Transition from Static to Kinetic Friction: Insights from a 2D Model

Abstract

We describe a 2D spring-block model for the transition from static to kinetic friction at an elastic slider/rigid substrate interface obeying a minimalistic friction law (Amontons-Coulomb). By using realistic boundary conditions, a number of previously unexplained experimental results on precursory micro-slip fronts are successfully reproduced. From the analysis of the interfacial stresses, we derive a prediction for the evolution of the precursor length as a function of the applied loads, as well as an approximate relationship between microscopic and macroscopic friction coefficients. We show that the stress build-up due to both elastic loading and micro-slip-related relaxations depend only weakly on the underlying shear crack propagation dynamics. Conversely, crack speed depends strongly on both the instantaneous stresses and the friction coefficients, through a non-trivial scaling parameter.Frictional interfaces are important in many areas of science and technology, including seismology [2], biology [3, 4] and nanomechanics [5]. Whereas a satisfactory picture of the steady sliding regime of such interfaces has been developed during the last twenty years [6][7][8], the dynamics of the transition from static to kinetic friction remains elusive. During the last decade, a renewed interest has grown in such transitions, due to experimental studies that directly measured the local dynamics of frictional interfaces [9][10][11][12][13]. They have shown that macroscopic sliding occurs only after shear crack-like micro-slip fronts have spanned the entire contact interface.Experimentally, micro-slip front nucleation, propagation and arrest was shown to be controlled by the instantaneous stress field at the interface. Fronts nucleate preferentially at the trailing edge of the contact area [9,11,[14][15][16][17], an effect explained either by the enhanced shear stress near the loading point in side-driven systems [11,14,16,18] or by a friction-induced pressure asymmetry in top-driven systems [9,19]. Fronts can arise well below the macroscopic static friction threshold and arrest before the whole contact area has ruptured [14][15][16]. The length and number of these precursors depends on the precise way in which shear [14] and normal [16] forces are applied. Moreover, precursors are associated with significant changes in the spatial distribution of the real contact area [14], a quantity related to the local interfacial pressure. Finally, the propagation speed of micro-slip fronts, which covers a wide range [9][10][11]20], correlates with the local shear to normal stress ratio at nucleation [17].Theoretically, some aspects of these observations have been studied using one-dimensional (1D) models. The conditions leading to a large range of front velocities were addressed using a 1D spring-block model with a timedependent friction law [18]. The role of an asymmetric normal loading on the length of precursors was considered using a 1D spring-block model with Amontons-Coulomb (A-C) friction and different normal forces ascribed...

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