Shear-induced contact area anisotropy explained by a fracture mechanics model

Abstract

This paper gives a theoretical analysis for the fundamental problem of anisotropy induced by shear forces on an adhesive contact, discussing the experimental data of the companion Letter. We present a fracture mechanics model where two phenomenological mode-mixity functions are introduced to describe the weak coupling between modes I and II or I and III, which changes the effective toughness of the interface. The mode-mixity functions have been interpolated using the data of a single experiment and then used to predict the behaviour of the whole set of experimental observations. The model extends an idea by Johnson and Greenwood, i.e. to solve purely mode I problems of adhesion in the presence of a non-axisymmetric Hertzian geometry, to the case of elliptical contacts sheared along their major or minor axis. Equality between the stress intensity factors and their critical values is imposed solely at the major and minor axes. We successfully validate our model against experimental data. The model predicts that the punch geometry will affect both the shape and the overall decay of the sheared contact area.

Sphere and cylinder contact mechanics during slip

“…This indicates that the origin of the area reduction in the size of the contact area in Ref. [15] and [16][17][18] may be due to some effect not taken into account in the model study, such as material viscoelasticity, elastic nonlinearity or contact time-dependent work of adhesion.…”

A Numerical Study on Roughness-Induced Adhesion Enhancement in a Sphere with an Axisymmetric Sinusoidal Waviness Using Lennard–Jones Interaction Law

“…Equation (10) constitutes the nonlinear problem to be solved. A problem arises in evaluating the integral (11) as the kernel function G (r, s) is singular in s = r. The common approach is to discretize Equation (11) assuming that the pressure σ (s) has a simple form over a discrete element.…”

“…Adhesion is a challenging topic in tribology [1][2][3] with relevance in several engineering applications that range from biomimetics [4], soft matters [5], soft robots [6], grippers [7], friction [8][9][10][11][12]. Although roughness is usually responsible for adhesion reduction [13][14][15], Briggs and Briscoe [16] showed already in 1977 that relatively small random roughness amplitude could enhance adhesion in pull-off experiments as well as relative rolling resistance by a factor up to 2.5.…”

A Macro Model for Electroadhesive Contact of a Soft Finger With a Touchscreen

“…It is to note that the issue of contact area reduction under tangential loading was observed in [41][42][43] in experiments with a soft rubber with high adhesive hysteresis and a rough elastomer block. Very recently, this phenomenon was modeled theoretically in [44][45][46] based on the linear elasticity fracture mechanics and using the concept of mixed-mode interfacial fracture [47]. Here we emphasize the effect of nonlinear shear deformation.…”