Department of Mechanics: Seminar: Abstract Bazant 2014

Comminution of solids due to kinetic energy of high-rate shear: Turbulence analogy, impact, shock and shale fracturing

Fragmentation, crushing and pulverization of solids, briefly called comminution, has long been a problem of interest for mining, tunneling, explosions, meteorite impact, missile impact, groundshock, defence against terrorist attack, and various kinds of industrial processes. Recently interest surged in the comminution of gas or oil shale, which can raise permeability by orders of magnitude. Particularly intriguing is an environmentally friendlier alternative to hydraulic fracturing, in which comminution of the shale would be achieved by shock waves generated by explosions or electro-hydraulic pulsed arc in the pipe of a horizontal borehole. In all these problems, the size of particles or their surface-volume ratio, which controls energy dissipation as well as permeability enhancement, is the key parameter to predict. Whereas the comminution in the so-called `Mescall' zones of impacted or shocked solids has theoretically been explained by branching of dynamically propagating cracks, no viable, theoretically well founded, comminution model appears to be available for macroscopic dynamic analysis of structures conducted, e.g., by finite elements. Comminution ignored, simulations of missile penetration through concrete walls grossly overestimate the exit velocities.

This paper presents a model inspired by noting that the local kinetic energy of shear strain rate plays a role analogous to the local kinetic energy of eddies in turbulent flow. In contrast to static fracture, in which the driving force is the release of strain energy, the high-rate comminution under compression is considered to be driven by the release of the local kinetic energy of shear strain rate, whose density is shown to exceed (at strain rates > 1000/s) the maximum possible strain energy density by several orders of magnitude. The new theory predicts the particle size or crack spacing to be proportional to the -2/3 power of the shear strain rate. A dimensionless indicator of the comminution intensity is formulated. The comminution process is shown to be macroscopically equivalent to an apparent shear viscosity proportional to the -1/3 power of the shear strain rate. This viscosity is combined with the latest version M7 of the microplane model for concrete and is shown to lead to correct predictions of missile penetration. Applications to shock loading of gas shale suggest a tantalizing potential of gas extraction with a negligible release of contaminated water to the surface (see Proc. Nat. Academy of Sciences 110, 2013, 19291-19294.)