Comminution of concrete due to kinetic energy of high shear strain rate

This paper outlines the basic idea of a macroscopic model on the dynamic comminution or fragmentation of rocks, concrete, metals, and ceramics. The key idea is that the driving force of comminution under high-rate shear and compression with shear is the release of the local kinetic energy of shear strain rate. The spatial derivative of the energy dissipated by comminution gives a force resisting the penetration, which is superposed on the nodal forces obtained from the static constitutive model in a finite element program. The present theory is inspired partly by Grady's model for comminution due to explosion inside a hollow sphere, and partly by analogy with turbulence. In high velocity turbulent flow, the energy dissipation rate gets enhanced by the formation of micro-vortices (eddies) which dissipate energy by viscous shear stress. Similarly, here it is assumed that the energy dissipation at fast deformation of a confined solid gets enhanced by the release of kinetic energy of the motion associated with a highrate shear strain of particles. For simplicity, the shape of these particles in the plane of maximum shear rate is considered to be regular space-filling hexagons. The particle sizes are considered to be distributed according to the Schuhmann power law, but the formulation for any other suitable distribution can easily be obtained by replacing the Schuhmann distribution by the desired distribution. The condition that the rate of release of the local kinetic energy must be equal to the interface fracture energy yields a relation between the particle size, the shear strain rate, the fracture energy and the mass density. The density of this energy at strain rates >1,000/s is found to exceed the maximum possible strain energy density by orders of magnitude, making the strain energy irrelevant. It is shown that particle size is proportional to the -2/3 power of the shear strain rate and the 2/3 power of the interface fracture energy or interface shear stress, and that the comminution process is macroscopically equivalent to an apparent shear viscosity that is proportional (at constant interface friction) to the -1/3 power of this rate. A dimensionless indicator of the comminution intensity is formulated. After comminution, the interface fracture energy takes the role of interface friction, and it is pointed out that if the friction depends on the slip rate, the aforementioned exponents would change. The effect of dynamic comminution can simply be taken into account by introducing the apparent viscosity into the material constitutive model. The theory was 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.