Adhesion and friction in hard and soft contacts: theory and experiment

Abstract

This paper is devoted to an analytical, numerical, and experimental analysis of adhesive contacts subjected to tangential motion. In particular, it addresses the phenomenon of instable, jerky movement of the boundary of the adhesive contact zone and its dependence on the surface roughness. We argue that the “adhesion instabilities” with instable movements of the contact boundary cause energy dissipation similarly to the elastic instabilities mechanism. This leads to different effective works of adhesion when the contact area expands and contracts. This effect is interpreted in terms of “friction” to the movement of the contact boundary. We consider two main contributions to friction: (a) boundary line contribution and (b) area contribution. In normal and rolling contacts, the only contribution is due to the boundary friction, while in sliding both contributions may be present. The boundary contribution prevails in very small, smooth, and hard contacts (as e.g., diamond-like-carbon (DLC) coatings), while the area contribution is prevailing in large soft contacts. Simulations suggest that the friction due to adhesion instabilities is governed by “Johnson parameter”. Experiments suggest that for soft bodies like rubber, the stresses in the contact area can be characterized by a constant critical value. Experiments were carried out using a setup allowing for observing the contact area with a camera placed under a soft transparent rubber layer. Soft contacts show a great variety of instabilities when sliding with low velocity — depending on the indentation depth and the shape of the contacting bodies. These instabilities can be classified as “microscopic” caused by the roughness or chemical inhomogeneity of the surfaces and “macroscopic” which appear also in smooth contacts. The latter may be related to interface waves which are observed in large contacts or at small indentation depths. Numerical simulations were performed using the Boundary Element Method (BEM).

Adhesive Boundary Element Method Using Virtual Crack Closure Technique

“…It is impossible to capture the snap-in instability. In a recent work of Popov et al (Popov et al, 2021), the model of Pohrt and Popov (Pohrt and Popov, 2015) has been extended to cover the loading stage with the capability of capturing the snap-in instability. The detailed implementation of the iterative process can be found in Algorithm 3.…”

“…The detailed implementation of the iterative process can be found in Algorithm 3. Neglecting the energy dissipation due to the unstable snap-in/pull-off at asperity level (Greenwood, 2017;Popov et al, 2021), this BEM model is valid for adhesive contact in both loading and unloading stages (i.e., loading and unloading stages are assumed to be reversible).…”

“…The mesh-dependent SERR formula is essential to the previous BEM model, which is responsible for an accurate delamination criterion. Even though their model has been validated in various numerical and experimental studies (Popov et al, 2017;Popov et al, 2021), the accuracy of Eq. 5 has never been proved.…”

“…Surprisingly, the BEM model adopts the mesh-dependent SERR formula has been extensively validated by the analytical solutions and empirical data (Pohrt and Popov, 2015;Popov et al, 2017;Popov et al, 2021). The above-contradicted conclusions may be due to the following reasons: 1).…”

“…Carbone et al (Carbone and Mangialardi, 2008;Carbone et al, 2009;Carbone et al, 2015) solved the adhesive contact problem between a thin elastic layer and a rigid rough profile using BEM where the locations of contact edges can be determined based on Griffith's criterion. Pohrt and Popov (Pohrt and Popov, 2015) developed a BEM adhesive contact model which is validated by various adhesion tests (Popov et al, 2017;Popov et al, 2021). The SERR in their model has a closed-form, which was derived based on the Boussinesq solutions.…”