's contact mechanics theory, able to handle anisotropic surfaces, as 1D interfaces. It is shown that, for any given load, Persson's theory underestimates the contact area of about 50% in comparison with our numerical calculations. We find that this discrepancy is larger than what is found for 2D rough surfaces in case of adhesionless contact. We argue that this increased difference might be explained, at least partially, by considering that Persson's theory is a mean field theory in spirit, so it should work better for 2D rough surfaces rather than for 1D rough surfaces. We also observe, that the predicted value of separation is in very good agreement with our numerical results as well as the exponent of the power spectral density of the contact pressure distribution and of the elastic displacement of the solid. Therefore, we conclude that Persson's theory captures almost exactly the main qualitative behavior of the rough contact phenomena.

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“…Recently, these models have been extended to study silicon wafer bonding (Turner & Spearing 2002;Pamp & Adams 2007) and biological and bio-inspired adhesives, in particular the peeling or attachment of plate-like spatulae or lamellae in wall-climbing insects and lizards. These latter structures are treated as a thin elastic plate in contact with a rigid, randomly rough substrate (Persson & Gorb 2003;Carbone et al 2004;Filippov & Popov 2007).…”

Section: Introductionmentioning

confidence: 99%

Adhesion of an elastic plate to a sphere

Majidi

Fearing

2008

Proc. R. Soc. A.

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Stationary principles and the von Kármán plate theory are used to study the adhesion of thin elastic plates to a rigid sphere. Contact requires both flexural and membrane strains that can lead to partial or complete delamination. Interestingly, whereas a large area plate might spontaneously delaminate from the sphere, dividing this plate into many smaller plates with equivalent thickness eliminates membrane strains and may allow complete contact. The theoretical predictions are compared to experimental results for low density polyethylene on a smooth glass sphere. The peel strength is estimated with a modified Kendall peel equation.

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Adhesion between a thin elastic plate and a hard randomly rough substrate

Cited by 63 publications

References 29 publications

Contact mechanics for randomly rough surfaces

Contact mechanics for randomly rough surfaces

Adhesive contact of rough surfaces: Comparison between numerical calculations and analytical theories

Adhesion of an elastic plate to a sphere

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