# Effect of high-rate dynamic comminution on penetration of projectiles of various velocities and impact angles into concrete

- Authors
- Type
- Published Article
- Journal
- International Journal of Fracture
- Publisher
- Springer Netherlands
- Publication Date
- Mar 05, 2019
- Volume
- 216
- Issue
- 2
- Pages
- 211–221
- Identifiers
- DOI: 10.1007/s10704-019-00354-0
- Source
- Springer Nature
- Keywords
- License
- Yellow

## Abstract

The dynamic ‘overstress’, i.e., the apparent increase of strength of concrete at very high strain rates (10–106\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^{6}$$\end{document}/s) experienced in projectile impact and penetration, has recently been explained by a new theory with partial analogy to turbulence. The increase is attributed to comminution of concrete driven by the release of local kinetic energy of the shear strain rate field of forming fragments which, in projectile impact problems, exceeds the strain energy of the fragments by orders of magnitude. This theory gives the particle size distribution and the additional local kinetic energy density, ΔK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta K$$\end{document}, proportional to the deviatoric strain rate square. To match test results, ΔK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta K$$\end{document} must be dissipated during finite element simulations of impact. In previous simulations, ΔK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta K$$\end{document} was, at first, dissipated by an artificial equivalent viscosity (not empirical but predicted by the theory). Later it was found that dissipation by upscaling material tensile strength is equally effective. This theoretically justified upscaling is adopted here since it is more realistic when microplane constitutive model M7 for fracturing damage in concrete is used. All artificial damping is eliminated from the computer program. While previous simulations with the comminution theory were limited to orthogonal impacts, and only the cases of penetration of slabs of various thickness by projectile of one velocity and penetration depths for different velocities, the present study also analyzes further test data on oblique impacts at various impact angles up to 35∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$35^\circ $$\end{document}, and on the exit velocities and penetration depths of projectiles of different velocities. For each test series on one and the same concrete, the material parameters are calibrated on one test and then, using the same parameters, all the other tests are predicted. All the predictions of exit velocities and penetration depths of projectiles, as well as entry and exit craters, are quite accurate.