Fracture mechanics determine the lengths of interface ruptures that mediate frictional motion

Abstract

The transition from static to sliding friction is mediated by rapid interfacial ruptures 1-5 propagating through the solid contacts forming a frictional interface 6 . While propagating, these ruptures correspond to true shear cracks 7 . Frictional sliding is initiated only when a rupture traverses the entire interface 1 ; however, arrested ruptures can occur at applied shears far below the transition to frictional motion 8-17 . Here we show, by measuring the real contact area and strain fields near rough frictional interfaces, that fracture mechanics quantitatively describe rupture arrest and therefore determine the onset of overall frictional sliding. Our measurements reveal both the local dissipation and the global elastic energy released by the rupture. The balance of these quantities entirely determines rupture lengths, whether finite or system-wide. These results confirm a fracture-mechanics-based paradigm 7,15,18 for describing frictional motion and shed light on the selection 18-21 of an earthquake's magnitude.A frictional interface is formed by the interlocked solid asperities of rough surfaces in contact, whose area is much smaller than the nominal one 6 . Failure of the asperities via rupture fronts is the fundamental mechanism responsible for the transition from static to sliding frictional motion 1,4 . Ruptures can propagate well before the onset of global sliding, and then arrest before spanning the entire interface. Rupture arrest can, for example, result from inhomogeneous stress distributions along the interface 8-10 . As no overall motion of the contacting bodies is induced by such events, they are often called precursors to sliding motion. Arrested events are analogous to earthquakes, which are dynamic ruptures of finite extent within pre-existing natural faults; the boundary between contacting tectonic plates 22,23 . Predicting the length of precursory ruptures is, therefore, closely related to the question of what determines the size of an earthquake [18][19][20][21] .Since their initial discovery 8 , a rich variety of models has been dedicated to the dynamics of precursory ruptures in frictional systems. Aimed at reproducing nucleation and arrest, these include minimalistic one-dimensional (1D) models 9 , discrete contacts descriptions 11,13,16 , rate-and-state friction laws 17 and fracture mechanics 12 . These models are able to reproduce the existence of arrested ruptures but they provide no explicit predictions of where and how arrest occurs in real systems. Recent theoretical work 15 explained the available data 8 by explicitly demonstrating how fracture mechanics can be used to predict rupture arrest. Here we describe new experiments that confirm these theoretical predictions and show that this general framework indeed enables us to understand the selection of rupture length for any system geometries and loading conditions.Recent experiments have shown that the strain fields driving ruptures along frictional interfaces are described 7 by the linear elastic fracture mechanics (LEFM; ref. ...

Slippery but Tough: The Rapid Fracture of Lubricated Frictional Interfaces

“…These fronts are true singular shear cracks; the strain fields during their propagation are well-described by Linear Elastic Fracture Mechanics (LEFM) [22]. Frictional rupture arrest is also governed by the same framework [23,24].…”

“…2a. Macroscopic sliding only occurs when a front traverses the entire interface [24][25][26][27]. For steady rupture fronts moving at a velocity c f , ε ij (x, t) = ε ij (x − c f t).…”

“…In dry friction, when contacts are plastically deformed, Γ grows linearly with the normal load [1,24]. Extracting Γ from the rescaling procedure, Fig.…”

“…During each sliding event, an array of 14 strain gages recorded the 3 components of the 2D-strain tensor, ε ij , 3.5 mm above the interface, each at 10 6 samples/s. Corresponding stresses, σ ij , are calculated from ε ij after accounting for the viscoelasticity of PMMA (see [24]). In parallel, the real area of contact, A(x, t), was measured at 1000 x 8 locations at 580000 frames/s, using an optical method based on total internal reflection (see [22]) where incident light only traverses the interface at contacts, and is otherwise reflected.…”

An analytical model of dynamic sliding friction during impact

“…Many studies have investigated the dynamic contact problem from analytical and experimental perspectives7891011 to elucidate influential factors, including the contact force121314151617, contact area18192021, sliding velocity14151722232425, surface roughness18, temperature2627, humidity222428, and interface wear1329. However, these effects are still not fully understood.…”