Static versus dynamic friction: the role of coherence

Abstract

A simple model for solid friction is analyzed. It is based on tangential springs representing interlocked asperities of the surfaces in contact. Each spring is given a maximal strain according to a probability distribution. At their maximal strain the springs break irreversibly. Initially all springs are assumed to have zero strain, because at static contact local elastic stresses are expected to relax. Relative tangential motion of the two solids leads to a loss of coherence of the initial state: The springs get out of phase due to differences in their sizes. This mechanism alone is shown to lead to a difference between static and dynamic friction forces already. We find that in this case the ratio of the static and dynamic coefficients decreases with increasing relative width of the probability distribution, and has a lower bound of 1 and an upper bound of 2.While the facts that dry solid friction is proportional to the normal load at the contact and does not depend on the apparent contact area were established experimentally at least as early as in the 16th century by Leonardo da Vinci and are now known under the names of Amonton (1699) or Coulomb (1781) [1], it was probably Euler (1750) who first distinguished between static and dynamic friction [2]. This difference has been explained in several, conceptually different ways. The reason was identified as: A collective depinning phenomenon [3], the time strengthening of individual pinning sites [4,5], the shear melting of a lubrication film [6], mobile impurities at the interface [7], or the formation and healing of microcracks [8]. The fact that all these mechanisms lead to the same macroscopic phenomenology raises the question whether they can be classified in terms of more abstract concepts.An attempt in this direction was made by Caroli and Nozières [9], who proposed a model for dry solid friction based on the following physical picture: The surfaces have randomly distributed asperities which get interlocked. These interlocked asperities act as pinning sites resisting tangential motion. Under tangential load they are deformed up to a threshold

Bridging the Gap Between the Atomic-Scale and Macroscopic Modeling of Friction

“…The evolution of the system in the quasi-static limit where inertia effects are neglected shows that, in the long term, the initial distribution approaches a stationary distribution Q s (x) and the total force F becomes independent of X. The final distribution is independent of the initial one (the mathematical proof of this statement for a simplified version of the EQ model was presented in [50]). The statement is valid for any distribution P c (x) except for the singular case of P c (x) = d(x -x s ).…”

Modeling Friction on a Mesoscale: Master Equation for the Earthquakelike Model

“…An elegant mathematical proof of this statement was presented in Ref. [7]. The statement is valid for any distribution P c (x) except for the singular case of P c (x) = δ(x − x s ).…”

A new method for evaluation nominal coefficient of friction and frictional forces in turning and inserts characterization using cutting forces profiles

“…So, according to the research cited on the literature (Farkas et al 2005) and the Eq. (3), the obtained coefficient of dynamic friction shown in Eq.…”

“…The basic idea is to use elastically soft solids and apply the external forces in such way that different parts of the contacting interface start to slip at different times during the (tangential) loading process. In contrast to previous work, (Farkas et al, 2005) take explicitly into account that the interlocked asperities are characterized by different threshold lengths with a probability distribution p(l), normalized as shown in Eq. (3):…”