It is crucial to investigate the dynamic mechanical behavior of materials at the nanoscale to create nanostructured protective systems that have superior ballistic impact resistance. Inspired from recent experimental advances that enable ballistic materials testing at small scales, here we report a comparative analysis of the dynamic behavior of nanoscale thin films made from multilayer graphene (MLG), polymer, gold, and aluminum under high-speed projectile impact. We employ atomistic and coarse-grained (CG) molecular dynamics (MD) simulations to measure the ballistic limit velocity (V50) and penetration energy (Ep) of these nanoscale films and investigate their distinctive failure mechanisms over a wide range of impact velocities (Vi). For the local penetration failure mechanism observed in polymer and metal films, we find that the intrinsic mechanical properties influence Ep at low Vi, while material density tends to govern Ep at high Vi. MLG films uniquely show a large impact propagation zone (IPZ), which transfers the highly localized impact energy into elastic deformation energy in a much larger area through cone wave propagation. We present theoretical analyses that corroborate that the size of IPZ should depend not only on material properties but also on a geometrical factor, specifically, the ratio between the projectile radius and film thickness. This study clearly illustrates how material properties and geometrical factors relate to the ballistic penetration energy, thereby allowing a quantitative comparison of the nanoscale ballistic response of different materials.

References

References
1.
Carter
,
T. J.
,
2005
, “
Common Failures in Gas Turbine Blades
,”
Eng. Failure Anal.
,
12
(
2
), pp.
237
247
.
2.
Grossman
,
E.
,
Gouzman
,
I.
, and
Verker
,
R.
,
2010
, “
Debris/Micrometeoroid Impacts and Synergistic Effects on Spacecraft Materials
,”
MRS Bull.
,
35
(
1
), pp.
41
47
.
3.
Anagnostopoulos
,
G.
,
Pappas
,
P.-N.
,
Li
,
Z.
,
Kinloch
,
I. A.
,
Young
,
R. J.
,
Novoselov
,
K. S.
,
Lu
,
C. Y.
,
Pugno
,
N.
,
Parthenios
,
J.
, and
Galiotis
,
C.
,
2016
, “
Mechanical Stability of Flexible Graphene-Based Displays
,”
ACS Appl. Mater. Interfaces
,
8
(
34
), pp.
22605
22614
.
4.
Lu
,
Y.
,
Song
,
J.
,
Huang
,
J. Y.
, and
Lou
,
J.
,
2011
, “
Surface Dislocation Nucleation Mediated Deformation and Ultrahigh Strength in Sub-10-Nm Gold Nanowires
,”
Nano Res.
,
4
(
12
), pp.
1261
1267
.
5.
McDowell
,
M. T.
,
Leach
,
A. M.
, and
Gall
,
K.
,
2008
, “
On the Elastic Modulus of Metallic Nanowires
,”
Nano Lett.
,
8
(
11
), pp.
3613
3618
.
6.
Diao
,
J.
,
Gall
,
K.
, and
Dunn
,
M. L.
,
2004
, “
Yield Strength Asymmetry in Metal Nanowires
,”
Nano Lett.
,
4
(
10
), pp.
1863
1867
.
7.
Gall
,
K.
,
Diao
,
J.
, and
Dunn
,
M. L.
,
2004
, “
The Strength of Gold Nanowires
,”
Nano Lett.
,
4
(
12
), pp.
2431
2436
.
8.
Meng
,
Z.
,
Bessa
,
M. A.
,
Xia
,
W.
,
Kam Liu
,
W.
, and
Keten
,
S.
,
2016
, “
Predicting the Macroscopic Fracture Energy of Epoxy Resins from Atomistic Molecular Simulations
,”
Macromolecules
,
49
(
24
), pp.
9474
9483
.
9.
Rottler
,
J.
,
Barsky
,
S.
, and
Robbins
,
M. O.
,
2002
, “
Cracks and Crazes: On Calculating the Macroscopic Fracture Energy of Glassy Polymers from Molecular Simulations
,”
Phys. Rev. Lett.
,
89
(
14
), p.
148304
.
10.
Yang
,
Z.
,
Fujii
,
Y.
,
Lee
,
F. K.
,
Lam
,
C.-H.
, and
Tsui
,
O. K.
,
2010
, “
Glass Transition Dynamics and Surface Layer Mobility in Unentangled Polystyrene Films
,”
Science
,
328
(
5986
), pp.
1676
1679
.
11.
Liu
,
Y.
,
Chen
,
Y.-C.
,
Hutchens
,
S.
,
Lawrence
,
J.
,
Emrick
,
T.
, and
Crosby
,
A. J.
,
2015
, “
Directly Measuring the Complete Stress -Strain Response of Ultrathin Polymer Films
,”
Macromolecules
,
48
(
18
), pp.
6534
6540
.
12.
Lee
,
J.-H.
,
Chung
,
J. Y.
, and
Stafford
,
C. M.
,
2011
, “
Effect of Confinement on Stiffness and Fracture of Thin Amorphous Polymer Films
,”
ACS Macro Lett.
,
1
(
1
), pp.
122
126
.
13.
Xia
,
W.
,
Hsu
,
D. D.
, and
Keten
,
S.
,
2015
, “
Molecular Weight Effects on the Glass Transition and Confinement Behavior of Polymer Thin Films
,”
Macromol. Rapid Commun.
,
36
(
15
), pp.
1422
1427
.
14.
Xia
,
W.
, and
Keten
,
S.
,
2015
, “
Interfacial Stiffening of Polymer Thin Films under Nanoconfinement
,”
Extreme Mech. Lett.
,
4
, pp.
89
95
.
15.
Xia
,
W.
,
Song
,
J.
,
Hsu
,
D. D.
, and
Keten
,
S.
,
2016
, “
Understanding the Interfacial Mechanical Response of Nanoscale Polymer Thin Films Via Nanoindentation
,”
Macromolecules
,
49
(10), pp. 3810–3817.
16.
Backman
,
M. E.
, and
Goldsmith
,
W.
,
1978
, “
The Mechanics of Penetration of Projectiles into Targets
,”
Int. J. Eng. Sci.
,
16
(
1
), pp.
1
99
.
17.
Wen
,
H.
,
2000
, “
Predicting the Penetration and Perforation of FRP Laminates Struck Normally by Projectiles with Different Nose Shapes
,”
Compos. Structures
,
49
(
3
), pp.
321
329
.
18.
Mohagheghian
,
I.
,
McShane
,
G.
, and
Stronge
,
W.
,
2016
, “
Impact Perforation of Polymer-Metal Laminates: Projectile Nose Shape Sensitivity
,”
Int. J. Solids Structures
,
88–89
, pp.
337
353
.
19.
Lee
,
J.-H.
,
Veysset
,
D.
,
Singer
,
J. P.
,
Retsch
,
M.
,
Saini
,
G.
,
Pezeril
,
T.
,
Nelson
,
K. A.
, and
Thomas
,
E. L.
,
2012
, “
High Strain Rate Deformation of Layered Nanocomposites
,”
Nat. Commun.
,
3
, p.
1164
.
20.
Lee
,
J.-H.
,
Loya
,
P. E.
,
Lou
,
J.
, and
Thomas
,
E. L.
,
2014
, “
Dynamic Mechanical Behavior of Multilayer Graphene Via Supersonic Projectile Penetration
,”
Science
,
346
(
6213
), pp.
1092
1096
.
21.
Veysset
,
D.
,
Hsieh
,
A. J.
,
Kooi
,
S.
,
Maznev
,
A. A.
,
Masser
,
K. A.
, and
Nelson
,
K. A.
,
2016
, “
Dynamics of Supersonic Microparticle Impact on Elastomers Revealed by Real–Time Multi–Frame Imaging
,”
Sci. Rep.
,
6
(
1
), p. 025577.
22.
Xie
,
W.
,
Tadepalli
,
S.
,
Park
,
S. H.
,
Kazemi-Moridani
,
A.
,
Jiang
,
Q.
,
Singamaneni
,
S.
, and
Lee
,
J.-H.
,
2018
, “
Extreme Mechanical Behavior of Nacre-Mimetic Graphene-Oxide and Silk Nanocomposites
,”
Nano Lett.
,
18
(2), pp. 987–993.
23.
Wang
,
Y.
,
Chen
,
X.
,
Young
,
R.
, and
Kinloch
,
I.
,
2016
, “
Finite Element Analysis of Effect of Inter-Yarn Friction on Ballistic Impact Response of Woven Fabrics
,”
Compos. Struct.
,
135
, pp.
8
16
.
24.
Wang
,
Y.
,
Chen
,
X.
,
Young
,
R.
, and
Kinloch
,
I.
,
2016
, “
A Numerical and Experimental Analysis of the Influence of Crimp on Ballistic Impact Response of Woven Fabrics
,”
Compos. Struct.
,
140
, pp.
44
52
.
25.
Xia
,
K.
,
Zhan
,
H.
,
Hu
,
D. A.
, and
Gu
,
Y.
,
2016
, “
Failure Mechanism of Monolayer Graphene under Hypervelocity Impact of Spherical Projectile
,”
Sci. Rep.
,
6
(
1
), p. 033139.
26.
Haque
,
B. Z. G.
,
Chowdhury
,
S. C.
, and
Gillespie
,
J. W.
,
2016
, “
Molecular Simulations of Stress Wave Propagation and Perforation of Graphene Sheets under Transverse Impact
,”
Carbon
,
102
, pp.
126
140
.
27.
Liu
,
N.
,
Pidaparti
,
R.
, and
Wang
,
X.
,
2017
, “
Mechanical Performance of Graphene-Based Artificial Nacres under Impact Loads: A Coarse-Grained Molecular Dynamic Study
,”
Polymer
,
9
(
12
), p.
134
.
28.
Zhang
,
Y.
,
Meng
,
Z.
,
Qin
,
X.
, and
Keten
,
S.
,
2018
, “
Ballistic Impact Response of Lipid Membranes
,”
Nanoscale
,
10
(
10
), pp.
4761
4770
.
29.
Ruiz
,
L.
,
Xia
,
W.
,
Meng
,
Z.
, and
Keten
,
S.
,
2015
, “
A Coarse-Grained Model for the Mechanical Behavior of Multi-Layer Graphene
,”
Carbon
,
82
, pp.
103
115
.
30.
Meng
,
Z.
,
Soler-Crespo
,
R. A.
,
Xia
,
W.
,
Gao
,
W.
,
Ruiz
,
L.
,
Espinosa
,
H. D.
, and
Keten
,
S.
,
2017
, “
A Coarse-Grained Model for the Mechanical Behavior of Graphene Oxide
,”
Carbon
,
117
, pp.
476
487
.
31.
Qin
,
X.
,
Feng
,
S.
,
Meng
,
Z.
, and
Keten
,
S.
,
2017
, “
Optimizing the Mechanical Properties of Cellulose Nanopaper through Surface Energy and Critical Length Scale Considerations
,”
Cellulose
,
24
(
8
), pp.
3289
3299
.
32.
Hsu
,
D. D.
,
Xia
,
W.
,
Arturo
,
S. G.
, and
Keten
,
S.
,
2014
, “
Systematic Method for Thermomechanically Consistent Coarse-Graining: A Universal Model for Methacrylate-Based Polymers
,”
J. Chem. Theory Comput.
,
10
(
6
), pp.
2514
2527
.
33.
Hsu
,
D. D.
,
Xia
,
W.
,
Arturo
,
S. G.
, and
Keten
,
S.
,
2015
, “
Thermomechanically Consistent and Temperature Transferable Coarse-Graining of Atactic Polystyrene
,”
Macromolecules
,
48
(
9
), pp.
3057
3068
.
34.
Meng
,
Z.
,
Singh
,
A.
,
Qin
,
X.
, and
Keten
,
S.
,
2017
, “
Reduced Ballistic Limit Velocity of Graphene Membranes Due to Cone Wave Reflection
,”
Extreme Mech. Lett.
,
15
, pp.
70
77
.
35.
Meng
,
Z.
,
Han
,
J.
,
Qin
,
X.
,
Zhang
,
Y.
,
Balogun
,
O.
, and
Keten
,
S.
,
2018
, “
Spalling-Like Failure by Cylindrical Projectiles Deteriorates the Ballistic Performance of Multi-Layer Graphene Plates
,”
Carbon
,
126
, pp.
611
619
.
36.
Plimpton
,
S.
,
1995
, “
Fast Parallel Algorithms for Short-Range Molecular Dynamics
,”
J. Comput. Phys.
,
117
(
1
), pp.
1
19
.
37.
Humphrey
,
W.
,
Dalke
,
A.
, and
Schulten
,
K.
,
1996
, “
VMD: Visual Molecular Dynamics
,”
J. Mol. Graphics
,
14
(
1
), pp.
33
38
.
38.
Wei
,
X.
,
Meng
,
Z.
,
Ruiz
,
L.
,
Xia
,
W.
,
Lee
,
C.
,
Kysar
,
J. W.
,
Hone
,
J. C.
,
Keten
,
S.
, and
Espinosa
,
H. D.
,
2016
, “
Recoverable Slippage Mechanism in Multilayer Graphene Leads to Repeatable Energy Dissipation
,”
ACS Nano
,
10
(
2
), pp.
1820
1828
.
39.
Qin
,
X.
,
Xia
,
W.
,
Sinko
,
R.
, and
Keten
,
S.
,
2015
, “
Tuning Glass Transition in Polymer Nanocomposites with Functionalized Cellulose Nanocrystals through Nanoconfinement
,”
Nano Lett.
,
15
(
10
), pp.
6738
6744
.
40.
Xia
,
W.
,
Song
,
J.
,
Meng
,
Z.
,
Shao
,
C.
, and
Keten
,
S.
,
2016
, “
Designing Multi-Layer Graphene-Based Assemblies for Enhanced Toughness in Nacre-Inspired Nanocomposites
,”
Mol. Syst. Des. Eng.
,
1
(
1
), pp.
40
47
.
41.
Daw
,
M. S.
, and
Baskes
,
M. I.
,
1984
, “
Embedded-Atom Method: Derivation and Application to Impurities, Surfaces, and Other Defects in Metals
,”
Phys. Rev. B
,
29
(
12
), p.
6443
.
42.
Foiles
,
S.
,
Baskes
,
M.
, and
Daw
,
M. S.
,
1986
, “
Embedded-Atom-Method Functions for the FCC Metals Cu, Ag, Au, Ni, Pd, Pt, and Their Alloys
,”
Phys. Rev. B
,
33
(
12
), p.
7983
.
43.
Park
,
H. S.
, and
Zimmerman
,
J. A.
,
2005
, “
Modeling Inelasticity and Failure in Gold Nanowires
,”
Phys. Rev. B
,
72
(
5
), p.
054106
.
44.
Park
,
H. S.
,
Gall
,
K.
, and
Zimmerman
,
J. A.
,
2006
, “
Deformation of FCC Nanowires by Twinning and Slip
,”
J. Mech. Phys. Solids
,
54
(
9
), pp.
1862
1881
.
45.
Häkkinen
,
H.
,
Mäkinen
,
S.
, and
Manninen
,
M.
,
1990
, “
Edge Dislocations in FCC Metals: Microscopic Calculations of Core Structure and Positron States in Al and Cu
,”
Phys. Rev. B
,
41
(
18
), p.
12441
.
46.
Bernal
,
J.
,
1924
, “
The Structure of Graphite
,”
Proc. R. Soc. London. Ser. A
,
106
(
740
), pp.
749
773
.
47.
Wells
,
A. F.
,
2012
,
Structural Inorganic Chemistry
,
Oxford University Press
, Oxford, UK.
48.
National Research Council
,
2011
,
Opportunities in Protection Materials Science and Technology for Future Army Applications
,
National Academies Press
, Washington, DC.
49.
Signetti
,
S.
,
Taioli
,
S.
, and
Pugno
,
N. M.
,
2017
, “
2D Material Armors Showing Superior Impact Strength of Few Layers
,”
ACS Appl. Mater. Interfaces
,
9
(
46
), pp.
40820
40830
.
50.
Bizao
,
R. A.
,
Machado
,
L. D.
,
de Sousa
,
J. M.
,
Pugno
,
N. M.
, and
Galvao
,
D. S.
,
2018
, “
Scale Effects on the Ballistic Penetration of Graphene Sheets
,”
Sci. Rep.
,
8
(
1
), p. 006750.
51.
Wei
,
Y.
,
Wu
,
J.
,
Yin
,
H.
,
Shi
,
X.
,
Yang
,
R.
, and
Dresselhaus
,
M.
,
2012
, “
The Nature of Strength Enhancement and Weakening by Pentagon–Heptagon Defects in Graphene
,”
Nat. Mater.
,
11
(
9
), pp.
759
763
.
52.
Li
,
H.
,
Zhang
,
H.
, and
Cheng
,
X.
,
2017
, “
The Effect of Temperature, Defect and Strain Rate on the Mechanical Property of Multi-Layer Graphene: Coarse-Grained Molecular Dynamics Study
,”
Physica E
,
85
, pp.
97
102
.
53.
Carpinteri
,
A.
, and
Pugno
,
N.
,
2002
, “
One, Two, and Three-Dimensional Universal Laws for Fragmentation Due to Impact and Explosion
,”
ASME J. Appl. Mech.
,
69
(
6
), pp.
854
856
.
54.
Sha
,
J.
,
Li
,
Y.
,
Villegas Salvatierra
,
R.
,
Wang
,
T.
,
Dong
,
P.
,
Ji
,
Y.
,
Lee
,
S.-K.
,
Zhang
,
C.
,
Zhang
,
J.
, and
Smith
,
R. H.
,
2017
, “
Three-Dimensional Printed Graphene Foams
,”
ACS Nano
,
11
(
7
), pp.
6860
6867
.
55.
Shen
,
Z.
,
Ye
,
H.
,
Zhou
,
C.
,
Kroeger
,
M.
, and
Li
,
Y.
,
2018
, “
Size of Graphene Sheets Determines the Structural and Mechanical Properties of 3D Graphene Foams
,”
Nanotechnol.
,
29
(10), p. 104001.
56.
Wang
,
C.
,
Pan
,
D.
, and
Chen
,
S.
,
2018
, “
Energy Dissipative Mechanism of Graphene Foam Materials
,”
Carbon
,
132
, pp. 641–650.
57.
Phoenix
,
S. L.
, and
Porwal
,
P. K.
,
2003
, “
A New Membrane Model for the Ballistic Impact Response and V50 Performance of Multi-Ply Fibrous Systems
,”
Int. J. Solids Struct.
,
40
(
24
), pp.
6723
6765
.
58.
Porwal
,
P. K.
, and
Phoenix
,
S. L.
,
2005
, “
Modeling System Effects in Ballistic Impact into Multi-Layered Fibrous Materials for Soft Body Armor
,”
Int. J. Fract.
,
135
(
1–4
), pp.
217
249
.
59.
Wetzel
,
E. D.
,
Balu
,
R.
, and
Beaudet
,
T. D.
,
2015
, “
A Theoretical Consideration of the Ballistic Response of Continuous Graphene Membranes
,”
J. Mech. Phys. Solids
,
82
, pp.
23
31
.
60.
Xia
,
W.
,
Ruiz
,
L.
,
Pugno
,
N. M.
, and
Keten
,
S.
,
2016
, “
Critical Length Scales and Strain Localization Govern the Mechanical Performance of Multi-Layer Graphene Assemblies
,”
Nanoscale
,
8
(
12
), pp.
6456
6462
.
61.
Natarajan
,
B.
,
Krishnamurthy
,
A.
,
Qin
,
X.
,
Emiroglu
,
C. D.
,
Forster
,
A.
,
Foster
,
E. J.
,
Weder
,
C.
,
Fox
,
D. M.
,
Keten
,
S.
, and
Obrzut
,
J.
,
2018
, “
Binary Cellulose Nanocrystal Blends for Bioinspired Damage Tolerant Photonic Films
,”
Adv. Funct. Mater.
, (
26
), p.
1800032
.
62.
Gu
,
G. X.
,
Takaffoli
,
M.
, and
Buehler
,
M. J.
,
2017
, “
Hierarchically Enhanced Impact Resistance of Bioinspired Composites
,”
Adv. Mater.
,
29
(
28
), p. 1700060.
63.
Huang
,
W.
,
Zaheri
,
A.
,
Jung
,
J.-Y.
,
Espinosa
,
H. D.
, and
Mckittrick
,
J.
,
2017
, “
Hierarchical Structure and Compressive Deformation Mechanisms of Bighorn Sheep (Ovis Canadensis) Horn
,”
Acta Biomater.
,
64
, pp.
1
14
.
64.
Yang
,
R.
,
Zaheri
,
A.
,
Gao
,
W.
,
Hayashi
,
C.
, and
Espinosa
,
H. D.
,
2017
, “
AFM Identification of Beetle Exocuticle: Bouligand Structure and Nanofiber Anisotropic Elastic Properties
,”
Adv. Funct. Mater.
,
27
(
6
), p. 1603993.
65.
Rittigstein
,
P.
,
Priestley
,
R. D.
,
Broadbelt
,
L. J.
, and
Torkelson
,
J. M.
,
2007
, “
Model Polymer Nanocomposites Provide an Understanding of Confinement Effects in Real Nanocomposites
,”
Nat. Mater.
,
6
(
4
), p.
278
.
66.
Bažant
,
Z. P.
, and
Caner
,
F. C.
,
2013
, “
Comminution of Solids Caused by Kinetic Energy of High Shear Strain Rate, with Implications for Impact, Shock, and Shale Fracturing
,”
Proc. Natl. Acad. Sci.
,
110
(
48
), pp.
19291
19294
.
67.
Bažant
,
Z. P.
, and
Caner
,
F. C.
,
2014
, “
Impact Comminution of Solids Due to Local Kinetic Energy of High Shear Strain Rate: I. Continuum Theory and Turbulence Analogy
,”
J. Mech. Phys. Solids
,
64
, pp.
223
235
.
68.
Alonso
,
L.
,
Navarro
,
C.
, and
García-Castillo
,
S. K.
,
2018
, “
Analytical Models for the Perforation of Thick and Thin Thickness Woven-Laminates Subjected to High-Velocity Impact
,”
Composites, Part B Eng.
,
143
, pp. 292–300.
69.
Cheeseman
,
B. A.
, and
Bogetti
,
T. A.
,
2003
, “
Ballistic Impact into Fabric and Compliant Composite Laminates
,”
Compos. Struct.
,
61
(
1–2
), pp.
161
173
.
70.
Wang
,
Y.
,
Chen
,
X.
,
Young
,
R.
,
Kinloch
,
I.
, and
Wells
,
G.
,
2015
, “
A Numerical Study of Ply Orientation on Ballistic Impact Resistance of Multi-Ply Fabric Panels
,”
Composites, Part B
,
68
, pp.
259
265
.
71.
Morye
,
S.
,
Hine
,
P.
,
Duckett
,
R.
,
Carr
,
D.
, and
Ward
,
I.
,
2000
, “
Modelling of the Energy Absorption by Polymer Composites Upon Ballistic Impact
,”
Compos. Sci. Technol.
,
60
(
14
), pp.
2631
2642
.
72.
Naik
,
N.
,
Shrirao
,
P.
, and
Reddy
,
B.
,
2006
, “
Ballistic Impact Behaviour of Woven Fabric Composites: Formulation
,”
Int. J. Impact Eng.
,
32
(
9
), pp.
1521
1552
.
73.
Caner
,
F. C.
, and
Bažant
,
Z. P.
,
2014
, “
Impact Comminution of Solids Due to Local Kinetic Energy of High Shear Strain Rate: II–Microplane Model and Verification
,”
J. Mech. Phys. Solids
,
64
, pp.
236
248
.
You do not currently have access to this content.