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Terminal Ballistics and Impact Physics

Influence of Length Scale on the Transition From Interface Defeat to Penetration in Unconfined Ceramic Targets

[+] Author and Article Information
Patrik Lundberg

e-mail: patrik.lundberg@foi.se

Olof Andersson

FOI,
Swedish Defence Research Agency,
SE-164 90 Stockholm, Sweden

Manuscript received June 29, 2012; final manuscript received December 2, 2012; accepted manuscript posted January 9, 2013; published online April 19, 2013. Assoc. Editor: Bo S. G. Janzon.

J. Appl. Mech 80(3), 031804 (Apr 19, 2013) (9 pages) Paper No: JAM-12-1282; doi: 10.1115/1.4023345 History: Received June 29, 2012; Revised December 02, 2012; Accepted January 09, 2013

One observation from interface defeat experiments with thick ceramic targets is that confinement and prestress becomes less important if the test scale is reduced. A small unconfined target can show similar transition velocity as a large and heavily confined target. A possible explanation for this behavior is that the transition velocity depends on the formation and growth of macro cracks. Since the crack resistance increases with decreasing length scale, the extension of a crack in a small-scale target will need a stronger stress field, viz., a higher impact velocity, in order to propagate. An analytical model for the relation between projectile load, corresponding stress field, and the propagation of a cone-shaped crack under a state of interface defeat has been formulated. It is based on the assumption that the transition from interface defeat to penetration is controlled by the growth of the cone crack to a critical length. The model is compared to experimentally determined transition velocities for ceramic targets in different sizes, representing a linear scale factor of ten. The model shows that the projectile pressure at transition is proportional to one over the square root of the length scale. The experiments with small targets follow this relation as long as the projectile pressure at transition exceeds the bound of tensile failure of the ceramic. For larger targets, the transition will become independent of length scale and only depend on the tensile strength of the ceramic material. Both the experiments and the model indicate that scaling of interface defeat needs to be done with caution and that experimental data from one length scale needs to be examined carefully before extrapolating to another.

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Figures

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Fig. 1

Projectile shape (solid line), axisymmetric pressure of projectile (dotted line), and crack trajectory in target (gray) during a state of interface defeat

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Fig. 2

Illustration of the relation between the principal stress σ¯1 (solid line) and the critical stress σ¯c (dotted and dashed line) in Eq. (13) versus the crack length r¯ for two different levels of projectile pressure. (i) p0 < p0* (dotted line): the crack will stop before passing the smallest double root r¯c1 = r¯c2 of Eq. (13). (ii) p0 = p0* (dashed line): the crack is determined by the double root close to the distinct minimum of the principal stress and a constant root r¯c, where the crack will stop. There are also larger single root solutions for a projectile pressure p0 = p0*, which satisfies Eq. (11).

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Fig. 3

Experimental setup in reverse mode: diameter 1 mm projectile mounted in Divinycell fixture and diameter 10 mm SiC-B cylinder mounted in a Lexan sabot

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Fig. 4

Dimensions of ceramic cylinders and copper covers used. Dimensions are in mm.

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Fig. 5

X-ray pictures of Y925 projectile (a =  0.25 mm) and SiC-B target at two different times after impact. (a) Impact velocity v0 =  1445 m/s, slightly below transition. (b) Impact velocity v0 =  1501 m/s, slightly above transition. The transition velocity is v0* =  1470 ± 25 m/s.

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Fig. 6

X-ray pictures of Y925 projectile (a = 0.5 mm) and SiC-B target at two different times after impact. (a) Impact velocity v0 = 1244 m/s, slightly below transition. (b) Impact velocity v0 = 1275 m/s, slightly above transition. The transition velocity is v0* = 1260 ± 16 m/s.

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Fig. 7

X-ray pictures of Y925 projectile (a = 1.0 mm) and SiC-B target at two different times after impact. (a) Impact velocity v0 = 1004 m/s, slightly below transition. (b) Impact velocity v0 = 1051 m/s, slightly above transition. The transition velocity is v0* = 1028 ± 23 m/s.

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Fig. 8

X-ray pictures of Y925 projectile (a =  2.5 mm) and SiC-B target, impact velocity v0 =  1148 m/s. In this test, a short period of interface defeat occurred before the penetration started.

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Fig. 9

(a) Position of maximum radial stress on target surface r¯i and (b) corresponding radial surface stress σ¯rr at the point r¯i versus Poisson's ratio ν

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Fig. 10

(a) Crack path z¯, (b) crack length c¯, and (c) principal tensile stress σ¯1 versus radial crack extension r¯

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Fig. 11

(a) Calculated principal tensile stress σ¯1 (solid line) and critical stress σ¯c (dashed line) along the crack for a projectile pressure p0 = p0*. The arrows indicate the point where the crack will stop, i.e., the critical crack length r¯c. Log-scale is used for the x-axis in order to highlight the region close to r¯ = 2. (b) The critical crack length r¯c versus length scale represented by projectile radius a.

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Fig. 12

(a) Transition velocity v0* and (b) estimated projectile pressure at transition p0* versus length scale represented by projectile radius a. Solid line corresponds to Eq. (14) and filled symbols to the SiC-B targets. Error bars indicate maximum and minimum values for projectile velocity and projectile pressure, respectively. Dashed lines correspond to the three bounds: tensile failure (TF), incipient plastic yield (IY), and full plastic yield (FY).

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