Abstract

A micromechanical multi-physics model for ceramics has been recalibrated and used to simulate impact experiments with boron carbide in abaqus. The dominant physical mechanisms in boron carbide have been identified and simulated in the framework of an integrated constitutive model that combines crack growth, amorphization, and granular flow. The integrative model is able to accurately reproduce some of the key cracking patterns of Sphere Indentation experiments and Edge On Impact experiments. Based on this integrative model, linear regression has been used to study the sensitivity of sphere indentation model predictions to the input parameters. The sensitivities are connected to physical mechanisms, and trends in model outputs have been intuitively explored. These results help suggest material modifications that might improve material performance, prioritize calibration experiments for materials-by-design iterations, and identify model parameters that require more in-depth understanding.

References

1.
Crouch
,
I.
,
Franks
,
G.
,
Tallon
,
C.
,
Thomas
,
S.
, and
Naebe
,
M.
,
2017
, “7 – Glasses and Ceramics,”
The Science of Armour Materials
,
I. G.
Crouch
, ed.,
Woodhead Publishing
,
Duxford, UK
, pp.
331
393
.
2.
Clemmer
,
J. T.
,
2019
, “
An Improved Computational Constitutive Model for Brittle Materials
,” Ph.D. Thesis, Physics, Johns Hopkins University, Baltimore, MD. https://jscholarship.library.jhu.edu/handle/1774.2/62208
3.
Daux
,
C.
,
Moës
,
N.
,
Dolbow
,
J.
,
Sukumar
,
N.
, and
Belytschko
,
T.
,
2000
, “
Arbitrary Branched and Intersecting Cracks With the Extended Finite Element Method
,”
Int. J. Numer. Methods Eng.
,
48
(
12
), pp.
1741
1760
. https://doi.org/10.1002/1097-0207
4.
Falk
,
M. L.
,
Needleman
,
A.
, and
Rice
,
J. R.
,
2001
, “
A Critical Evaluation of Cohesive Zone Models of Dynamic Fracture
,”
J. Phys. IV France
,
11
(
PR5
), pp.
Pr5–43
Pr5–50
. https://doi.org/10.1051/jp4:2001506
5.
Bažant
,
Z. P.
, and
Oh
,
B.
,
1983
, “
Crack Band Theory for Fracture of Concrete
,”
JMatériaux et Construction
,
16
(
3
), pp.
155
177
. 10.1007/BF02486267
6.
Le
,
J.-L.
, and
Eliáš
,
J.
,
2016
, “
A Probabilistic Crack Band Model for Quasibrittle Fracture
,”
ASME J. Appl. Mech.
,
83
(
5
), p.
051005
. 10.1115/1.4032692
7.
Spatschek
,
R.
,
Brener
,
E.
, and
Karma
,
A.
,
2011
, “
Phase Field Modeling of Crack Propagation
,”
Philos. Mag.
,
91
(
1
), pp.
75
95
. 10.1080/14786431003773015
8.
Hofacker
,
M.
, and
Miehe
,
C.
,
2012
, “
Continuum Phase Field Modeling of Dynamic Fracture: Variational Principles and Staggered FE Implementation
,”
Int. J. Fracture
,
178
(
1–2
), pp.
113
129
. 10.1007/s10704-012-9753-8
9.
Borden
,
M. J.
,
Verhoosel
,
C. V.
,
Scott
,
M. A.
,
Hughes
,
T. J.
, and
Landis
,
C. M.
,
2012
, “
A Phase-Eield Description of Dynamic Brittle Fracture
,”
Comput. Methods Appl. Mech. Eng.
,
217–220
, pp.
77
95
. 10.1016/j.cma.2012.01.008
10.
Schlüter
,
A.
,
Willenbücher
,
A.
,
Kuhn
,
C.
, and
Müller
,
R.
,
2014
, “
Phase Field Approximation of Dynamic Brittle Fracture
,”
Comput. Mech.
,
54
(
5
), pp.
1141
1161
. 10.1007/s00466-014-1045-x
11.
Johnson
,
G. R.
, and
Holmquist
,
T. J.
,
1994
, “
An Improved Computational Constitutive Model for Brittle Materials
,”
AIP. Conf. Proc.
,
309
(
1
), pp.
981
984
. 10.1063/1.46199
12.
Ravichandran
,
G.
, and
Subhash
,
G.
,
1995
, “
A Micromechanical Model for High Strain Rate Behavior of Ceramics
,”
Int. J. Solids. Struct.
,
32
(
17
), pp.
2627
2646
. 10.1016/0020-7683(94)00286-6
13.
Deshpande
,
V.
, and
Evans
,
A.
,
2008
, “
Inelastic Deformation and Energy Dissipation in Ceramics: A Mechanism-Based Constitutive Model
,”
J. Mech. Phys. Solids.
,
56
(
10
), pp.
3077
3100
. 10.1016/j.jmps.2008.05.002
14.
Fernández-Fdz
,
D.
,
Zaera
,
R.
, and
Fernández-Sáez
,
J.
,
2011
, “
A Constitutive Equation for Ceramic Materials Used in Lightweight Armors
,”
Comput. Struct.
,
89
(
23
), pp.
2316
2324
. 10.1016/j.compstruc.2011.08.003
15.
Hogan
,
J. D.
,
Farbaniec
,
L.
,
Daphalapurkar
,
N.
, and
Ramesh
,
K.
,
2016
, “
On Compressive Brittle Fragmentation
,”
J. Am. Ceram. Soc.
,
99
(
6
), pp.
2159
2169
. 10.1111/jace.14171
16.
Mescall
,
J.
, and
Weiss
,
V.
,
1983
,
Material Behavior Under High Stress and Ultrahigh Loading Rates
, Vol.
29
,
Springer
,
New York, United States
. https://www.springer.com/gp/book/9780306414749
17.
Curran
,
D.
,
Seaman
,
L.
,
Cooper
,
T.
, and
Shockey
,
D.
,
1993
, “
Micromechanical Model for Comminution and Granular Flow of Brittle Material Under High Strain Rate Application to Penetration of Ceramic Targets
,”
Int. J. Impact Eng.
,
13
(
1
), pp.
53
83
. 10.1016/0734-743X(93)90108-J
18.
Farbaniec
,
L.
,
Hogan
,
J.
,
Xie
,
K.
,
Shaeffer
,
M.
,
Hemker
,
K.
, and
Ramesh
,
K.
,
2017
, “
Damage Evolution of Hot-Pressed Boron Carbide Under Confined Dynamic Compression
,”
Int. J. Impact Eng.
,
99
, pp.
75
84
. 10.1016/j.ijimpeng.2016.09.008
19.
Bhattacharjee
,
A.
,
Hurley
,
R.
, and
Graham-Brady
,
L.
,
2020
, Predicting High Rate Granular Transition and Fragment Statistics at the Onset of Granular Flow for Brittle Ceramics, Nov. arXiv:2011.08331.
20.
Chen
,
M.
,
McCauley
,
J. W.
, and
Hemker
,
K. J.
,
2003
, “
Shock-Induced Localized Amorphization in Boron Carbide
,”
Science
,
299
(
5612
), pp.
1563
1566
. 10.1126/science.1080819
21.
Huq
,
F.
,
Liu
,
J.
,
Tonge
,
A.
, and
Graham-Brady
,
L.
,
2019
, “
A Micromechanics Based Model to Predict Micro-Crack Coalescence in Brittle Materials Under Dynamic Compression
,”
Eng. Fract. Mech.
,
217
, p.
106515
. 10.1016/j.engfracmech.2019.106515
22.
Shockey
,
D. A.
,
Marchand
,
A.
,
Skaggs
,
S.
,
Cort
,
G.
,
Burkett
,
M.
, and
Parker
,
R.
,
1990
, “
Failure Phenomenology of Confined Ceramic Targets and Impacting Rods
,”
Int. J. Impact Eng.
,
9
(
3
), pp.
263
275
. 10.1016/0734-743X(90)90002-D
23.
Tonge
,
A. L.
, and
Ramesh
,
K.
,
2016
, “
Multi-scale Defect Interactions in High-Rate Brittle Material Failure. Part I: Model Formulation and Application to ALON
,”
J. Mech. Phys. Solids.
,
86
, pp.
117
149
. 10.1016/j.jmps.2015.10.007
24.
Zeng
,
Q.
,
Tonge
,
A. L.
, and
Ramesh
,
K.
,
2019
, “
A Multi-Mechanism Constitutive Model for the Dynamic Failure of Quasi-Brittle Materials. Part II: Integrative Model
,”
J. Mech. Phys. Solids.
,
131
, pp.
20
42
. 10.1016/j.jmps.2019.06.015
25.
Cil
,
M. B.
,
Zeng
,
Q.
,
Hurley
,
R. C.
, and
Graham-Brady
,
L.
,
2020
, “
An Integrative Model for the Dynamic Behavior of Brittle Materials Based on Microcracking and Breakage Mechanics
,”
J. Dyn. Behav. Mater.
,
6
(
4
), pp.
472
88
. 10.1007/s40870-020-00251-x
26.
Leavy
,
R. B.
,
Brannon
,
R. M.
, and
Strack
,
O. E.
,
2010
, “
The Use of Sphere Indentation Experiments to Characterize Ceramic Damage Models
,”
Int. J. Appl. Ceram. Technol.
,
7
(
5
), pp.
606
615
. 10.1111/j.1744-7402.2010.02487.x
27.
Strassburger
,
E.
,
2002
, Investigation of Fracture Propagation During Impact in Boron Carbide. Technical Report, United States Army, European Research Office of the U.S. Army, 01.
28.
Strassburger
,
E.
,
2004
, “
Visualization of Impact Damage in Ceramics Using the Edge-On Impact Technique
,”
Int. J. Appl. Ceram. Technol.
,
1
(
3
), pp.
235
242
. 10.1111/j.1744-7402.2004.tb00175.x
29.
Strassburger
,
E.
,
2013
, “Edge‐On Impact Investigation of Fracture Propagation in Boron Carbide,”
Advances in Ceramic Armor
, Vol.
IX
,
J. C.
LaSalvia
,
S.
Kirihara
, and
S.
Widjaja
, eds.,
John Wiley & Sons, Ltd
,
New Jersey
.
30.
Borgonovo
,
E.
, and
Plischke
,
E.
,
2016
, “
Sensitivity Analysis: A Review of Recent Advances
,”
Eur. J. Oper. Res.
,
248
(
3
), pp.
869
887
. 10.1016/j.ejor.2015.06.032
31.
Saltelli
,
A.
,
Ratto
,
M.
,
Andres
,
T.
,
Campolongo
,
F.
,
Cariboni
,
J.
,
Gatelli
,
D.
,
Saisana
,
M.
, and
Tarantola
,
S.
,
2008
,
Global Sensitivity Analysis: The Primer
,
John Wiley & Sons
,
West Sussex, UK
.
32.
Saltelli
,
A.
,
Annoni
,
P.
,
Azzini
,
I.
,
Campolongo
,
F.
,
Ratto
,
M.
, and
Tarantola
,
S.
,
2010
, “
Variance Based Sensitivity Analysis of Model Output. Design and Estimator for the Total Sensitivity Index
,”
Comput. Phys. Commun.
,
181
(
2
), pp.
259
270
. 10.1016/j.cpc.2009.09.018
33.
Campbell
,
J. E.
,
Carmichael
,
G. R.
,
Chai
,
T.
,
Mena-Carrasco
,
M.
,
Tang
,
Y.
,
Blake
,
D. R.
,
Blake
,
N. J.
,
Vay
,
S. A.
,
Collatz
,
G. J.
,
Baker
,
I.
, and
Berry
,
J. A.
,
2008
, “
Photosynthetic Control of Atmospheric Carbonyl Sulfide During the Growing Season
,”
Science
,
322
(
5904
), pp.
1085
1088
. 10.1126/science.1164015
34.
Helton
,
J. C.
,
1993
, “
Uncertainty and Sensitivity Analysis Techniques for Use in Performance Assessment for Radioactive Waste Disposal
,”
Reliab. Eng. Syst. Saf.
,
42
(
2–3
), pp.
327
367
. 10.1016/0951-8320(93)90097-I
35.
Kleijnen
,
J. P.
,
2010
, “Sensitivity Analysis of Simulation Models.” Wiley Encyclopedia of Operations Research and Management Science.
36.
Errico
,
R. M.
,
1997
, “
What is An Adjoint Model?
Bull. Am. Meteorol. Soc.
,
78
(
11
), pp.
2577
2592
. 10.1175/1520-0477(1997)078<2577:WIAAM>2.0.CO;2
37.
IM
,
S.
,
1993
, “
Sensitivity Estimates for Nonlinear Mathematical Models
,”
Math. Model. Comput. Exp
,
1
(
4
), pp.
407
414
.
38.
Homma
,
T.
, and
Saltelli
,
A.
,
1996
, “
Importance Measures in Global Sensitivity Analysis of Nonlinear Models
,”
Reliab. Eng. Syst. Saf.
,
52
(
1
), pp.
1
17
. 10.1016/0951-8320(96)00002-6
39.
Chatterjee
,
S.
, and
Hadi
,
A. S.
,
1988
,
Sensitivity Analysis in Linear Regression
(
Wiley Series in Probability and Statistics
),
Wiley
,
Hoboken, NJ
.
40.
Yan
,
X.
, and
Su
,
X. G.
,
2009
,
Linear Regression Analysis
,
World Scientific
,
Singapore
.
41.
Buhmann
,
M. D.
,
2003
,
Radial Basis Functions: Theory and Implementations
, Vol.
12
,
Cambridge University Press
,
Cambridge, MA
.
42.
Bhaduri
,
A.
, and
Graham-Brady
,
L.
,
2018
, “
An Efficient Adaptive Sparse Grid Collocation Method Through Derivative Estimation
,”
Probab. Eng. Mech.
,
51
, pp.
11
22
. 10.1016/j.probengmech.2017.11.002
43.
Bhaduri
,
A.
,
He
,
Y.
,
Shields
,
M. D.
,
Graham-Brady
,
L.
, and
Kirby
,
R. M.
,
2018
, “
Stochastic Collocation Approach With Adaptive Mesh Refinement for Parametric Uncertainty Analysis
,”
J. Comput. Phys.
,
371
, pp.
732
750
. 10.1016/j.jcp.2018.06.003
44.
Bhaduri
,
A.
,
Brandyberry
,
D.
,
Shields
,
M. D.
,
Geubelle
,
P.
, and
Graham-Brady
,
L.
,
2020
, “
On the Usefulness of Gradient Information in Surrogate Modeling: Application to Uncertainty Propagation in Composite Material Models
,”
Probab. Eng. Mech.
,
60
, p.
103024
. 10.1016/j.probengmech.2020.103024
45.
Zeng
,
Q.
,
Tonge
,
A. L.
, and
Ramesh
,
K.
,
2019
, “
A Multi-Mechanism Constitutive Model for the Dynamic Failure of Quasi-Brittle Materials. Part I: Amorphization As a Failure Mode
,”
J. Mech. Phys. Solids.
,
130
, pp.
370
392
. 10.1016/j.jmps.2019.06.012
46.
Paliwal
,
B.
, and
Ramesh
,
K.
,
2008
, “
An Interacting Micro-Crack Damage Model for Failure of Brittle Materials Under Compression
,”
J. Mech. Phys. Solids.
,
56
(
3
), pp.
896
923
. 10.1016/j.jmps.2007.06.012
47.
Cil
,
M. B.
,
Hurley
,
R. C.
, and
Graham-Brady
,
L.
,
2019
, “
A Rate-Dependent Constitutive Model for Brittle Granular Materials Based on Breakage Mechanics
,”
J. Am. Ceram. Soc.
,
102
(
9
), pp.
5524
5534
. 10.1111/jace.16376
48.
Cil
,
M. B.
,
Hurley
,
R. C.
, and
Graham-Brady
,
L.
,
2020
, “
Constitutive Model for Brittle Granular Materials Considering Competition Between Breakage and Dilation
,”
J. Eng. Mech.
,
146
(
1
), p.
04019110
. 10.1061/(ASCE)EM.1943-7889.0001690
49.
Simo
,
J.
, and
Ortiz
,
M.
,
1985
, “
A Unified Approach to Finite Deformation Elastoplastic Analysis Based on the Use of Hyperelastic Constitutive Equations
,”
Comput. Methods Appl. Mech. Eng.
,
49
(
2
), pp.
221
245
. 10.1016/0045-7825(85)90061-1
50.
Ashby
,
M.
, and
Hallam
,
S.
,
1986
, “
The Failure of Brittle Solids Containing Small Cracks Under Compressive Stress States
,”
Acta Metall.
,
34
(
3
), pp.
497
510
. 10.1016/0001-6160(86)90086-6
51.
Nemat-Nasser
,
S.
, and
Horii
,
H.
,
1982
, “
Compression-Induced Nonplanar Crack Extension With Application to Splitting, Exfoliation, and Rockburst
,”
J. Geophys. Res.: Solid Earth
,
87
(
B8
), pp.
6805
6821
. 10.1029/JB087iB08p06805
52.
Freund
,
L. B.
,
1990
,
Dynamic Fracture Mechanics
(
Cambridge Monographs on Mechanics
),
Cambridge University Press
.
53.
Einav
,
I.
,
2007
, “
Breakage Mechanics–Part I: Theory
,”
J. Mech. Phys. Solids.
,
55
(
6
), pp.
1274
1297
. 10.1016/j.jmps.2006.11.003
54.
Einav
,
I.
,
2007
, “
Breakage Mechanics–Part II: Modelling Granular Materials
,”
J. Mech. Phys. Solids.
,
55
(
6
), pp.
1298
1320
. 10.1016/j.jmps.2006.11.004
55.
Einav
,
I.
,
2007
, “
Fracture Propagation in Brittle Granular Matter
,”
Proc. R. Soc. A: Math., Phys. Eng. Sci.
,
463
(
2087
), pp.
3021
3035
. 10.1098/rspa.2007.1898
56.
Nicewicz
,
P.
,
Peciar
,
P.
,
Macho
,
O.
,
Sano
,
T.
, and
Hogan
,
J. D.
,
2020
, “
Quasi-Static Confined Uniaxial Compaction of Granular Alumina and Boron Carbide Observing the Particle Size Effects
,”
J. Am. Ceram. Soc.
,
103
(
3
), pp.
2193
2209
. 10.1111/jace.16871
57.
Thévenot
,
F.
,
1990
, “
Boron Carbide–A Comprehensive Review
,”
J. Eur. Ceram. Soc.
,
6
(
4
), pp.
205
225
. 10.1016/0955-2219(90)90048-K
58.
Dandekar
,
D. P.
,
2001
, Shock Response of Boron Carbide. Technical Report, Army Research Lab, Aberdeen Proving Ground, MD, USA, 04.
59.
Chocron
,
S.
,
Nicholls
,
A. E.
, and
King
,
N. L.
,
2012
, “
Intact and Predamaged Boron Carbide Strength Under Moderate Confinement Pressures
,”
J. Am. Ceram. Soc.
,
95
(
1
), pp.
350
357
. 10.1111/j.1551-2916.2011.04931.x
60.
Sammis
,
C.
,
King
,
G.
, and
Biegel
,
R.
,
1987
, “
The Kinematics of Gouge Deformation
,”
Pure Appl. Geophys.
,
125
(
5
), pp.
777
812
. 10.1007/BF00878033
61.
Åström
,
J.
, and
Herrmann
,
H.
,
1998
, “
Fragmentation of Grains in a Two-Dimensional Packing
,”
Eur. Phys. J. B - Condens. Matter Complex Syst.
,
5
(
3
), pp.
551
554
. 10.1007/s100510050476
62.
McDowell
,
G.
, and
Amon
,
A.
,
2000
, “
The Application of Weibull Statistics to the Fracture of Soil Particles
,”
Soils and Found.
,
40
(
5
), pp.
133
141
. 10.3208/sandf.40.5_133
63.
Holmquist
,
T.
, and
Johnson
,
G.
,
2005
, “
Modeling the 14.5 Mm BS41 Projectile for Ballistic Impact Computations
,”
Comput. Ballistics II, WIT Trans. on Modelling and Simul.
,
4
(
2087
), pp.
61
75
.
64.
Tonge
,
A. L.
, and
Ramesh
,
K.
,
2016
, “
Multi-Scale Defect Interactions in High-Rate Failure of Brittle Materials, Part II: Application to Design of Protection Materials
,”
J. Mech. Phys. Solids.
,
86
, pp.
237
258
. 10.1016/j.jmps.2015.10.006
65.
Iqbal
,
M.A.
,
Senthil
,
K.
,
Bhargava
,
P.
, and
Gupta
,
N.K.
,
2015
, “
The characterization and ballistic evaluation of mild steel
,”
International Journal of Impact Engineering
,
78
, pp.
98
113
. 10.1016/j.ijimpeng.2014.12.006
66.
LaSalvia
,
J. C.
,
Normandia
,
M. J.
,
Miller
,
H. T.
, and
MacKenzie
,
D. E.
,
2005
, “Sphere Impact Induced Damage in Ceramics: II. Armor‐Grade B4C and WC,”
Advances in Ceramic Armor
, Vol.
26
,
J. J.
Swab
, ed.,
John Wiley & Sons, Ltd.
,
Ohio
.
67.
Aydelotte
,
B.
, and
Schuster
,
B.
,
2016
, “Observation and Modeling of Cone Cracks in Ceramics,”
Dynamic Behavior of Materials
, Vol.
1
,
B.
Song
,
L.
Lamberson
,
D.
Casem
, and
J.
Kimberley
, eds.,
Springer International Publishing
,
Cham, Switzerland
, pp.
19
23
.
68.
Toksoy
,
M. F.
,
Rafaniello
,
W.
,
Xie
,
K. Y.
,
Ma
,
L.
,
Hemker
,
K. J.
, and
Haber
,
R. A.
,
2017
, “
Densification and Characterization of Rapid Carbothermal Synthesized Boron Carbide
,”
Int. J. Appl. Ceram. Technol.
,
14
(
3
), pp.
443
453
. 10.1111/ijac.12654
69.
Kim
,
H.-W.
,
Koh
,
Y.-H.
, and
Kim
,
H.-E.
,
2000
, “
Densification and Mechanical Properties of B4C With Al2O3 As a Sintering Aid
,”
J. Am. Ceram. Soc.
,
83
(
11
), pp.
2863
2865
. 10.1111/j.1151-2916.2000.tb01647.x
70.
Yamada
,
S.
,
Hirao
,
K.
,
Yamauchi
,
Y.
, and
Kanzaki
,
S.
,
2003
, “
High Strength B4C–TiB2 Composites Fabricated by Reaction Hot-Pressing
,”
J. Eur. Ceram. Soc.
,
23
(
7
), pp.
1123
1130
. 10.1016/S0955-2219(02)00274-1
71.
Frage
,
N.
,
Hayun
,
S.
,
Kalabukhov
,
S.
, and
Dariel
,
M. P.
,
2007
, “
The Effect of Fe Addition on the Densification of B4C Powder by Spark Plasma Sintering
,”
Powder. Metall. Met. Ceram.
,
46
(
11–12
), pp.
533
538
. 10.1007/s11106-007-0082-9
72.
Subramanian
,
C.
,
Roy
,
T.
,
Murthy
,
T.
,
Sengupta
,
P.
,
Kale
,
G.
,
Krishnaiah
,
M.
, and
Suri
,
A.
,
2008
, “
Effect of Zirconia Addition on Pressureless Sintering of Boron Carbide
,”
Ceram. Int.
,
34
(
6
), pp.
1543
1549
. 10.1016/j.ceramint.2007.04.017
73.
Sun
,
J.
,
Liu
,
C.
, and
Duan
,
C.
,
2009
, “
Effect of Al and TiO2 on Sinterability and Mechanical Properties of Boron Carbide
,”
Mater. Sci. Eng. A.
,
509
(
1
), pp.
89
93
. 10.1016/j.msea.2009.01.067
74.
Madhav Reddy
,
K.
,
Guo
,
J.
,
Shinoda
,
Y.
,
Fujita
,
T.
,
Hirata
,
A.
,
Singh
,
J.
,
McCauley
,
J.
, and
Chen
,
M.
,
2012
, “
Enhanced Mechanical Properties of Nanocrystalline Boron Carbide by Nanoporosity and Interface Phases
,”
Nat. Commun.
,
3
(
1
), p.
1052
. 10.1038/ncomms2047
75.
Shen
,
Y.
,
Li
,
G.
, and
An
,
Q.
,
2019
, “
Enhanced Fracture Toughness of Boron Carbide From Microalloying and Nanotwinning
,”
Scr. Mater.
,
162
, pp.
306
310
. 10.1016/j.scriptamat.2018.11.035
76.
He
,
Y.
,
Shen
,
Y.
,
Tang
,
B.
, and
An
,
Q.
,
2020
, “
Strengthening Boron Carbide Through Lithium Dopant
,”
J. Am. Ceram. Soc.
,
103
(
3
), pp.
2012
2023
. 10.1111/jace.16889
77.
Proctor
,
J. E.
,
Bhakhri
,
V.
,
Hao
,
R.
,
Prior
,
T. J.
,
Gregoryanz
,
T. S. E.
,
Chhowalla
,
M.
, and
Giulani
,
F.
,
2015
, “
Stabilization of Boron Carbide Via Silicon Doping
,”
J. Phys.: Condens. Matter.
,
27
(
1
), p.
015401
. 10.1088/0953-8984/27/1/015401
78.
Khan
,
A. U.
,
Etzold
,
A. M.
,
Yang
,
X.
,
Domnich
,
V.
,
Xie
,
K. Y.
,
Hwang
,
C.
,
Behler
,
K. D.
,
Chen
,
M.
,
An
,
Q.
,
LaSalvia
,
J. C.
,
Hemker
,
K. J.
,
Goddard
,
W. A.
, and
Haber
,
R. A.
,
2018
, “
Locating Si Atoms in Si-doped Boron Carbide: A Route to Understand Amorphization Mitigation Mechanism
,”
Acta Mater.
,
157
, pp.
106
113
. 10.1016/j.actamat.2018.07.021
79.
Chauhan
,
A.
,
Schaefer
,
M. C.
,
Haber
,
R. A.
, and
Hemker
,
K. J.
,
2019
, “
Experimental Observations of Amorphization in Stoichiometric and Boron-Rich Boron Carbide
,”
Acta Mater.
,
181
, pp.
207
215
. 10.1016/j.actamat.2019.09.052
80.
Schaefer
,
M. C.
, and
Haber
,
R. A.
,
2020
, “
Amorphization Mitigation in Boron-Rich Boron Carbides Quantified by Raman Spectroscopy
,”
Ceramics
,
3
(
3
), pp.
297
305
. 10.3390/ceramics3030027
81.
Sun
,
X.
,
Chauhan
,
A.
,
Mallick
,
D. D.
,
Tonge
,
A. L.
,
McCauley
,
J. W.
,
Hemker
,
K. J.
,
LaSalvia
,
J. C.
, and
Ramesh
,
K.
,
2020
, “
Granular Flow of An Advanced Ceramic Under Ultra-high Strain Rates and High Pressures
,”
J. Mech. Phys. Solids.
,
143
, p.
104031
. 10.1016/j.jmps.2020.104031
82.
Batra
,
R.
, and
Pydah
,
A.
,
2020
, “
Impact Analysis of PEEK/ceramic/gelatin Composite for Finding Behind the Armor Trauma
,”
Composite Struct.
,
237
, p.
111863
. 10.1016/j.compstruct.2020.111863
83.
Shen
,
Z.
,
Hu
,
D.
,
Yang
,
G.
, and
Han
,
X.
,
2019
, “
Ballistic Reliability Study on SiC/UHMWPE Composite Armor Against Armor-Piercing Bullet
,”
Composite Struct.
,
213
, pp.
209
219
. 10.1016/j.compstruct.2019.01.078
84.
Matoušek
,
J.
,
1998
, “
On the L2-discrepancy for Anchored Boxes
,”
J. Complex.
,
14
(
4
), pp.
527
556
. 10.1006/jcom.1998.0489
85.
Joe
,
S.
, and
Kuo
,
F. Y.
,
2003
, “
Remark on Algorithm 659: Implementing Sobol’s Quasirandom Sequence Generator
,”
ACM Trans. Math. Softw. (TOMS)
,
29
(
1
), pp.
49
57
. 10.1145/641876.641879
86.
James
,
G.
,
Witten
,
D.
,
Hastie
,
T.
, and
Tibshirani
,
R.
,
2013
,
An Introduction to Statistical Learning
, Vol.
112
,
Springer
,
New York
.
87.
Sheather
,
S.
,
2009
,
A Modern Approach to Regression With R
,
Springer Science & Business Media
,
New York
.
88.
Farbaniec
,
L.
,
Hogan
,
J.
, and
Ramesh
,
K.
,
2015
, “
Micromechanisms Associated with the Dynamic Compressive Failure of Hot-pressed Boron Carbide
,”
Scr. Mater.
,
106
, pp.
52
56
. 10.1016/j.scriptamat.2015.05.004
89.
Xie
,
K. Y.
,
Kuwelkar
,
K.
,
Haber
,
R. A.
,
LaSalvia
,
J. C.
, and
Hemker
,
K. J.
,
2016
, “
Microstructural Characterization of a Commercial Hot-Pressed Boron Carbide Armor Plate
,”
J. Am. Ceram. Soc.
,
99
(
8
), pp.
2834
2841
. 10.1111/jace.14295
90.
Bakhshi
,
M.
,
Souri
,
A.
, and
Amin
,
M. K.
,
2019
, “
Carbothermic Synthesis of Boron Carbide With Low Free Carbon Using Catalytic Amount of Magnesium Chloride
,”
J. Iranian Chem. Soc.
,
16
(
6
), pp.
1265
1272
. 10.1007/s13738-019-01602-9
91.
Alshibli
,
K. A.
, and
Cil
,
M. B.
,
2018
, “
Influence of Particle Morphology on the Friction and Dilatancy of Sand
,”
J. Geotech. Geoenviron. Eng.
,
144
(
3
), p.
04017118
. 10.1061/(ASCE)GT.1943-5606.0001841
92.
Li
,
H.
,
Lo
,
C.
,
Toussaint
,
G.
,
Sano
,
T.
, and
Hogan
,
J. D.
,
2020
, “Dynamic Fracture and Fragmentation of Boron Carbide,”
Boron Carbide: Structure, Processing, Properties and Applications
,
Kolan Madhav
Reddy
, ed.,
Nova Science Publishers
,
New York
.
93.
Salem
,
J.
,
Quinn
,
G.
, and
Jenkins
,
M.
,
2005
, “Measuring the Real Fracture Toughness of Ceramics: ASTM C 1421,”
Fracture Mechanics of Ceramics
, Vol.
6
,
R. C.
Bradt
,
D.
Munz
,
M.
Sakai
, and
K. W.
White
, eds.,
Springer
,
New York
, pp.
531
553
.
You do not currently have access to this content.