Roughness-Induced Adhesive Hysteresis in Self-Affine Fractal Surfaces

Guido Violano,Luciano Afferrante

doi:10.3390/lubricants9010007

Abstract

It is known that in the presence of surface roughness, adhesion can lead to distinct paths of loading and unloading for the area–load and penetration–load relationships, thus causing hysteretic loss. Here, we investigate the effects that the surface roughness parameters have on such adhesive hysteresis loss. We focus on the frictionless normal contact between soft elastic bodies and, for this reason, we model adhesion according to Johnson, Kendall, and Roberts (JKR) theory. Hysteretic energy loss is found to increase linearly with the true area of contact, while the detachment force is negligibly influenced by the maximum applied load reached at the end of the loading phase. Moreover, for the micrometric roughness amplitude hrms considered in the present work, adhesion hysteresis is found to be affected by the shorter wavelengths of roughness. Specifically, hysteresis losses decrease with increasing fractal dimension and cut-off frequency of the roughness spectrum. However, we stress that a different behavior could occur in other ranges of roughness amplitude.

Highlights

The hysteretic dissipation is given by the difference between the work needed to bring two bodies into contact and that required to detach them
For the micrometric roughness amplitude hrms considered in the present work, adhesion hysteresis is found to be affected by the shorter wavelengths of roughness
We propose an investigation of the adhesive elastic contact of rough surfaces, described by self-affine fractal geometries, with an advanced multiasperity model taking into account lateral interactions of asperities according to the authors of [19,20] and adhesion according to JKR theory

Summary

Introduction

The hysteretic dissipation is given by the difference between the work needed to bring two bodies into contact and that required to detach them. Moving from the assumption of full-contact conditions, Dalvi et al applied Persson and Tosatti (PT) adhesion theory [10] for predicting the magnitude of adhesion hysteresis They found that the hysteretic dissipation increases almost linearly with the true contact area A, and it is equal to the product between A and the intrinsic surface energy ∆γ, which depends on the interfacial adhesive properties of contacting bodies. We propose an investigation of the adhesive elastic contact of rough surfaces, described by self-affine fractal geometries, with an advanced multiasperity model taking into account lateral interactions of asperities according to the authors of [19,20] and adhesion according to JKR theory. The energy loss is independent on the maximum penetration (or, equivalently, applied force)

Adhesion Hysteresis of Rough Elastic Surfaces

Results

Adhesive Hysteresis and Pull-Off Force

Discussion and Conclusions