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# The Influence of Material Properties and Confinement on the Dynamic Penetration of Alumina by Hard Spheres

[+] Author and Article Information
Z. Wei

Department of Materials, University of California, Santa Barbara, CA 93106

A. G. Evans

Department of Materials, and Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106

V. S. Deshpande

Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106

The time at which maximum penetration occurs is $t=tp≈3 μs$, except for the $σY=1 GPa$ case, when $tp≈5 μs$.

J. Appl. Mech 76(5), 051305 (Jun 15, 2009) (8 pages) doi:10.1115/1.3129765 History: Received April 30, 2008; Revised January 26, 2009; Published June 15, 2009

## Abstract

The ability of a ceramic to resist penetration by projectiles depends, in a coupled manner, on its confinement and its mechanical properties. In order to explore the fundamental inter-relationships, a simulation protocol is required that permits the microstructure and normative properties (hardness and toughness) to be used as input parameters. Potential for attaining this goal has been provided by a recent constitutive model, devised by Deshpande and Evans (DE) [2008, “Inelastic Deformation and Energy Dissipation in Ceramics: A Mechanics-Based Dynamic Constitutive Model,” J. Mech. Phys. Solids, 56, pp. 3077–3100] that incorporates the contributions to the inelastic strain from both plasticity and microcracking. Before implementing the DE model, various comparisons with experimental measurements are required. Previously, the model has been successfully used to predict the quasistatic penetration of alumina by hard spheres. In the present assessment, simulations of the dynamic penetration of confined alumina cylinders are presented as a function of microstructure and properties and compared with literature measurements of the ballistic mass efficiency. It is shown that the model replicates the measured trends with hardness and grain size. Motivated by this comparison, further simulations are used to gain a basic understanding of the respective roles of plasticity and microcracking on penetration and to elucidate the phenomena governing projectile defeat.

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## Figures

Figure 2

Schematic of the alumina cylinder impacted by a hard sphere. The dashed line represents the symmetry axis. (a) The confined target and (b) the unconfined target.

Figure 1

Measured values of the ballistic mass efficiency Em of alumina as a function of (a) the grain size d(13) and (b) Vickers hardness (15). Em is defined in the insets with Tc the thickness of the ceramic layer, PR the residual penetration into RHA, and Pref the penetration of the projectile into a reference RHA block without the ceramic front plate. Here ρc and ρm are the densities of the ceramic and RHA, respectively. σY=4 GPa.

Figure 3

The distribution of (a) damage D and (b) plastic strain εepl in the confined ceramic target with reference properties at selected times t after the impact of the sphere traveling at vo=1000 m s−1. The contours in (a) are shaded so as to only illustrate the fully damaged (D=1) and undamaged (D=D0) regions.

Figure 4

The variation of the normalized maximum penetration δ/Dp of the d=3 μm confined ceramic target as a function of the normalized inverse yield strength σf/σY. Results are shown for three selected values of the normalized kinetic energy Ω corresponding to impact velocities vo=1000, 500, and 100 m s−1. For comparison purposes, the corresponding results with damage inhibited are also included and labeled “plasticity-only.”

Figure 5

Predictions of the normalized maximum penetration of the projectile (δ/Dp) as a function of the normalized grain size d/Dp for three selected values of the normalized kinetic energy Ω corresponding to impact velocities vo=1000, 500, and 100 m s−1. The results pertain to the confined ceramic target with σY=4 GPa.

Figure 6

Distributions of damage at maximum penetration in the confined ceramic targets with grain sizes (a) d=3 μm and (b) d=20 μm impacted at vo=1000 m s−1. The ceramic yield strength is taken as σY=4 GPa. The contours are shaded so as to only illustrate the fully damaged (D=1) and undamaged (D=D0) regions.

Figure 7

The distribution of (a) damage D and (b) plastic strain εepl in the confined ceramic targets impacted by a hard sphere traveling at vo=1000 m s−1. The distributions are shown at the instant of maximum penetration, tp, for the d=3 μm ceramic with yield strengths in the range 1 GPa≤σY≤20 GPa. The contours in (a) are shaded so as to only illustrate the fully damaged (D=1) and undamaged (D=D0) regions.

Figure 8

The variation of the normalized final velocity of the impacting sphere −vr/vo with the normalized inverse yield strength σf/σY. The numerical results are for the d=3 μm confined ceramic target and three selected values of the normalized kinetic energy Ω corresponding to impact velocities vo=1000, 500, and 100 m s−1. By convention a positive velocity is in the direction of the impact velocity of the projectile.

Figure 9

(a) The temporal variations of the energy dissipations, strain energy, and kinetic energy of the alumina cylinder impacted by a sphere traveling at vo=1000 m s−1. The alumina has a grain size d=3 μm and yield strength σY=4 GPa. (b) The normalized final plastic and fracture dissipations in the d=3 μm confined ceramic target as a function of the normalized inverse yield strength σf/σY. The dissipations are normalized by the initial kinetic energy of the projectile and the results are shown for two selected values of the normalized kinetic energy Ω corresponding to impact velocities vo=1000 and 100 m s−1.

Figure 10

The temporal variation of the normalized displacement u/Dp of the hard sphere impacting the unconfined ceramic target at vo=1000 m s−1. The ceramic has a yield strength σY=4 GPa and results are shown for grain sizes d=3 and 20 μm.

Figure 11

Distributions of damage at two selected times in the unconfined ceramic targets with grain sizes ((a) and (b)) d=3 μm and ((c) and (b)) d=20 μm impacted at vo=1000 m s−1. The ceramic yield strength is taken as σY=4 GPa. The contours are shaded so as to only illustrate the fully damaged (D=1) and undamaged (D=D0) regions.

Figure 12

A sketch of a microcracked solid containing a distribution of wing cracks. The insets show an isolated crack with the wedging force Fw acting at the midpoint and the matrix stress σ3i that determines the interaction of adjacent cracks.

Figure 13

Predictions of the trend in von Mises stress with effective strain for the (a) d=3 μm and (b) d=20 μm alumina. Results are shown for selected stress triaxialities λ for an applied strain rate ε̇e=100 s−1 and yield strength.

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