Adhesion-Induced Instability in Asperities

Abstract

Adhesive forces between two approaching asperities will deform the asperities, and under certain conditions this will result in a sudden runaway deformations leading to a jump-to-contact instability. We present finite element-based numerical studies on adhesioninduced deformation and instability in asperities. We consider the adhesive force acting on an asperity, when it is brought near a rigid half-space, due to van der Waals interaction between the asperity and the half-space. The adhesive force is considered to be distributed over the volume of the asperity (body force), thus resulting in more realistic simulations for the length scales considered. Iteration scheme based on a ''residual stress update'' algorithm is used to capture the effect of deformation on the adhesion force, and thereby the equilibrium configuration and the corresponding force. The numerical results are compared with the previous approximate analytical solutions for adhesion force, deformation of the asperity and adhesioninduced mechanical instability (jump-to-contact). It is observed that the instability can occur at separations much higher, and could possibly explain the higher value of instability separation observed in experiments. The stresses in asperities, particularly in case of small ones, are found to be high enough to cause yielding before jump-to-contact. The effect of roughness is considered by modeling a spherical protrusion on the hemispherical asperity. This small-scale roughness at the tip of the asperities is found to control the deformation behavior at small separations, and hence are important in determining the friction and wear due to the jump-to-contact instability.

An efficient computational model for adhesive contact mechanics based on a lumped parameter formulation

“…When the interacting bodies’ resistance to deformation is less than or equal to the adhesion force gradient, a mechanical instability ensues, resulting in jump-to-contact phenomenon. 29, 35 For characterising this phenomenon, Pethica and Sutton 34 studied the adhesive contact between two elastic spheres and developed an expression which predicted that jump-to-contact would occur for a separation given by: Attard and Parker 36 using perturbation theory, derived a similar expression for instability separation, with difference only in the numerical constants. In the above equations, reduced modulus E * is defined as 1 E * = 1 − ν 1 2 E 1 + 1 − ν 2 2 E 2, R is the radius of the sphere, A normalH is the Hamaker constant and d inst is the separation at which the instability occurs.…”

“…When the interacting bodies' resistance to deformation is less than or equal to the adhesion force gradient, a mechanical instability ensues, resulting in jump-to-contact phenomenon. 29,35 For characterising this phenomenon, Pethica and Sutton 34 studied the adhesive contact between two elastic spheres and developed an expression which predicted that jump-to-contact would occur for a separation given by:…”

“…Computational studies conducted earlier were limited to the surface force formulation, which becomes inaccurate when the tip of the cantilever is less than about 10nm. 35 In the present study, we use body force formulation using Lumped Parameter Model, which can eliminate the above-mentioned difficulty. 37 The schematic diagram of the cantilever used for the study is as shown in Figure 6.…”

A Survey of Computational Models for Adhesion

“…Instead of the surface-based tractionseparation law (39), the Lennard-Jones potential can also be used within a body force-based separation law. Examples are given in [240], [119], [241], and [242,243]. The last two references apply the formulation to study the adhesive impact of elastic rods and spheres, examining the apparent energy loss during impact.…”