Equation of Motion of Frictional Rupture Fronts


  Ilya Svetlizky [1]  ,  David S. Kammer [2]  ,  Elsa Bayart [1]  ,  Gil Cohen [1]  ,  Jay Fineberg [1]  
[1] The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, Israel
[2] School of Civil and Environmental Engineering, Cornell University, Ithaca, New York 14853, USA

 

A system of two bodies in contact, subject to shear loading, is prone to lose stability and generate frictional slip. The onset of this motion is mediated by dynamically propagating fronts that rupture the discrete contacts forming the frictional interface and separate the sticking and sliding regions. A wide range of rupture front velocities, have been observed. These span from slow ruptures propagating at a small fraction of the Rayleigh wave speed, CR , to ruptures that asymptotically approach CR.

We conduct an experimental study of rupture fronts propagating along the frictional interface, formed by two polymer plates. We perform simultaneous high-speed measurements (at μsec time scale) of the interface real contact area and the strain fields in the region surrounding the propagating rupture. We first demonstrate that the strains surrounding propagating rupture tips are described by classical singular solutions, originally derived to describe rapid brittle shear cracks. We then show that the velocity evolution of these frictional ruptures is determined by the classical equation of motion for cracks, predicted by the brittle fracture theory. Our measurements determine both the energy dissipated by the rupture tip and the energy flux into the dissipation region. Their balance provides a quantitative prediction of the rupture velocity. These observations demonstrate the extensive applicability of dynamic brittle fracture theory to friction.