Research Papers

Impact Comminution of Solids Due to Progressive Crack Growth Driven by Kinetic Energy of High-Rate Shear

[+] Author and Article Information
Zdeněk P. Bažant

McCormick Institute Professor and
W.P. Murphy Professor of Civil Engineering
and Materials Science
Northwestern University,
2145 Sheridan Road,
Evanston, IL 60208
e-mail: z-bazant@northwestern.edu

Yewang Su

Research Assistant Professor
Department of Civil and
Environmental Engineering,
Northwestern University,
Evanston, IL 60208
State Key Laboratory of Nonlinear Mechanics,
Institute of Mechanics,
Chinese Academy of Sciences,
Beijing 100190, China
e-mail: yewangsu@imech.ac.cn

1Corresponding authors.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 20, 2014; final manuscript received January 15, 2015; published online February 11, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(3), 031007 (Mar 01, 2015) (5 pages) Paper No: JAM-14-1593; doi: 10.1115/1.4029636 History: Received December 20, 2014; Revised January 15, 2015; Online February 11, 2015

A new theory, inspired by analogy with turbulence, was recently proposed to model the apparent dynamic overstress due to the energy that is dissipated by material comminution during penetration of missiles into concrete walls. The high-rate interface fracture comminuting the material to small particles was considered to be driven by the release of kinetic energy of high-rate shear of the forming particles, and the corresponding energy dissipation rate was characterized in the damage constitutive law by additional viscosity. However, in spite of greatly improved predictions for missile impact and penetration, the calculation of viscosity involved two simplifications—one crude simplification in the calculation of viscosity from the shear strain rate, and another debatable simplification in treating the comminution as an instantaneous event, as in the classical rate-independent fracture mechanics. Presented is a refined theory in which both simplifications are avoided without making the theory significantly more complicated. The interface fracture is considered to be progressive and advance according to Evans' power law extended to the fast growth of interface crack area. The growth rate of interface cracks naturally leads to an additional viscosity, which allows close matching of the published test data. In combination with the microplane damage constitutive model M7 for concrete, the refined theory gives a close match of the exit velocities of missiles penetrating concrete walls of different thicknesses and of the penetration depths of missiles of different velocities into a massive block.

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Grahic Jump Location
Fig. 1

Schematic illustration of material comminution into prismatic hexagonal particles: (a) undeformed state, (b) shearing regime, and (c) comminuted regime

Grahic Jump Location
Fig. 2

Comparison of the exit velocity predicted by two methods (M7 with and without implementation of comminution effect) with the experimental data for missile perforation of concrete walls (the thicknesses of impacted walls range 127–280 mm)

Grahic Jump Location
Fig. 3

Comparison of the penetration depth predicted by two methods (M7 with and without implementation of comminution effect) and the experimental data (the entry velocities of the missiles range from 277 m/s to 800 m/s)



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