Transition from static to kinetic friction: insights from a 2D model.

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 microslip 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 buildup due to both elastic loading and microslip-related relaxations depends 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 nontrivial scaling parameter.

Fracture patterns generated by diffusion controlled volume changing reactions.

A simple two-dimensional model was developed for the growth of fractures in a chemically decomposing solid. Simulations were carried out under rapid chemical decomposition conditions for which the kinetics of fracture growth is controlled by diffusion of the volatile reaction product or the kinetics of evaporation. The growth of the fracture pattern is self-sustaining due to the volume reduction associated with the decomposition process. Consistent with the theoretical analysis of Yakobson [Phys. Rev. Lett. 67, 1590 (1991)10.1103/PhysRevLett.67.1590], the fracture front propagates with a constant velocity v approximately=k2/3(Dl0)1/3 under evaporation controlled conditions and v approximately=D/l0 under diffusion controlled conditions, where k is the evaporation rate constant, D is the diffusion constant for the volatile reaction product in the solid, and l0 is the critical stable crack length. Under diffusion controlled conditions, the front width w scales as w approximately=(kl0/)D.

Accelerated hydration of the Earth's deep crust induced by stress perturbations.

The metamorphic cycle associated with the formation of mountain belts produces a lower crust containing little or no free fluid. The introduction of external fluids to dry and impermeable volumes of the Earth's crust is thus a prerequisite for the retrogressive metamorphism later observed in such regimes. Such metamorphism can cause significant changes in the crust's physical properties, including its density, rheology and elastic properties. On a large scale, the introduction of fluids requires the presence of high-permeability channels, such as faults or fractures, which are the result of external tectonic stresses. But extensive interaction between externally derived fluids and the fractured rock requires efficient mass transport away from the initial fractures into the rock itself, and this transport often occurs over distances much longer than expected from grain-boundary diffusion. Here we present both field observations and a simple network model that demonstrate how the transport of fluids into initially dry rock can be accelerated by perturbations in the local stress field caused by reactions with fluids. We also show that the morphology of reaction fronts separating 'dry' from 'wet' rocks depends on the anisotropy of the external stress field.