The Interaction of Frictional Slip and Adhesion for a Stiff Sphere on a Compliant Substrate

Abstract

How friction affects adhesion is addressed. The problem is considered in the context of a very stiff sphere adhering to a compliant, isotropic, linear elastic substrate, and experiencing adhesion and frictional slip relative to each other. The adhesion is considered to be driven by very large attractive tractions between the sphere and the substrate that can act only at very small distances between them. As a consequence, the adhesion behavior can be represented by the Johnson-Kendall-Roberts model, and this is assumed to prevail also when frictional slip is occurring. Frictional slip is considered to be resisted by a uniform, constant shear traction at the slipping interface, a model that is considered to be valid for small asperities and for compliant elastomers in contact with stiff material. A model for the interaction of friction and adhesion, known to agree with some experimental data, is utilized. This model is due to Johnson, and its adhesionfriction interaction is assumed to stem, upon shrinkage of the contact area, from a postulated reversible energy release associated with frictional slip. This behavior is considered to arise from surface microstructures generated or eliminated by frictional slip, where these microstructures store some elastic strain energy in a reversible manner. The associated reversible energy release rate is derived from the energy exchanges that occur in the system. The Johnson model, and an asymptotic analysis of it for small amounts of frictional slip, is shown to be consistent with the reversible energy release rate that we identify.

Incipient sliding of adhesive contacts

“…At higher values of  t , slip occurs instead, and the results are more similar to those of Johnson's approach. However, our model and Johnson's approach differed significantly: The slip in our model is fully reversible for tangential gaps smaller than t / 2  and fully irreversible otherwise, whereas in Johnson's approach, both reversible and irreversible slip occurs at a fixed ratio [11,14,15]. In reality, one can expect dissipation to begin as soon as slip occurs, with most of the slip being reversible initially and the irreversible component increasing rapidly until it dominates at large distances.…”

“…This resulted in a slower decrease in the contact area. The second approach, pioneered by Johnson [11] and further extended by McMeeking et al [14], and Ciavarella and Papangelo [15], allows slip and assumes that a portion of this slip is reversible. This reversible slip accumulates energy at the interface and hence reduces the work of adhesion.…”

“…The withdrawal of adhesive balls has been addressed analytically by several authors using models based on linear elastic fracture mechanics (LEFM) [4,[10][11][12][13][14][15][16][17]. These authors successfully replicated most experimental observations in which adhesion is strong, including the power law decay of the contact area with increasing tangential load, and its shape transformation from circular to elliptical [13].…”

Sphere and cylinder contact mechanics during slip

“…For stationary contact with F x = 0, where F x is the applied tangential force, the adhesive interaction is well described by the Johnson-Kendall-Roberts (JKR) theory [4,5] which has been tested in great detail. However, when the tangential force F x is non-zero the problem becomes much more complex and not fully understood [6][7][8][9][10][11].…”

Cylinder–flat-surface contact mechanics during sliding

“…For stationary contact with F x = 0, where F x is the applied tangential force, the adhesive interaction is well described by the Johnson-Kendall-Roberts (JKR) theory [5,6] which has been tested in great detail. However, when the tangential force F x is nonzero, the problem becomes much more complex and not fully understood [7][8][9][10][11][12].…”