Energetic criterion for adhesion in viscoelastic contacts with non-entropic surface interaction

Valentin Popov

doi:10.31181/rme200102057p

Abstract

We suggest a detachment criterion for a viscoelastic elastomer contact based on Griffith's idea about the energy balance at an infinitesimal advancement of the boundary of an adhesive crack. At the moment of detachment of a surface element at the boundary of an adhesive contact, there is some quick (instant) relaxation of stored elastic energy which can be expressed in terms of the creep function of the material. We argue that it is only this "instant part" of stored energy which is available for doing work of adhesion and thus it is only this part of energy relaxation that must be used in Griffith's energy balance. The described idea has several restrictions. Firstly, in this pure form, it is only valid for adhesive forces having an infinitely small range of action (which we call the JKR-limit). Secondly, it is only applicable to non-entropic (energetic) interfaces, which detach "at once" and do not possess their own kinetics of detachment.

Highlights

Adhesion of elastic bodies can be understood and described using the principle of virtual work
We argue that it is only this "instant part" of stored energy which is available for doing work of adhesion and it is only this part of energy relaxation that must be used in Griffith's energy balance
The intention of the present paper was not to solve a particular problem in the theory of adhesion but to raise a question: Is it possible to apply the energy balance by Griffith to adhesive contacts of viscoelastic materials? We argue that this might be possible, at least for a limited class of interface interactions, namely the "non-entropic" or "energetic" interfaces

Summary

Introduction

Adhesion of elastic bodies can be understood and described using the principle of virtual work. For nondissipative systems it can be used in the form of "energy balance", first suggested by Griffith (1921) and used in the theory of Johnson, Kendall and Roberts (1971), (Popova & Popov, 2018). The detachment can only occur if the instant relaxation part of the elastic energy is equal to the work of separation of surfaces. This means that the energy balance can be used for viscoelastic bodies too, in a modified form. Note that the same energetic balance method was used in (Pohrt & Popov, 2015) and (Popov et al, 2017) for deriving the detachment criterion of single simulation cells in the Boundary Element Method

Energetic detachment criterion in the case of a viscoelastic material

Discussion and conclusion