Abstract
A local, elastic deformation model is combined with a dynamic simulation to investigate nanoscale slip between a rigid, curved pin and an elastic slab, and its influence on static and kinetic friction. The elastic deformation model utilizes a novel multiscale grid based on a binary hierarchy. To maximize accuracy, bi-quadratic functions are introduced to interpolate the stresses on the boundaries of the nodal elements. The onset of slip is based on a maximum allowable nodal shear stress to nodal pressure ratio. A nanoscale friction function is developed by translating the pin quasistatically across the slab. The effect of the nanoscale friction profile on a dynamic system is investigated by integrating the equations of motions governing the pin as it is pulled by a stage via a coupling spring. A direct connection is found between the nanoscale slip characteristics and macroscopically observed static and kinetic coefficients of friction.
Highlights
Friction has been investigated for many years and early published work on the subject includes that of Amontons (Amontons, 1699), and Coulomb (Coulomb, 1785)
Amontons was probably the first to formally state the laws of friction. The first of these states that the friction force is proportional to the normal load, while the second asserts that the friction force is independent of the apparent area of contact
Despite these relationships being referred to as “laws”, it is recognized that they are only approximately held. It is found for a given material pair, that the ratio of friction force to normal load remains nearly constant over a wide range of load, apparent contact area and sliding speed, leading to the concept of assigning a coefficient of friction (COF) to an interface of given material type
Summary
Friction has been investigated for many years and early published work on the subject includes that of Amontons (Amontons, 1699), and Coulomb (Coulomb, 1785). Despite these relationships being referred to as “laws”, it is recognized that they are only approximately held It is found for a given material pair, that the ratio of friction force to normal load remains nearly constant over a wide range of load, apparent contact area and sliding speed, leading to the concept of assigning a coefficient of friction (COF) to an interface of given material type. The totality of slips from the first slip until the re-establishment of the condition whereby no blocks experience a friction force above the static friction limit is considered an “avalanche” or an “earthquake” Despite its simplicity, this and similar models have enjoyed success in capturing important experimentally-observed phenomena, such as the Gutenberg-Richter law (Gutenberg and Richter, 1955), which relates the energy released in an avalanche of slips to the frequency of occurrence. The force-displacement curve, in turn, is used with a spring-massdamper system to simulate macroscopic observations of static and kinetic friction
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