The present work examines the inertial effects on void growth in viscoplastic materials which have been largely neglected in analyses of dynamic crack growth and spallation phenomena using existing continuum porous material models. The dynamic void growth in porous materials is investigated by analyzing the finite deformation of an elastic/viscoplastic spherical shell under intense hydrostatic tensile loading. Under typical dynamic loading conditions, inertia is found to have a strong stabilizing effect on void growth process and consequently to delay coalescence even when the high rate-sensitivity of materials at very high strain rates is taken into account. Effects of strain hardening and thermal softening are found to be relatively small. Approximate relations are suggested to incorporate inertial effects and rate sensitivity of matrix materials into the porous viscoplastic material constitutive models for dynamic ductile fracture analyses for certain loading conditions.

Issue Section:
Technical Papers
Topics:
Constitutive equations, Deformation, Delays, Ductile fracture, Dynamic testing (Materials), Fracture (Materials), Hydrostatics, Inertia (Mechanics), Porous materials, Spallation (Nuclear physics), Spherical shells, Work hardening
1.
Carroll
M. M.
, and
Holt
A. C.
,
1972
, “
Static and Dynamic Pore-Collapse Relations for Ductile Porous Materials
,”
Journal of Applied Physics
, Vol.
43
, pp.
1626
–
1636
.
2.
Cortes
R.
,
1992
a, “
The Growth of Microvoid Under Intense Dynamic Loading
,”
International Journal of Solids and Structures
, Vol.
29
, pp.
1339
–
1350
.
3.
Cortes
R.
,
1992
b, “
Dynamic Growth of Microvoids Under Combined Hydrostatic and Deviatoric Stresses
,”
International Journal of Solids and Structures
, Vol.
29
, pp.
1637
–
1645
.
4.
Curran
D. R.
,
Seaman
L.
, and
Shockey
D. A.
,
1987
, “
Dynamic Failure of Solids
,”
Physics Reports
, Vol.
147
, pp.
253
–
388
.
5.
Follansbee
P. S.
, and
Kocks
U. F.
,
1988
, “
A Constitutive Description of the Deformation of Copper Based on the Use of the mechanical Threshold Stress as an Internal State Variable
,”
Acta Metallurgica
, Vol.
36
, pp.
81
–
93
.
6.
Freund, B., 1990, Dynamic Fracture, Cambridge University Press, New York.
7.
Glennie
E. B.
,
1972
, “
The Dynamic Growth of a Void in a Plastic Material and An Application to Fracture
,”
Journal of the Mechanics and Physics of Solids
, Vol.
20
, pp.
415
–
429
.
8.
Godse
R.
,
Ravichandran
G.
, and
Clifton
R. J.
,
1989
, “
Micromechanisms of Dynamic Crack Propagation in an AISI 4340 Steel
,”
Materials Science & Engineering
, Vol.
A122
, pp.
79
–
88
.
9.
Gurson
A. L.
,
1977
, “
Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criterion and Flow Rules for Porous Ductile Media
,”
ASME Journal of Engineering Materials and Technology
, Vol.
99
, pp.
2
–
15
.
10.
Haghi
M.
, and
Anand
L.
,
1991
, “
Analysis of Strain-Hardening Viscoplastic Thick-Walled Sphere and Cylinder Under External Pressure
,”
International Journal of Plasticity
, Vol.
7
, pp.
123
–
140
.
11.
Hutchinson, J. W., 1987, Micro-Mechanics of Damage in Deformation and Fracture, Department of Solid Mechanics, The Technical University of Denmark, Lyngby, Denmark.
12.
Johnson
J. N.
,
1981
, “
Dynamic Fracture and Spallation in Ductile Solids
,”
Journal of Applied Physics
, Vol.
52
, pp.
2812
–
2825
.
13.
Klocker
H.
, and
Monthellet
F.
,
1991
, “
Influence of Flow Rule and Inertia on Void Growth in a Rate Sensitive Material
,”
Journal de Physique IV
, Vol.
C3
, pp.
733
–
738
.
14.
Klopp
R. W.
,
Clifton
R. J.
, and
Shawki
T. G.
,
1985
, “
Pressure-Shear Impact and the Dynamic Viscoplastic Response of Metals
,”
Mechanics & Materials
, Vol.
4
, pp.
375
–
385
.
15.
Linse, V. D., 1983, Dynamic Compaction of Metal and Ceramic Powders, NMAB-394, National Academy Press, Washington, D.C.
16.
Luk
V. K.
,
Forrestal
M. J.
, and
Amos
D. E.
,
1991
, “
Dynamic Spherical Cavity-Expansion of Strain-Hardening Materials
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
58
, pp.
1
–
6
.
17.
McClintock
F. A.
,
1968
, “
A Criterion for Ductile Fracture by Growth of Holes
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
35
, pp.
363
–
370
.
18.
Needleman
A.
, and
Tvergaard
V.
,
1991
, “
An Analysis of Dynamic, Ductile Crack Growth in a Double Edge Cracked Specimen
,”
International Journal of Fracture
, Vol.
49
, pp.
41
–
67
.
19.
Nemat-Nasser
S.
, and
Hori
M.
,
1987
, “
Void Collapse and Void Growth in Crystalline Solids
,”
Journal of Applied Physics
, Vol.
62
, pp.
2746
–
2757
.
20.
Nemes
J. A.
, and
Eftis
,
1992
, “
Pressure-Shear Waves and Spall Fracture Described by a Viscoplastic-Damage Constitutive Model
,”
International Journal of Plasticity
, Vol.
8
, pp.
185
–
207
.
21.
Ortiz
M.
, and
Molinari
A.
,
1992
, “
Effect of Strain Hardening and Rate Sensitivity on the Dynamic Growth of a Void in a Plastic Material
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
59
, pp.
48
–
53
.
22.
Perzyna
P.
,
1986
, “
Internal State Variable Description of Dynamic Fracture of Ductile Solids
,”
International Journal of Solids and Structures
, Vol.
22
, pp.
797
–
818
.
23.
Ranganath
S.
, and
Clifton
R. J.
,
1972
, “
A Second-Order Accurate Difference Method for Systems of Hyperbolic Partial Differential Equations
,”
Computer Methods in Mechanics and Engineering
, Vol.
1
, pp.
173
–
188
.
24.
Rice
J. R.
, and
Tracey
D. M.
,
1969
, “
On the Ductile Enlargement of Voids in Triaxial Stress Fields
,”
Journal of the Mechanics and Physics of Solids
, Vol.
17
, pp.
201
–
217
.
25.
Spitzig
W. A.
,
Smelser
R. E.
, and
Richmond
O.
,
1988
, “
The Evolution of Damage and Fracture in Iron Compacts with Various Initial Porosities
,”
Acta Metallurgica
, Vol.
36
, pp.
1201
–
1211
.
26.
Sun
L.
, and
Huang
Z.
,
1992
, “
Dynamic Void Growth in Rate-Sensitive Plastic Solids
,”
International Journal of Plasticity
, Vol.
8
, pp.
903
–
924
.
27.
Thadhani
N. N.
,
1988
, “
Shock Compression Processing of Powders
,”
Advances in Materials & Manufacturing Processes
, Vol.
3
, pp.
493
–
549
.
28.
Tong
W.
,
Clifton
R. J.
, and
Huang
S.
,
1992
, “
Pressure-Shear Impact Investigation of Strain Rate History Effects in Oxygen-Free High-Conductivity Copper
,”
Journal of the Mechanics and Physics of Solids
, Vol.
40
, pp.
1251
–
1294
.
29.
Tong
W.
, and
Ravichandran
G.
,
1993
a, “
Dynamic Pore Collapse in Viscoplastic Materials
,”
Journal of Applied Physics
, Vol.
74
, pp.
2425
–
2435
.
30.
Tong, W., and Ravichandran, G., 1993b, “Inertial Effects on Void Growth in Porous Viscoplastic Materials,” GALCIT Technical Report SM93-18, California Institute of Technology, Pasadena, CA.
31.
Tong, W., Ravichandran, G., Christman, T., and Vreeland, T., Jr., 1993, “Processing SiC Particulate Reinforced Titanium Metal Matrix Composites by Shock Wave Consolidation,” Acta Metallurgica et Materials, submitted for publication.
32.
Tvergaard
V.
,
1982
, “
On Localization in Ductile Materials Containing Spherical Voids
,”
International Journal of Fracture
, Vol.
18
, pp.
237
–
252
.
33.
Wilkinson
D. S.
, and
Ashby
M. F.
,
1975
, “
Pressure Sintering by Power Law Creep
,”
Acta Metallurgica
, Vol.
23
, pp.
1277
–
1285
.
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