Influence of tangential displacement on the adhesion strength of a contact between a parabolic profile and an elastic half-space.

Valentin L Popov,Alexander E Filippov,Iakov A Lyashenko

doi:10.1098/rsos.161010

Abstract

The adhesion strength of a contact between a rotationally symmetric indenter and an elastic half-space is analysed analytically and numerically using an extension of the method of dimensionality reduction for superimposed normal/tangential adhesive contacts. In particular, the dependence of the critical adhesion force on the simultaneously applied tangential force is obtained and the relevant dimensionless parameters of the problem are identified. The fracture criterion used coincides with that suggested by Johnson. In this paper, it is used to develop a method that is applicable straightforwardly to adhesive contacts of arbitrary bodies of revolution with compact contact area.

Highlights

Kendall and Roberts developed in 1971 their classical theory of normal adhesive contact between two parabolic, isotropic elastic bodies (JKR theory) [1] using the similarity between the boundary of an adhesive contact and the tip of a
In the JKR theory—just as in the theory of Griffith—the equilibrium configuration of an adhesive contact is determined by minimizing the total energy of the system including the energy of elastic deformation of contacting bodies, the interface energy and the work of external forces [4]
The application of tangential force leads to a decrease of the normal adhesive force

Summary

Introduction

Kendall and Roberts developed in 1971 their classical theory of normal adhesive contact between two parabolic, isotropic elastic bodies (JKR theory) [1] using the similarity between the boundary of an adhesive contact and the tip of a. In his paper of 1997, Johnson approaches the problem of adhesive contact under superimposed normal and tangential loading by considering the complete energy release rate at the boundary of an adhesive contact [6]. The actual work of detachment may be much larger than the pure surface energy In this case, the main part of elastic energy will disappear irreversibly and the relatively weak interfacial interactions will not be able to restore the integrity of the interface again. In [14], a model of tangential adhesion contact was proposed, which, requires the assumption that the effects of normal and tangential force can be considered independently In this investigation, the authors showed that in the tangential contact problem the influence of adhesion can be approximately described in terms of equivalent load. Method of dimensionality reduction formulation for adhesive contact and analytical solution

Method of dimensionality reduction for normal adhesive contacts

Superimposed normal and tangential loading

Adhesion force under load-controlled conditions

Adhesion under displacement-controlled conditions

Numerical procedure and comparison with analytical results

Conclusion