TY - JOUR

T1 - Comminution of solids caused by kinetic energy of high shear strain rate, with implications for impact, shock, and shale fracturing

AU - Bažant, Zdeněk P.

AU - Caner, Ferhun C.

PY - 2013/11/26

Y1 - 2013/11/26

N2 - Although there exists a vast literature on the dynamic comminution or fragmentation of rocks, concrete, metals, and ceramics, none of the known models suffices for macroscopic dynamic finite element analysis. This paper outlines the basic idea of themacroscopic model. Unlike static fracture, in which the driving force is the release of strain energy, here the essential idea is that the driving force of comminution under high-rate compression is the release of the local kinetic energy of shear strain rate. The density of this energy at strain rates <1,000/s is found to exceed themaximum 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 stress) to the -1/3 power of this rate. A dimensionless indicator of the comminution intensity is formulated. 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.

AB - Although there exists a vast literature on the dynamic comminution or fragmentation of rocks, concrete, metals, and ceramics, none of the known models suffices for macroscopic dynamic finite element analysis. This paper outlines the basic idea of themacroscopic model. Unlike static fracture, in which the driving force is the release of strain energy, here the essential idea is that the driving force of comminution under high-rate compression is the release of the local kinetic energy of shear strain rate. The density of this energy at strain rates <1,000/s is found to exceed themaximum 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 stress) to the -1/3 power of this rate. A dimensionless indicator of the comminution intensity is formulated. 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.

KW - Dimensional analysis

KW - Dynamic fracture

KW - Fracture mechanics

KW - Shale gas

UR - http://www.scopus.com/inward/record.url?scp=84888390825&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84888390825&partnerID=8YFLogxK

U2 - 10.1073/pnas.1318739110

DO - 10.1073/pnas.1318739110

M3 - Article

C2 - 24218624

AN - SCOPUS:84888390825

VL - 110

SP - 19291

EP - 19294

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

IS - 48

ER -