Analysis of Stick-Slip Motion as a Jump Phenomenon

TL;DR

This paper models the stick-slip motion of a soft elastomeric block on a hard surface as a bond rupture phenomenon, providing insights into the transition between sticking and slipping phases through a bond-population balance framework.

Contribution

It introduces a novel bond-population balance model to analyze stick-slip motion, contrasting with traditional rate-and-state models, and validates it with experimental data.

Findings

Stick-slip occurs below a critical velocity.

Major bond rupture causes slip, while bond aging leads to sticking.

The model aligns well with experimental observations.

Abstract

In this work, we analyse the stick-slip motion of a soft elastomeric block on a smooth, hard surface under the application of shear, which is induced by a puller moving at a steady velocity. The frictional stress is generated by make-break of bonds between the pendent chains of the elastomeric block and bonding sites on the hard surface. Relation between velocity and frictional stress has been estimated using the bond-population balance model. Stick-slip motion occurs when the pulling velocity is lower than a critical value. Unlike, the rate-and-state friction model which views the stick-slip motion as a limit cycle, we show that during the stick phase, the sliding surface actually sticks to the hard surface and remains stationary till the shear exerted by puller causes rupture of all bonds between contacting surfaces. The major fraction of the bonds undergo catastrophic rupture so as to cause the sliding surface to slip and attain a significantly higher velocity than the pulling velocity. During the slip phase, the sliding friction is balanced by rapid make-break of weak bonds. As the sliding velocity decreases, the bonds undergo aging and the adhesion stress increases. When the bond adhesion stress exceeds the pulling stress, the contacting surfaces stick together. We have mathematically modeled both the stick and the slip regimes using the bond-population balance model. We have validated the model using the experimental data from the work of Baumberger et al (2002) on sliding of an elastomeric gelatine-gel block on a glass surface.