Abstract
Tribology is concerned with the influence of mechanically applied forces on interfacial phenomena that accompany and control sliding. A wide range of models has been developed to describe these phenomena, which include frictional dissipation, wear and tribochemical reactions. This paper shows that these apparently disparate models are based on the same fundamental concept that an externally applied force accelerates the rate of thermal transition of atoms or molecules across energy barriers present in solid and liquid materials, thereby promoting flow, slip or bond cleavage. Such “stress-assisted” effects and the associated thermal activation concepts were developed independently and in different forms by Prandtl (Z Angew Math Mech 8:85, 1928) and Eyring (J Chem Phys 4(4):283–291, 1936). These two works have underpinned subsequent theories of dry friction, boundary lubrication, EHD rheology, tribochemistry and nanoscale wear modelling. This paper first reviews the historical development of the concepts, focussing in particular on the models of Prandtl and Eyring and how they have subsequently been used and adapted by others. The two approaches are then compared and contrasted, noting that although superficially similar, they contain quite different assumptions and constraints. First, the Prandtl model assumes that the force is exerted through a compliant spring, while constant force sliding is assumed by Eyring. Second, different approximations are made in the two models to describe the change in energy barrier with external force. Prandtl explores the asymptotic behaviour of the energy barrier as the applied force become sufficiently high to reduce it to zero, while Eyring assumes that the energy barrier is reduced by an amount equal to the external work carried out on the system. The theoretical underpinnings of these differences are discussed along with the implications of compliant coupling and constant force sliding on the velocity and temperature dependence of the friction forces for the two models.
Highlights
This paper shows that these apparently disparate models are based on the same fundamental concept that an externally applied force accelerates the rate of thermal transition of atoms or molecules across energy barriers present in solid and liquid materials, thereby promoting flow, slip or bond cleavage
Tribology is concerned with the influence of mechanically applied forces on interfacial phenomena that accompany and control sliding, including frictional dissipation, wear and tribochemical reactions
Much of physics and chemistry is concerned with the way in which the equilibrium state is modified by the application of some external potential, for example an electric field, pressure or change in chemical potential
Summary
Tribology is concerned with the influence of mechanically applied forces on interfacial phenomena that accompany and control sliding, including frictional dissipation, wear and tribochemical reactions. A wide range of models has been developed to describe these phenomena. They all aim to understand the way in which an external force affects the state of a solid or liquid at a sliding interface, so that the underlying principles of these models are essentially identical, often framed in somewhat different language. In the case of relatively small perturbations, the change is completely reversible; removal of the external potential restores the initial, unperturbed state and can be modelled by non-equilibrium thermodynamics [4] or perturbation theory [5]. In case of external forces acting on solid materials, the mechanical response is expressed by the elastic moduli
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