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.

References

References
1.
Hauver
,
G. E.
,
Netherwood
,
P. H.
,
Benck
,
R. F.
, and
Kecskes
,
L. J.
,
1993
, “
Ballistic Performance of Ceramic Targets
,”
Army Symposium on Solid Mechanics
, Plymouth, MA, August 17–19.
2.
Hauver
,
G. E.
,
Netherwood
,
P. H.
,
Benck
R. F.
, and
Kecskes
,
L. J.
,
1994
, “
Enhanced Ballistic Performance of Ceramic Targets
,”
19th Army Science Conference
, Orlando, FL, June 20–24.
3.
Rapacki
,
E. J.
,
Hauver
,
G. E.
,
Netherwood
,
P. H.
, and
Benck
,
R. F.
,
1996
, “
Ceramics for Armours—A Material System Perspective
,”
7th Annual TARDEC Ground Vehicle Survivability Symposium
, Monterey, CA, March 26—28.
4.
Lundberg
,
P.
,
Renström
,
R.
, and
Lundberg
,
B.
,
2000
, “
Impact of Metallic Projectiles on Ceramic Targets: Transition Between Interface Defeat and Penetration
,”
Int. J. Impact Eng.
,
24
, pp.
259
275
.10.1016/S0734-743X(99)00152-9
5.
Hauver
,
G. E.
,
Rapacki
,
E. J.
,
Netherwood
,
P. H.
, and
Benck
,
R. F.
,
2005
, “
Interface Defeat of Long Rod Projectiles by Ceramic Armor
,” U.S. Army Research Laboratory Technical Report No. ARL-TR-3590.
6.
Holmquist
,
T. J.
,
Anderson
,
C. E.
, Jr.
, and
Behner
,
T.
,
2005
, “
Design, Analysis and Testing of an Unconfined Ceramic Target to Induce Dwell
,”
22nd International Symposium on Ballistics
, Vancouver, Canada, November 14–18, pp.
860
868
.
7.
Lundberg
,
P.
, and
Lundberg
,
B.
,
2005
, “
Transition Between Interface Defeat and Penetration for Tungsten Projectiles and Four Silicon Carbide Materials
,”
Int. J. Impact Eng.
,
31
, pp.
781
792
.10.1016/j.ijimpeng.2004.06.003
8.
Anderson
,
O.
,
Lundberg
,
P.
, and
Renström
,
R.
,
2007
, “
Influence of Confinement on the Transition Velocity of Silicon Carbide
,”
Proc. 23rd International Symposium on Ballistics
, Tarragona, Spain, April 16–20, Vol.
2
, pp.
1273
1280
.
9.
Behner
,
T.
,
Anderson
,
C. E.
, Jr.
,
Holmquist
,
T. J.
,
Wickert
,
M.
, and
Templeton
,
D. W.
,
2008
, “
Interface Defeat for Unconfined SiC Ceramics
,”
Proc. 24th International Symposium on Ballistics
, New Orleans, LA, September 22–26, Vol.
1
, pp.
35
42
.
10.
Anderson
,
C. E.
, Jr.
,
Behner
,
T.
,
Orphal
,
D. L.
,
Nicholls
,
A. E.
,
Holmquist
,
T. J.
, and
Wickert
,
M.
,
2008
, “
Long Rod Penetration Into Intact and Pre-damaged SiC Ceramic
,”
Proc. 24th International Symposium on Ballistics
, New Orleans, LA, September 22–26, Vol.
2
, pp.
822
829
.
11.
Anderson
,
C. E.
, Jr.
,
Behner
,
T.
,
Holmquist
,
T. J.
,
Orphal
,
D. L.
, and
Wickert
M.
,
2009
, “
Dwell, Interface Defeat, and Penetration of Long Rods Impacting Silicon Carbide
,” Southwest Research Institute Technical Report No. 18.12544/008.
12.
LaSalvia
,
J. C.
,
Horwath
,
E. J.
,
Rapacki
,
E. J.
,
Shih
,
C. J.
, and
Meyers
,
M. A.
,
2001
, “
Microstructural and Micromechanical Aspects of Ceramic/Long-Rod Projectiles Interactions: Dwell/Penetration Transitions
,”
Fundamental Issues and Applications of Shock-Wave and High-Strain-Rate Phenomena
,
K. P.
Staudhammer
,
K. P.
Murr
, and
M. A.
Meyers
, eds.,
Elsevier Science
,
New York
, pp.
437
446
.
13.
Renström
,
R.
,
Lundberg
,
P.
, and
Lundberg
,
B.
,
2004
, “
Stationary Contact Between a Cylindrical Metallic Projectile and a Flat Target Under Conditions of Dwell
,”
Int. J. Impact Eng.
,
30
, pp.
1265
1282
.10.1016/j.ijimpeng.2003.09.001
14.
Lundberg
,
P.
,
Renström
,
R.
, and
Lundberg
,
B.
,
2006
, “
Impact of Conical Tungsten Projectiles on Flat Silicon Carbide Targets: Transition From Interface Defeat to Penetration
,”
Int. J. Impact Eng.
,
32
, pp.
1842
1856
.10.1016/j.ijimpeng.2005.04.004
15.
Vogler
,
T. J.
, and
Chhabildas
,
L. C.
,
2006
, “
Strength Behaviour of Materials at High Pressure
,”
Int. J. Impact Eng.
,
33
, pp.
812
825
.10.1016/j.ijimpeng.2006.09.069
16.
Liebowitz
,
H.
,
1968
,
Fracture
, Vol.
II
, Mathematical Fundamentals,
Academic
,
New York
.
17.
Broberg
,
K. B.
,
1971
, “
Crack-Growth Criteria and Non-Linear Fracture Mechanics
,”
J. Mech. Phys. Solids
,
19
, pp.
407
418
.10.1016/0022-5096(71)90008-1
18.
Johnson
,
K. L.
,
1985
,
Contact Mechanics
,
Cambridge University Press
,
Cambridge, England
.
19.
Anderson
,
C. E.
, Jr.
,
Mullin
,
S. A.
,
Piekutowski
,
A. J.
,
Blaylock
,
N. W.
, and
Poormon
,
K. L.
,
1996
, “
Scale Model Experiments With Ceramic Laminated Targets
,”
Int. J. Impact Eng.
,
18
(
1
), pp.
1
22
.10.1016/0734-743X(95)00026-1
20.
Lundberg
,
P.
,
Westerling
,
L.
, and
Lundberg
,
B.
,
1996
, “
Influence of Scale on the Penetration of Tungsten Rods Into Steel-Backed Alumina Targets
,”
Int. J. Impact Eng.
,
18
(
4
), pp.
403
416
.10.1016/0734-743X(95)00049-G
21.
Wereszczak
,
A. A.
,
Johanns
,
K. E.
, and
Jadaan
,
O. M.
,
2009
, “
Hertzian Ring Crack Initiation in Hot-Pressed Silicon Carbides
,”
J. Am. Ceram. Soc.
,
92
(
8
), pp.
1788
1795
.10.1111/j.1551-2916.2009.03146.x
22.
Holmquist
,
T. J.
, and
Johnson
,
G. R.
,
2002
, “
Response of Silicon Carbide to High Velocity Impact
,”
J. Appl. Phys.
,
91
(
9
), pp.
5858
5866
.10.1063/1.1468903
23.
Holmquist
,
T. J.
, and
Johnson
,
G. R.
,
2005
, “
Characterisation and Evaluation of Silicon Carbide for High-Velocity Impact
,”
J. Appl. Phys.
,
97
, pp.
1
12
.10.1063/1.1881798
24.
Skoglund
,
P.
,
2003
, “
Constitutive Modelling of a Tungsten Heavy Metal Alloy
,”
J. Phys. IV
,
110
, pp.
207
212
.10.1051/jp4:20030695
25.
Reich
,
F.
,
1926
, “
Umlenkung eines freien Flüssigkeitstrahles an einer senkrecht zur Strömungsrichtung stehenden ebenen platte
,” Diss. Hannover, (oder VDI-Forsch.-Heft 290).
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