Fracture and Friction: Stick-Slip Motion

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.

12 pages, 7 figures

References in corpus (5)

• Self healing slip pulses along a gel/glass interface
• Self-healing slip pulses and the friction of gelatin gels
• Stick-slip friction and nucleation dynamics of ultra-thin liquid films
• Frictional shear cracks
• On slip pulses at a sheared frictional viscoelastic/ non deformable interface

Cited by in corpus (12)

• Cracklike Dynamics at the Onset of Frictional Sliding
• Role of friction-induced torque in stick-slip motion
• Unstable slip pulses and earthquake nucleation as a non-equilibrium first-order phase transition
• Velocity-strengthening friction significantly affects interfacial dynamics, strength and dissipation
• The emergence of crack-like behavior of frictional rupture: The origin of stress drops
• Velocity-driven frictional sliding: Coarsening and steady-state pulse trains
• The slow slip of viscous faults
• Theory of unconventional singularities of frictional shear cracks
• Opposite moving detachment waves mediate stick-slip friction at soft interfaces
• Self-healing (solitonic) slip pulses in frictional systems
• The dynamics of unsteady frictional slip pulses
• Fifty years of Schallamach waves: From rubber friction to nanoscale fracture