The response of polycrystalline metals, which possess adequate mechanisms for plastic deformation under extreme loading conditions, is often accompanied by the formation of pores within the structure of the material. This large deformation process is broadly identified as progressive with nucleation, growth, coalescence, and failure the physical path taken over very short periods of time. These are well known to be complex processes strongly influenced by microstructure, loading path, and the loading profile, which remains a significant challenge to represent and predict numerically. In the current study, the influence of loading path on the damage evolution in high-purity tantalum is presented. Tantalum samples were shock loaded to three different peak shock stresses using both symmetric impact, and two different composite flyer plate configurations such that upon unloading the three samples displayed nearly identical “pull-back” signals as measured via rear-surface velocimetry. While the “pull-back” signals observed were found to be similar in magnitude, the sample loaded to the highest peak stress nucleated a connected field of ductile fracture which resulted in complete separation, while the two lower peak stresses resulted in incipient damage. The damage evolution in the “soft” recovered tantalum samples was quantified using optical metallography, electron-back-scatter diffraction, and tomography. These experiments are examined numerically through the use of a model for shock-induced porosity evolution during damage. The model is shown to describe the response of the tantalum reasonably well under strongly loaded conditions but less well in the nucleation dominated regime. Numerical results are also presented as a function of computational mesh density and discussed in the context of improved representation of the influence of material structure upon macro-scale models of ductile damage.

1.
J. S.
Rinehart
and
J.
Pearson
,
Behavior of Metals under Impulsive Loads
(
American Society for Metals
,
Cleveland, OH
,
1954
).
2.
J. N.
Johnson
, “
Dynamic fracture and spallation in ductile solids
,”
J. Appl. Phys.
52
,
2812
(
1981
).
3.
M. A.
Meyers
and
C. T.
Aimone
, “
Dynamic fracture (spalling) of metals
,”
Prog. Mater. Sci.
28
,
1
96
(
1983
).
4.
G. T.
Gray
 III
,
N. K.
Bourne
, and
B. L.
Henrie
, “
On the influence of loading profile upon the tensile failure of stainless steel
,”
J. Appl. Phys.
101
,
093507
(
2007
).
5.
J. S.
Rinehart
, “
Scabbing of metals under explosive attack: Multiple scabbing
,”
J. Appl. Phys.
23
,
1229
(
1952
).
6.
B. M.
Butcher
,
L. M.
Barker
,
D. E.
Munson
, and
C. D.
Lundergan
, “
Influence of stress history on time-dependent spall in metals
,”
AIAA J.
2
,
977
990
(
1964
).
7.
J. P.
Escobedo
,
E. N.
Brown
,
C. P.
Trujillo
,
E. K.
Cerreta
, and
G. T.
Gray
 III
, “
The effect of shock-wave profile on dynamic brittle failure
,”
J. Appl. Phys.
113
,
103506
(
2013
).
8.
G. T.
Gray
 III
, “
High-strain-rate deformation: mechanical behavior and deformation substructures induced
,”
Annu. Rev. Mater. Res.
42
,
285
303
(
2012
).
9.
S. R.
Chen
and
G. T.
Gray
 III
, “
Constitutive behavior of tantalum and tantalum-tungsten alloys
,”
Metall. Mater. Trans. A
27A
,
2994
3006
(
1996
).
10.
J. N.
Johnson
,
G. T.
Gray
 III
, and
N. K.
Bourne
, “
Effect of pulse duration and strain rate on incipient spall fracture in copper
,”
J. Appl. Phys.
86
,
4892
4901
(
1999
).
11.
F. L.
Addessio
and
J. N.
Johnson
, “
Rate-dependent ductile failure model
,”
J. Appl. Phys.
74
,
1640
1648
(
1993
).
12.
A. L.
Gurson
, “
Continuum theory of ductile rupture by void nucleation and growth: Part 1—yield criteria and flow rules for porous ductile media
,”
J. Eng. Mater. Technol.
99
,
2
15
(
1977
).
13.
P. J.
Maudlin
,
E. N.
Harstad
,
T. A.
Mason
,
Q. H.
Zuo
, and
F. L.
Addessio
, “
TEPLA-a: Coupled anisotropic elastoplasticity and damage
,”
The Joint DoD/DOE Munitions Technology Program progress report, LA-UR-14015-PR
(
2003
).
14.
Q. H.
Zuo
and
J. R.
Rice
, “
An implicit algorithm for a rate-dependent ductile fracture model
,”
J. Appl. Phys.
104
,
083526
(
2008
).
15.
G. T.
Gray
 III
,
V.
Livescu
,
E. K.
Cerreta
,
T. A.
Mason
,
P. J.
Maudlin
, and
J. A.
Bingert
, “
Influence of shockwave obliquity on deformation twin formation in Ta
,” in
DYMAT 2009: 9th International Conference on the Mechanical and Physical Behaviour of Materials Under Dynamic Loading
(
EDP Sciences
,
Brussels, Belgium
,
2009
), p.
963
.
16.
B. J.
Jensen
,
D. B.
Holtkamp
,
P. A.
Rigg
, and
D. H.
Dolan
, “
Accuracy limits and window corrections for photon Doppler velocimetry
,”
J. Appl. Phys.
101
,
013523
(
2007
).
17.
G. T.
Gray
 III
, “
Shock wave testing of ductile materials
,” in
ASM Handbook
(
Materials Park
,
Ohio
,
2000
).
18.
B. L.
Adams
,
S. I.
Wright
, and
K.
Kunze
, “
Orientation imaging—the emergence of a new microscopy
,”
Metall. Trans. A
24A
,
819
831
(
1993
).
19.
S. A.
Novikov
,
I. I.
Divnov
, and
A. G.
Ivanov
, “
Failure of steel, aluminum and copper under explosive shock loading
,”
Phys. Met. Metall.
21
,
122
128
(
1966
).
20.
G. I.
Kanel
, “
Distortion of the wave profiles in an elastoplastic body upon spalling
,”
J. Appl. Mech. Tech. Phys.
42
,
358
(
2001
).
21.
G. T.
Gray
 III
and
K. S.
Vecchio
, “
Influence of peak pressure and temperature on the structure/property response of shock-loaded Ta and Ta-10W
,”
Metall. Mater. Trans. A
26A
,
2555
(
1995
).
22.
P. J.
Maudlin
,
J. F.
Bingert
,
J. W.
House
, and
S. R.
Chen
, “
On the modeling of the Taylor cylinder impact test for orthotropic textured materials: Experiments and simulations
,”
Int. J. Plast.
15
,
139
166
(
1999
).
23.
Q. H.
Zou
, “
Modified formulation of a rate-dependent damage model for ductile materials
,”
J. Appl. Phys.
107
,
053513
(
2010
).
24.
J. W.
Hancock
and
A. C.
Mackenzie
, “
On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states
,”
J. Mech. Phys. Solids
24
,
147
169
(
1976
).
25.
S.
Nemat-Nasser
and
J. B.
Isaacs
, “
Direct measurement of isothermal flow stress of metals at elevated temperatures and high strain rates with application to Ta and Ta-W alloys
,”
Acta. Mater.
45
,
907
919
(
1997
).
26.
M.
Kothari
and
L.
Anand
, “
Elasto-viscoplastic constitutive equations for polycrystalline metals: application to tantalum
,”
J. Mech. Phys. Solids
46
,
51
83
(
1998
).
27.
C. A.
Bronkhorst
,
E. K.
Cerreta
,
Q.
Xue
,
P. J.
Maudlin
,
T. A.
Mason
, and
G. T.
Gray
 III
, “
An experimental and numerical study of the localization behavior of tantalum and stainless steel
,”
Int. J. Plast.
22
,
1304
1335
(
2006
).
28.
C. A.
Bronkhorst
,
B. L.
Hansen
,
E. K.
Cerreta
, and
J. F.
Bingert
, “
Modeling the microstructural evolution of metallic polycrystal materials under localization conditions
,”
J. Mech. Phys. Solids
55
,
2351
2383
(
2007
).
29.
U. F.
Kocks
,
A. S.
Argon
, and
M. F.
Ashby
, “
Thermodynamics and kinetics of slip
,” in
Progress in Materials Science
(
Pergamon
,
Oxford
,
1975
).
30.
P. S.
Follansbee
and
U. F.
Kocks
, “
A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable
,”
Acta Metall.
36
,
81
93
(
1988
).
31.
Y. P.
Varshni
, “
Temperature dependence of the elastic constants
,”
Phys. Rev. B
2
,
3952
3958
(
1970
).
32.
U. F.
Kocks
, “
Laws for work-hardening and low-temperature creep
,”
J. Eng. Mater. Technol.
98
,
76
85
(
1976
).
33.
G. R.
Johnson
and
W. H.
Cook
, “
A constitutive model and data for metals subjected to large strains, high strain rates, and high temperatures
,” in
Seventh International Symposium on Ballistics
(
The Hague
,
The Netherlands
, April
1983
).
34.
T. A.
Mason
and
P. J.
Maudlin
, “
Effects of higher-order anisotropy elasticity using textured polycrystals in three-dimensional wave propagation problems
,”
Mech. Mater.
31
,
861
882
(
1999
).
35.
LASL Shock Hugoniot Data
, edited by
S. P.
Marsh
(
Univ. Calif. Press
,
Berkeley, CA
,
1980
), p.
136
.
36.
S.
Crockett
,
private communication
(
2013
).
37.
Metals Handbook
, Desk edition, edited by
H. E.
Boyer
and
T. L.
Gall
(
ASM
,
Metals Park, OH
,
1985
).
38.
T. A.
Mason
, private communication (
2004
).
39.
G. R.
Johnson
,
S. R.
Beissel
,
C. A.
Gerlach
,
R. A.
Stryk
,
T. J.
Holmquist
,
A. A.
Johnson
,
S. E.
Ray
, and
J. J.
Arata
,
User Instructions for the 2006 Version of the EPIC Code
(
Network Computing Services Inc.
,
Minneapolis, MN
,
2006
).
40.
T.
Belytschko
,
W. K.
Liu
,
B.
Moran
, and
K. I.
Elkhodary
,
Nonlinear Finite Elements for Continua and Structures
(
John Wiley & Sons
,
West Sussex, UK
,
2014
).
41.
F. R.
Ahad
,
K.
Enakoutsa
,
K. N.
Solanski
, and
D. J.
Bammann
, “
Nonlocal modeling in high-velocity impact failure of 6061-T6 aluminum
,”
Int. J. Plast.
55
,
108
132
(
2014
).
42.
L.
Anand
,
O.
Aslan
, and
S. A.
Chester
, “
A large-deformation gradient theory for elastic-plastic materials: Strain softening and regularization of shear bands
,”
Int. J. Plast.
30–31
,
116
143
(
2012
).
43.
R.
Becker
, “
Ring fragmentation predictions using the Gurson model with material stability conditions as failure criteria
,”
Int. J. Solids Struct.
39
,
3555
3580
(
2002
).
44.
C.
Czarnota
,
N.
Jacques
,
S.
Mercier
, and
A.
Molinari
, “
Modeling of dynamic ductile fracture and application to the simulation of plate impact tests on tantalum
,”
J. Mech. Phys. Solids
56
,
1624
1650
(
2008
).
45.
G. T.
Gray
 III
,
N. K.
Bourne
,
V.
Livescu
,
C. P.
Trujillo
,
S.
MacDonald
, and
P.
Withers
, “
The influence of shock-loading path on the spallation response of Ta
,” in
Proceedings of APS Topical Group of Shock Compression of Condensed Matter
, Seattle, 7–12 July
2013
.
46.
S. A.
Maloy
,
G. T.
Gray
 III
,
C. M.
Cady
,
R. W.
Rutherford
, and
R. S.
Hixson
, “
The influence of explosive-driven “Taylor-wave” shock prestraining on the structure\property behavior of 304 stainless steel
,”
Metall. Mater. Trans. A
35A
,
2617
(
2004
).
47.
B. H.
Sencer
,
S. A.
Maloy
, and
G. T.
Gray
 III
, “
The influence of explosive-driven shock prestraining at 35 GPa and of high deformation on the structure/property behavior of 316L austenitic stainless steel
,”
Metall. Mater. Trans. A
36A
,
1825
(
2005
).
48.
B. H.
Sencer
,
S. A.
Maloy
, and
G. T.
Gray
 III
, “
The influence of shock-pulse shape on the structure/property behavior of copper and 316L austenitic stainless steel
,”
Acta Mater.
53
,
3293
(
2005
).
49.
Q.
Xue
,
G. T.
Gray
 III
,
B. L.
Henrie
,
S. A.
Maloy
, and
S. R.
Chen
, “
Influence of shock prestraining on the formation of shear localization in 304 stainless steel
,”
Metall. Mater. Trans. A
36A
,
1471
(
2005
).
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