Contact mechanics for randomly rough surfaces

By B. Persson. 2006

761 citations recorded by the source corpus.

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 the 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 suggests a new explanation for puzzling experimental results [L. Bureau, T. Baumberger, C. Caroli, arXiv:cond-mat/0510232 v1] 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.

Subfields: Materials Chemistry, Mechanics of Materials, Surfaces, Coatings and Films

View Paper: https://www.semanticscholar.org/paper/88a096ec65825f5e6394af9112bd53d622baa946

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In Materials Chemistry

In Mechanics of Materials

In Surfaces, Coatings and Films

Citations in the corpus

Optical In Situ Micro Tribometer for Analysis of Real Contact Area for Contact Mechanics, Adhesion, and Sliding Experiments (2011, methodology): “3d) [29] and the resulting fractal dimension is Df * 2.”
A new efficient numerical method for contact mechanics of rough surfaces (2012, methodology): “Also, the numerical convergence of the proposed method has been verified by comparing the numerical results with the Hertzian solution and by checking the trend of the stress probability distribution at the interface which must vanish as the interfacial stress r goes to zero (Persson et al., 2002; P”
Interfacial separation between elastic solids with randomly rough surfaces: Comparison between theory and numerical techniques (2011, methodology): “Recently, an analytical contact mechanics model that does not use the asperity concept and becomes exact in the limit of complete contact has been developed by Persson (2001, 2006, 2007), Yang and Persson (2008), and Persson and Yang (2008).”
Colloquium: Modeling friction: From nanoscale to mesoscale (2011, background): “The effect of elastic interactions due to the contact of self-affine surfaces has been studied analytically and numerically, revealing that the solid indeed deforms elastically due to the contact (Persson, 2006; Campana, Müser, and Robbins, 2008; Campana, Persson, and Müser, 2011).”