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

Authors
Type
Published Article
Journal
Proceedings of the National Academy of Sciences
0027-8424
Publisher
Proceedings of the National Academy of Sciences
Publication Date
Volume
110
Issue
48
Pages
19291–19294
Identifiers
DOI: 10.1073/pnas.1318739110
PMID: 24218624
Source
Medline
Keywords
  • Dimensional Analysis
  • Dynamic Fracture
  • Fracture Mechanics
  • Shale Gas

Abstract

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 the macroscopic 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 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 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.

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