Stickiness of randomly rough surfaces with high fractal dimension: is there a fractal limit?

Two surfaces are "sticky" if breaking their mutual contact requires a finite tensile force. At low fractal dimensions D, there is consensus stickiness does not depend on the upper truncation frequency of roughness spectrum (or "magnification"). As debate is still open for the cas...

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Bibliographic Details
Published in:arXiv.org 2020-12
Main Authors: Violano, G, Papangelo, A, Ciavarella, M
Format: Article
Language:English
Subjects:
Fractal geometry
Fractals
Roughness
Online Access:Get full text
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Summary:Two surfaces are "sticky" if breaking their mutual contact requires a finite tensile force. At low fractal dimensions D, there is consensus stickiness does not depend on the upper truncation frequency of roughness spectrum (or "magnification"). As debate is still open for the case at high D, we exploit BAM theory of Ciavarella and Persson-Tosatti theory, to derive criteria for all fractal dimensions. For high D, we show that stickiness is more influenced by short wavelength roughness with respect to the low D case. BAM converges at high magnifications to a simple criterion which depends only on D, in agreement with theories that includes Lennard-Jones traction-gap law, while Persson-Tosatti disagrees because of its simplifying approximations.
ISSN:2331-8422