Models of Friction Based on Contact and Fracture Mechanics

Abstract

Theoretical models of dry friction of solids are presented and discussed. The emphasis is placed on the basic aspects related to adhesion at the interface and the relative motion between surfaces of solids. First the standard approach of contact mechanics will be described and the Cattaneo-Mindlin theory [I] based on Coulomb friction is examined. The conventional approach recognizes static friction as a constraint on the relative tangential displacements and tacitly acknowledges adhesion, but it falls short of exploring its fulI implications. Instead of invoking friction laws, the more recent and basic approach treats the contact interface as a bonded joint where adhesion acts to constrain relative displacements in any direction. Considering the geometry outside the contact as an external crack, the methods of fracture mechanics arc introduced and applied to study the initiation and growth of the crack that leads to the separation of solids. The effectiveness of this approach has already been proven by the JKRS theory [2], which describes the influence of adhesion between solids loaded by purely normal forces. Shear tractions arising due to friction at the interface of dissimilar materials, again loaded by normal forces, influence both the contact area and adhesion but this has a minor effect on the JKRS equation. When a tangential force is applied, depending upon its magnitude and the given situation, the contact interface responds in one of the many different ways- by peeling, by slipping, by maintaining the status quo and under certain special conditions by buckling. Tangential forces smaller than the peeling limit force cause stable normal separation which is controlled by the stress intensity factors of mode I, and the shear modes II and III. Next, the paper considers the contact interactions when the tangential force exceeds the peeling limit and continues to increase until shear fracture is initiated and slipping becomes inevitable. This point marks the limit force of static friction. The fracture characteristics of the shear mode are essentially different from those of the normal mode associated with peeling. Whereas peeling is ideally a reversible process, the process of slipping by shear mode is not. These physical aspects consider the essentially irreversible nature of the slipping process and the wear associated with it. This discussion serves as a basis of a model of an ideal process of frictional slipping. It is characterized by a two parameter model for describing the fracture strength of interfacial films in the initial virgin and in the damaged states. The model rules are set up to define the boundary conditions of shear fracture and the analysis is carried out to describe the transition from static to sliding friction under conditions of partial slip. Some thoughts are recorded to indicate how these rules may be extended to develop models for describing kinetic friction.