Emergence of Cracklike Behavior of Frictional Rupture: The Origin of Stress Drops

Abstract

The failure of frictional interfaces -the process of frictional rupture -is widely assumed to feature crack-like properties, with far-reaching implications for various disciplines, ranging from engineering tribology to earthquake physics. Yet, how the effective crack-like behavior emerges from basic physics and what its range of validity is are not understood. Here we show that for rapid rupture a finite and well-defined stress drop, which is a necessary condition for the existence of a crack-like behavior, is directly related to wave radiation from the frictional interface to the bulks surrounding it (the so-called radiation damping effect) and to long-range bulk elastodynamics, and not exclusively to interfacial physics. Furthermore, we show that the emergence of a stress drop is a finite time effect, mainly limited by the wave travel time in finite systems. The results for rapid rupture are supplemented by predictions for slow rupture. All of the theoretical predictions are supported by available experimental data and by extensive computations. They offer a comprehensive and basic understanding of why, how and to what extent frictional rupture might be viewed as an ordinary fracture process. I. BACKGROUND AND MOTIVATIONRapid slip along interfaces separating bodies in frictional contact is mediated by the spatiotemporal dynamics of frictional rupture [1,2]. Frictional rupture is a fundamental process of prime importance for a broad range of physical systems, e.g. it is responsible for squealing in car brake pads [3], for bowing on a violin string [4], and for earthquakes along geological faults [5][6][7], to name just a few well-known examples. The essence of frictional rupture propagation is that a state of relatively high slip rate (the rate of interfacial shear displacement discontinuity) behind the rupture edge propagates into a low/vanishing slip rate state ahead of it, cf. Fig. 1. As such, frictional rupture appears to be essentially similar to ordinary tensile (opening) cracks, where a finite tensile displacement discontinuity (broken material) state behind the crack edge propagates into a zero tensile displacement discontinuity (intact material) state ahead of it [8].There is, however, an important fundamental difference between frictional rupture and ordinary tensile cracks that manifests itself in the stress states associated with these two processes. A tensile crack is composed of surfaces that cannot support stress, so the stress behind its edge vanishes. Consequently, tensile crack propagation is a process in which far-field driving stresses that characterize the material state far ahead of the crack edge are eliminated altogether behind it. The stress drop that accompanies tensile crack propagation has dramatic implications. Most notably, the loss of stress bearing capac- * eran.bouchbinder@weizmann.ac.il † jean-francois.molinari@epfl.ch ity along the crack surfaces is compensated by large concentration of deformation and stress near the crack edge, oftentimes in a way that mimics a mathematical s...

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

“…This observation enables us to map frictional rupture fronts to cracks by employing the linearity of the governing equations and subtracting τ r . Interestingly, however, recent work [55,56] demonstrated the emergence of crack-like behavior of frictional rupture fronts for more realistic rate dependent friction. The simplicity of the adopted model (slip-weakening) enables us to highlight the importance of non-steady propagation (section 3.2) and geometrical effects (section 3.3) present during propagation of supershear rupture fronts.…”

Spatiotemporal Dynamics of Frictional Systems: The Interplay of Interfacial Friction and Bulk Elasticity

“…(3)), is finite for transient, out of steady-state rapid rupture (due to both the radiation-damping term and the long-ranged interaction term s(x, t) in Eq. (13)), while it vanishes under steady-state conditions in finite-H systems [106]. These findings demonstrate that even a quantity such as the residual stress τ r , which is traditionally regarded as a property of interfacial friction law [109,110], is in fact strongly affected by bulk elasticity and bulk dynamics.…”

“…(c) A non-steady 2D infinite-H rapid rupture front generated through a spectral boundary integral method calculation (adapted from Fig. 3 in [106]). The curve is truncated in the vertical axis for visual clarify.…”

“…Put differently, the former features a vanishing stress drop ∆τ 0−r ≡ τ 0 − τ r → 0 (∆τ 0−r should be distinguished from the dynamic stress drop ∆τ p−r discussed above), while the latter features a finite stress drop ∆τ 0−r . The existence of stress drops has important implications for frictional rupture [3,[106][107][108]. The origin of this qualitative difference is that F τ of Eq.…”

Finite element modeling of dynamic frictional rupture with rate and state friction

“…using a fracture-like energy balance. [25,26]. An essential condition is the existence of a well-defined drop of frictional stress behind the rupture front, for which the rate-dependent aspects of friction are crucial..…”