Fracture and Friction: Stick-Slip Motion

TL;DR

This paper investigates the transition from stick to slip in elastic blocks, modeling crack propagation and pattern formation, and provides a theoretical framework for understanding the critical conditions and internal parameters of slip patterns.

Contribution

It introduces a theoretical model linking fracture mechanics and frictional slip, analyzing steady-state patterns and proposing a soft selection mechanism for pattern parameters.

Findings

Critical shear stress corresponds to Griffith threshold for crack propagation.

Derived equations of motion for slip pulse tips and resticking ends.

Estimated pattern parameters based on driving velocity and phase transition analogy.

Abstract

We discuss the stick-slip motion of an elastic block sliding along a rigid substrate. We argue that for a given external shear stress this system shows a discontinuous nonequilibrium transition from a uniform stick state to uniform sliding at some critical stress which is nothing but the Griffith threshold for crack propagation. An inhomogeneous mode of sliding occurs, when the driving velocity is prescribed instead of the external stress. A transition to homogeneous sliding occurs at a critical velocity, which is related to the critical stress. We solve the elastic problem for a steady-state motion of a periodic stick-slip pattern and derive equations of motion for the tip and resticking end of the slip pulses. In the slip regions we use the linear viscous friction law and do not assume any intrinsic instabilities even at small sliding velocities. We find that, as in many other pattern forming system, the steady-state analysis itself does not select uniquely all the internal parameters of the pattern, especially the primary wavelength. Using some plausible analogy to first order phase transitions we discuss a ``soft'' selection mechanism. This allows to estimate internal parameters such as crack velocities, primary wavelength and relative fraction of the slip phase as function of the driving velocity. The relevance of our results to recent experiments is discussed.