Dynamic fields at the tip of sub-Rayleigh and supershear frictional rupture fronts

Abstract

The onset of frictional motion at the interface between two distinct bodies in contact is characterized by the propagation of dynamic rupture fronts. We combine friction experiments and numerical simulations to study the properties of these frictional rupture fronts. We extend previous analysis of slow and sub-Rayleigh rupture fronts and show that strain fields and the evolution of real contact area in the tip vicinity of supershear ruptures are well described by analytical fracture-mechanics solutions. Fracture-mechanics theory further allows us to determine long sought-after interface properties, such as local fracture energy and frictional peak strength. Both properties are observed to be roughly independent of rupture speed and mode of propagation. However, our study also reveals discrepancies between measurements and analytical solutions that appear as the rupture speed approaches the longitudinal wave speed. Further comparison with dynamic simulations illustrates that, in the supershear propagation regime, transient and geometrical (finite sample thickness) effects cause smaller near-tip strain amplitudes than expected from the fracturemechanics theory. By showing good quantitative agreement between experiments, simulations and theory over the entire range of possible rupture speeds, we demonstrate that frictional rupture fronts are classic dynamic cracks despite residual friction.

Supershear Frictional Ruptures Along Bimaterial Interfaces

“…Beyond , the exponent q changes dramatically with C f (Figure 9). This behavior is qualitatively similar to the characteristic form of supershear ruptures within homogeneous interfaces (Broberg, 1989; Svetlizky et al., 2020), although predicted values of q are, quantitatively, quite different. Dynamically reduced contact area only occurs at the tips of negatively propagating supershear ruptures (Figure 8).…”

“…We note that the values of the wave speeds may shift slightly as a result of the finite width of our experimental samples. Recent studies of supershear ruptures within homogeneous interfaces (Svetlizky et al, 2020) have indeed demonstrated that effects due to finite sample thickness can increase longitudinal wave speeds by 3-4%. This shift toward higher velocities is consistent with the ∼4% shift of the experimentally observed supershear velocities above predicted values.…”

“…They had, for many years, existed only in theory (Albertini & Kammer, 2017; Andrews, 1976; Broberg, 1994, 1999; Dunham & Archuleta, 2004; Liu & Lapusta, 2008; Liu et al., 2014; Mello et al., 2010). This situation changed dramatically over the past two decades (Ben‐David et al., 2010; Kammer et al., 2018; Mello et al., 2016; Rosakis et al., 1999, 2007; Rubinstein et al., 2004; Svetlizky et al., 2020), as supershear ruptures have been conclusively observed experimentally, once such measurements became technically possible. Supershear ruptures will occur when the elastic energy stored in the stressed material is sufficiently high, prior to the rupture onset (Ben‐David et al., 2010; Kammer et al., 2018; Rosakis et al., 2007; Svetlizky et al., 2016; Wang et al., 1998; Xia et al., 2004).…”

Stochastic Properties of Static Friction

“…While proportionality of friction to normal load is mostly valid, the friction coefficient is geometry-dependent and thus varies for different experimental setups with the same material pair (Ben-David and Fineberg, 2011). The underlying cause for this observation is the mechanism governing the onset of frictional sliding, which has been shown to be a fracture-like phenomenon (Svetlizky and Fineberg, 2014;Svetlizky et al, 2020;Rubino et al, 2017). The geometry and deformability of the solids lead to a non-uniform stress state along the interface.…”

Effective toughness of heterogeneous materials with rate-dependent fracture energy

“…We study the amplitude of the speed jumps as the crack crosses the interface between regions of different toughness and show that it stems from rate-dependency of fracture energy in both phases in addition to inertia of the medium. Rate-dependent effects -features that result from the non-equilibrium nature of fracture problems and that are generally neglected [17,18] -however, significantly affect the effective toughness of periodic heterogeneous materials. Overall, our experimental observations show that as soon as non-smooth material heterogeneities are concerned, the description of fracture as an equilibrium phenomenon is too limited, and rate dependency must be taken into account.…”