This article presents a computational constitutive model for glass subjected to large strains, high strain rates and high pressures. The model has similarities to a previously developed model for brittle materials by Johnson, Holmquist and Beissel (JHB model), but there are significant differences. This new glass model provides a material strength that is dependent on the location and/or condition of the material. Provisions are made for the strength to be dependent on whether it is in the interior, on the surface (different surface finishes can be accommodated), adjacent to failed material, or if it is failed. The intact and failed strengths are also dependent on the pressure and the strain rate. Thermal softening, damage softening, time-dependent softening, and the effect of the third invariant are also included. The shear modulus can be constant or variable. The pressure-volume relationship includes permanent densification and bulking. Damage is accumulated based on plastic strain, pressure and strain rate. Simple (single-element) examples are presented to illustrate the capabilities of the model. Computed results for more complex ballistic impact configurations are also presented and compared to experimental data.

References

References
1.
Bridgman
,
P. W.
, 1948, “
The Compression of 39 Substances to 100,000 kg/cm2
,”
Proceedings of the American Academy of Arts and Sciences
,
76
(
3
), pp.
55
87
.
2.
Bridgman
,
P. W.
and
Simon
,
I.
, 1953, “
Effects of Very High Pressures on Glass
,”
J. Appl. Phys.
,
24
(
4
), pp.
405
413
.
3.
Uhlmann
,
D. R.
, 1973, “
Densification of Alkali Silicate Glasses at High Pressure
,”
J. Non-Cryst. Solids
,
13
, pp.
89
99
.
4.
Rouxel
,
T.
,
Ji
,
H.
,
Hammouda
,
T.
, and
Moreac
,
A.
, 2008, “
Poisson’s Ratio and the Densification of Glass Under High Pressure
,”
Phys. Rev. Lett.
,
100
, p.
225501
.
5.
Sakka
,
S.
and
Mackenzie
,
J. D.
, 1969, “
High Pressure Effects on Glass
,”
J. Non-Cryst. Solids
,
1
, pp.
107
142
.
6.
Mackenzie
,
J. D.
, 1963, “
High-Pressure Effects on Oxide Glasses: I, Densification in Rigid State
,”
J. Am. Ceram. Soc.
,
46
(
10
), pp.
461
470
.
7.
Rosenberg
,
Z.
,
Yaziv
,
D.
, and
Bless
,
S.
, 1985, “
Spall Strength of Shock-Loaded Glass
,”
J. Appl. Phys.
,
58
(
8
), pp
3249
3251
.
8.
Brar
,
N.
,
Rosenberg
,
S.
, and
Bless
,
S.
, 1991, “
Spall Strength and Failure Waves in Glass
,”
J. Phys. (Paris)
,
1
, pp.
639
634
.
9.
Cagnoux
,
J.
, 1985, “
Deformation et Ruine d’un Verre Pyrex Soumis a un Choc Intense: Etude Experimentale et Modelisation du Comportement
,” Ph.D. thesis, L’Universite de Poitiers.
10.
Cagnoux
,
J.
and
Longy
,
F.
, 1988, “
Spallation and Shock-Wave Behaviour of Some Ceramics
,”
J. Phys. (Paris)
,
49
(
9
), pp.
3
10
.
11.
Kanel
,
G. I.
,
Bogatch
,
A. A.
,
Razorenov
,
S. V.
, and
Chen
,
Z.
, 2002, “
Transformation of Shock Compression Pulses in Glass due to the Failure Wave Phenomena
,”
J. Appl. Phys.
,
92
(
9
), pp.
5045
5052
.
12.
Anderson
,
C. E.
, Jr.
,
Orphal
,
D. L.
,
Behner
,
T.
, and
Templeton
,
D. W.
, 2009, “
Failure and Penetration Response of Borosilicate Glass During Short-Rod Impact
,”
International Journal of Impact Engineering
,
36
, pp.
789
798
.
13.
Nie
,
X.
,
Chen
,
W.
,
Wereszczak
,
A.
, and
Templeton
,
D.
, 2009, “
Effect of Loading Rate and Surface Conditions on the Flexural Strength of Borosilicate Glass
,”
J. Am. Ceram. Soc.
,
92
(
6
), pp.
1287
1295
.
14.
Anderson
,
C.
Jr.
,
Weiss
,
C.
, and
Chocron
,
S.
, 2009, “
Impact Experiments into Borosilicate Glass at Three Scale Sizes
,”
Southwest Research Institute
, San Antonio, TX, Technical Report No. 18.12544/018.
15.
Sun
,
X.
,
Khaleel
,
M.
, and
Davies
,
R.
, 2005, “
Modeling of Stone-Impact Resistance of Monolithic Glass Ply using Continuum Damage Mechanics
,
Int. J. Damage Mech.
,
14
, pp.
165
178
.
16.
Wereszczak
,
A. A.
,
Kirkland
,
T. P.
,
Ragan
,
M. E.
,
Strong
,
K. T.
, Jr.
, and
Lin
,
H.
, 2010, “
Size Scaling of Tensile Failure Stress in a Float Soda-Lime-Silicate Glass
,”
International Journal of Applied Glass Science
,
1
(
2
), pp.
143
150
.
17.
Chocron
,
S.
,
Anderson
,
C. E.
, Jr.
,
Nicholls
,
E.
, and
Dannemann
,
K. A.
, “
Characterization of Confined Intact and Damaged Borosilicate Glass
,”
J. Am. Ceram. Soc.
(to be published).
18.
Simha
,
C.
and
Gupta
,
Y.
, 2004, “
Time-Dependent Inelastic Deformation of Shocked Soda-Lime Glass
,”
J. Appl. Phys.
,
96
(
4
), pp.
1880
1890
.
19.
Sundaram
,
S.
, 1993, “
Pressure-Shear Plate Impact Studies of Alumina Ceramics and the Influence of an Intergranular Glassy Phase
,” Ph.D. thesis, Brown University, Providence, RI.
20.
Cagnoux
,
J.
, 1982, “
Shock-Wave Compression of a Borosilicate Glass up to 170 kbar
,” Shock Compression of Condensed Matter-1982, pp.
392
296
.
21.
Alexander
,
C. S.
,
Chhabildas
,
L. C.
,
Reinhart
,
W. D.
, and
Templeton
,
D. W.
, 2008, “
Changes to the Shock Response of Fused Quartz due to Glass Modification
,”
International Journal of Impact Engineering
,
35
, pp.
1376
1385
.
22.
Handin
,
J.
,
Heard
,
H. C.
, and
Magouirk
,
J. N.
, 1967, “
Effects of the Intermediate Principal Stress on the Failure of Limestone, Dolomite, and Glass at Different Temperatures and Strain Rates
,”
J. Geophys. Res.
,
72
(
2
), pp.
611
640
.
23.
Chen
,
W.
, 2010, Purdue University, private communication.
24.
Glenn
,
L. A.
,
Moran
,
B.
, and
Kusubov
,
A. S.
, 1990, “
Modeling Jet Penetration in Glass
,”
Lawrence Livermore National Laboratory
, CA., Technical Report No. UCRL-JC-103512.
25.
Behner
,
T.
,
Anderson
,
C.
, Jr.
,
Orphal
,
D.
,
Hohler
,
V.
,
Moll
,
M.
, and
Templeton
,
D.
, 2008, “
Penetration and Failure of Lead and Borosilicate Glass against Rod Impact
,”
International Journal of Impact Engineering
,
35
, pp.
447
456
.
26.
Anderson
,
C. E.
, Jr.
,
Behner
,
Th.
,
Holmquist
,
T. J.
,
Wickert
,
M.
,
Hohler
,
V.
, and
Templeton
,
D. W.
, 2007, “
Interface Defeat of Long Rods Impacting Borosilicate Glass
,”
Proceedings of the 23rd International Symposium on Ballistics
,
Tarragona, Spain
, pp.
1049
1056
.
27.
Johnson
,
G. R.
,
Holmquist
,
T. J.
, and
Beissel
,
S. R.
, 2003, “
Response of Aluminum Nitride (Including a Phase Change) to Large Strains, High Strain Rates, and High Pressures
,”
J. Appl. Phys.
,
94
(
3
), pp.
1639
1646
.
28.
Frank
,
A.
and
Adley
,
M.
, 2007, “
On the Importance of a Three-Invariant Model for Simulating the Perforation of Concrete Targets
,”
Proceedings from the 78th Shock and Vibration Symposium
,
Philadelphia, PA
.
29.
Johnson
,
G. R.
and
Holmquist
,
T. J.
, 1994, “
An Improved Computational Constitutive Model for Brittle Materials
,”
High Pressure Science and Technology–1993
,
S. C.
Schmidt
,
J. W.
Schaner
,
G. A.
Samara
, and
M.
Ross
, eds.,
AIP
,
New York
, pp.
981
984
.
30.
Johnson
,
G. R.
,
Stryk
,
R. A.
,
Holmquist
,
T. J.
, and
Beissel
,
S. R.
, 1997, “
Numerical Algorithms in a Lagrangian Hydrocode
,”
Wright Laboratory
, FL, Technical Report No. WL-TR-1997-7039.
31.
Johnson
,
G. R.
,
Beissel
,
S. R.
, and
Stryk
,
R. A.
, 2002, “
An Improved Generalized Particle Algorithm that Includes Boundaries and Interfaces
,”
Int. J. Numer. Methods Eng.
,
53
, pp.
875
904
.
32.
Johnson
,
G. R.
,
Stryk
,
R. A.
,
Beissel
,
S. R.
, and
Holmquist
,
T. J.
, 2002, “
Conversion of Finite Elements into Meshless Particles for Penetration Computations Involving Ceramic Targets
,”
Shock Compression of Condensed Matter–2001
,
M. D.
Furnish
,
N. N.
Thadhani
, and
Y.
Horie
, eds.,
AIP
,
New York
.
You do not currently have access to this content.