Abstract
Damage modeling of metallic materials under high strain rate loading conditions is reviewed. The emphasis is on the modeling efforts based on continuum damage mechanics, although many important references dealing with general aspects of dynamic behavior of materials are also discussed. Relevant issues on the use of continuum damage mechanics and on the damage modeling of composites are addressed as well. This review article deals with 134 references
Issue Section:
Review
Articles
1.
Johnson W (1972), Impact Strength of Materials, Edward Arnold, London.
2.
Nicholas T and Recht RF (1990), Introduction to impact phenomena, High Velocity Impact Dynamics, JA Zukas (eds), John Wiley & Sons, New York, 1–63.
3.
Meyers MA (1994), Dynamic Behavior of Materials, Wiley & Sons, New York.
4.
Clifton
RJ
(2000
), Response of materials under dynamic loading
, Int. J. Solids Struct.
37
, 105
–113
.5.
Nicholas T (1982), Material behavior at high strain rates, Impact Dynamics, JA Zukas, et al. (eds), John Wiley & Sons, New York, 277–332.
6.
Nicholas T and Rajendran AM (1990), Material characterization at high strain rates, High Velocity Impact Dynamics, JA Zukas (ed), John Wiley & Sons, New York, 127–296.
7.
Regazzoni
G
, Johnson
JN
, and Follansbee
PS
(1986
), Theoretical study of the dynamic tension test
, ASME J. Appl. Mech.
53
, 519
–528
.8.
Ravid
M
, Bodner
SR
, and Holcman
I
(1987
), Analysis of very high speed impact
, Int. J. Eng. Sci.
, 25
, 473
–482
.9.
Dudzinski D, Majdoubi ME, and Molinari A (1992), Plastic flow localization at high strain rates, Shock-Wave and High-Strain-Rate Phenomena in Materials, MA Meyers, et al. (eds), Marcel Dekker, New York, 193–201.
10.
Zhao
H
, and Gary
G
(1995
), A three dimensional analytical solution of the longitudinal wave propagation in an infinite linear viscoelastic cylindrical bar: Application to experimental techniques
, J. Mech. Phys. Solids
43
, 1335
–1348
.11.
Zukas JA (1982a), Numerical simulation of impact phenomena, Impact Dynamics, JA Zukas et al. (eds), John Wiley & Sons, New York, 367–417.
12.
Zukas JA (1982b), Three-dimensional computer codes for high velocity impact simulation, Impact Dynamics, JA Zukas et al. (eds), John Wiley & Sons, New York, 419–447.
13.
Anderson
CE
, Cox
PA
, Johnson
GR
, and Maudlin
PJ
(1994
), A constitutive formulation for anisotropic materials suitable for wave propagation computer programs-II
, Comput. Mech.
15
, 201
–223
.14.
Zukas JA (1990), Survey of computer codes for impact simulation, High Velocity Impact Dynamics, JA Zukas (ed), John Wiley & Sons, New York, 593–714.
15.
Wilkins ML (1999), Computer Simulation of Dynamic Phenomena, Springer, Berlin.
16.
Nemat-Nasser S (1992), Dynamic deformation and failure, Shock-Wave and High-Strain-Rate Phenomena in Materials, MA Meyers et al. (eds), Marcel Dekker, New York, 3–19.
17.
Nemat-Nasser S (2000), Recovery Hopkinson bar techniques, ASM Handbook, Vol 8, Mechanical Testing and Evaluation, H Kuhn and D Medlin (eds), ASM Int, Materials Park OH, 477–487.
18.
Noble
JP
, Goldthorpe
BD
, Church
P
, and Harding
J
(1999
), The use of the Hopkinson bar to validate constitutive relations at high rates of strain
, J. Mech. Phys. Solids
47
, 1187
–1206
.19.
Gray GT (2000), Classic Split-Hopkinson pressure bar testing, ASM Handbook, Vol 8, Mechanical Testing and Evaluation, H Kuhn and D Medlin (eds), ASM Int Materials Park OH, 462–476.
20.
Gray GT and Blumenthal WR (2000), Split-Hopkinson pressure bar testing of soft materials, ASM Handbook, Vol 8, Mechanical Testing and Evaluation, H Kuhn and D Medlin (eds), ASM Int, Materials Park OH, 488–496.
21.
Subhash G and Ravichandran G (2000), Split-Hopkinson pressure bar for testing of ceramics, ASM Handbook, Vol 8, Mechanical Testing and Evaluation, H Kuhn and D Medlin (eds), ASM Int, Materials Park OH, 497–504.
22.
Field
JE
, Walley
SM
, Bourne
NK
, and Huntley
JM
(1994
), Experimental methods at high rates of strain
, J. Phys. IV
4
(C8
), 3
–22
.23.
Field JE, Walley SM, Bourne NK, and Huntley JM (1998), Review of experimental techniques for high rate deformation studies, Proc of 1998 Asian Acoustics and Vibrations Conf, Singapore, Nov 1998, 9–38.
24.
Subhash G (2000), Dynamic indentation testing, ASM Handbook, Vol 8, Mechanical Testing and Evaluation, H Kuhn and D Medlin (eds), ASM Int, Materials Park OH, 519–529.
25.
Voyiadjis GZ and Kattan P (1999), Advances in Damage Mechanics: Metals and Metal Matrix Composites, Elsevier, Oxford.
26.
Bruhns
OT
and Diehl
H
(1989
), An internal variable theory of inelastic behavior at high rates of strain
, Arch. Mech.
41
, 427
–460
.27.
Harding J Ed (1974), Mechanical Properties at High Rates of Strain, Conf Series No. 21, Institute of Physics, London.
28.
Harding J (ed) (1979), Mechanical Properties at High Rates of Strain, Conf Series No. 47, Ins of Physics, London.
29.
Harding J (ed) (1984), Mechanical Properties at High Rates of Strain, Conf Series No. 70, Inst of Physics, London.
30.
Harding J (ed) (1989), Mechanical Properties of Materials at High Rates of Strain, Conf Series No. 102, Inst of Physics, London.
31.
Meyers MA and Murr L (eds) (1981), Shock Waves and High-Strain-Rate Phenomena in Metals, Plenum Press, New York.
32.
Meyers MA, Murr LE, and Staudhammer KP (eds) (1992), Shock-Wave and High-Strain-Rate Phenomena in Materials, Marcel Dekker, New York.
33.
Kawata K and Shioiri J (eds) (1996), Constitutive Relation in High/Very High Strain Rates, Springer-Verlag, Tokyo.
34.
Woodward RL (1990), Material failure at high strain rates, High Velocity Impact Dynamics, JA Zukas (ed), John Wiley & Sons, New York, 65–125.
35.
Valanis
KC
(1990
), Back stress and Jaumann rates in finite plasticity
, Int. J. Plast.
6
, 353
–367
.36.
Benallal
A
, Billardon
R
, and Lemaitre
J
(1991
), Continuum damage mechanics and local approach to fracture: numerical procedures
, Comput. Methods Appl. Mech. Eng.
92
, 141
–155
.37.
Kachanov
M
(1992
), Effective elastic properties of cracked solids: critical review of some basic concepts
, Appl. Mech. Rev.
45
, 304
–335
.38.
Petrova
V
, Tamuzs
V
, and Romalis
N
(2000
), A survey of macro-microcrack interaction problems
, Appl. Mech. Rev.
53
, 117
–146
.39.
Curran
DR
, Seaman
L
, and Shockey
DA
(1987
), Dynamic failure of solids
, Phys. Rep.
147
, 253
–388
.40.
Rosakis
AJ
, and Ravichandran
G
(2000
), Dynamic failure mechanics
, Int. J. Solids Struct.
37
, 331
–348
.41.
Cho K, Lee S, and Won B (1993), Formation of adiabatic shear band in AL-SiCw metal matrix, Proc of Int Conf on Adv Composite Materials, Feb 1993, Aust, 1265–1269.
42.
Ireck
E
, Heinol
C
, Clayton
T
, Hashemi
J
, Cardenas-Garcia
JF
, and Sadhneni
R
(1995
), Numerical and experimental investigation of adiabatic shear bands in metal under low-velocity impact conditions
, J. Mater. Eng. Perform.
4
, 709
–716
.43.
Lebourier
A
, Lipinski
P
, and Molinari
A
(2000
), Numerical study of the propagation of an adiabatic shear band
, J. Phys. (France)
10
, 403
–408
.44.
Clos
R
, Schreppel
U
, and Viet
P
(2000
), Experimental investigation of adiabatic shear band formation in steels
, J. Phys. (France)
10
, 257
–262
.45.
Molinari
A
(1997
), Collective behavior and spacing of adiabatic shear band
, J. Mech. Phys. Solids
45
, 1551
–1575
.46.
Perez-Prado
MT
(2001
), Micro structural evolution in adiabatic shear bands in Ta and Ta-W alloys
, Acta Mater.
49
, 2905
–2917
.47.
Grady
DE
(1988
), The spall strength of condensed matter
, J. Mech. Phys. Solids
36
, 353
–384
.48.
Meyers
MA
and Aimone
CT
(1983
), Dynamic fracture (spalling) of metals
, Prog. Mater. Sci.
28
, 1
–96
.49.
Bai
Y
, Bai
J
, Li
HL
, Ke
FJ
, and Xia
MF
(2000
), Damage evolution, localization and failure of solids subjected to impact loading
, Int. J. Impact Eng.
24
, 685
–701
.50.
Bai YL and Dodd B (1992), Adiabatic Shear Localization, Pergamon, Oxford.
51.
Bodner SR (1988), Material modeling at high rates of strain, Impact Loading and Dynamic Behavior of Materials, CY Chiem et al. (eds), Vol 1, Informationsgesellschaft, Verlag, Germany, 77–92.
52.
Harding J (1988), Material behavior at high rates of strain, Impact Loading and Dynamic Behavior of Materials, CY Chiem et al. (eds), Vol 1, Informationsgesellschaft, Verlag, Germany, 23–42.
53.
Chiem CY (1992), Material deformation at high strain rate, Shock-Wave and High-Strain-Rate Phenomena in Materials, MA Meyers et al. (eds), Marcel Dekker, New York, 69–85.
54.
Meyer LW (1992), Constitutive equations at high strain rates, Shock-Wave and High-Strain-Rate Phenomena in Materials, MA Meyers et al. (eds), Marcel Dekker, New York, 49–68.
55.
Radchenko
AV
, Kobenko
SV
, Marzenyuk
IN
, Khorev
IE
, Kanel
GI
, and Fortov
VE
(1999
), Research on features of behavior of isotropic and anisotropic materials under impact
, Int. J. Impact Eng.
23
, 745
–756
.56.
Gurson
AL
(1977
), Continuum theory of ductile rupture by void nucleation and growth: Part I-Yield criteria and flow rules for porous ductile media
, ASME J. Eng. Mater. Technol.
99
, 2
–15
.57.
Tvergaard
V
(1990
), Material failure by void coalescence
, Adv. Appl. Mech.
27
, 83
–151
.58.
Wang
ZP
and Jiang
Q
(1997
), A yield criterion for porous ductile media at high strain rate
, ASME J. Appl. Mech.
64
, 503
–509
.59.
Wang
ZP
(1997
), Void-containing nonlinear materials subject to high-rate loading
, J. Appl. Phys.
81
, 7213
–7227
.60.
Pardoen
T
and Hutchinson
JW
(2000
), An extended model for void growth and coalescence
, J. Mech. Phys. Solids
48
, 2467
–2512
.61.
Li
QM
(2000
), Energy correlations between a damaged macroscopic continuum and its subscale
, Int. J. Solids Struct.
37
, 4539
–4556
.62.
Coleman
BD
and Gurtin
ME
(1967
), Thermodynamics with internal state variables
, J. Chem. Phys.
47
, 597
–613
.63.
Rice
JR
(1971
), Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity
, J. Mech. Phys. Solids
19
, 433
–455
.64.
Lubliner
J
(1972
), On the thermodynamic foundations of non-linear solid mechanics
, Int. J. Non-Linear Mech.
7
, 237
–254
.65.
Germain
P
, Nguyen
QS
, and Suquet
P
(1983
), Continuum thermodynamics
, ASME J. Appl. Mech.
50
, 1010
–1020
.66.
Li
QM
(1999
), Dissipative flow model based on dissipative surface and irreversible thermodynamics
, Arch. Appl. Mech.
69
, 379
–392
.67.
Murakami
S
(1988
), Mechanical modeling of material damage
, ASME J. Appl. Mech.
55
, 280
–286
.68.
Krajcinovic
D
(1984
), Continuum damage mechanics
, Appl. Mech. Rev.
37
, 1
–6
.69.
Krajcinovic
D
(1989
), Damage mechanics
, Mech. Mater.
8
, 117
–197
.70.
Krajcinovic
D
(2000
), Damage mechanics: accomplishments, trends and needs
, Int. J. Solids Struct.
37
, 267
–277
.71.
Chaboche
JL
(1988
), Continuum damage mechanics: Part I-General concepts
, ASME J. Appl. Mech.
55
, 59
–64
.72.
Chaboche
JL
(1988
), Continuum damage mechanics: Part II-Damage growth, crack initiation, and crack growth
, ASME J. Appl. Mech.
55
, 65
–72
.73.
Murakami
S
and Liu
Y
(1996
), Local approach of fracture based on continuum damage mechanics and the related problems
, Mater. Sci. Res. Int.
2
, 131
–142
.74.
Lemaitre J and Chaboche JL (1990), Mechanics of Solid Materials, Ch 7, Cambridge Univ. Press, Cambridge, 346–450.
75.
Krajcinovic D (1996), Damage Mechanics, North-Holland, Amsterdam.
76.
Valanis
KC
(1966
), Some exact wave propagation solutions in viscoplastic materials
, Iowa State Univ Bull
, 65
Ames, Iowa.77.
Baste
S
and Audoin
B
(1991
), On internal variables in anisotropic damage
, Eur. J. Mech. A/Solids
10
, 587
–606
.78.
Voyiadjis
GZ
and Deliktas
B
(2000
), A coupled anisotropic damage model for the inelastic response of composite materials
, Comput. Methods Appl. Mech. Eng.
183
, 159
–199
.79.
Krajcinovic
D
and Mastilovic
S
(1995
), Some fundamental issues of damage mechanics
, Mech. Mater.
21
, 217
–230
.80.
Budiansky
B
and O’Connell
R
(1976
), Elastic moduli of cracked solids
, Int. J. Solids Struct.
12
, 81
–97
.81.
Cauvin
A
and Testa
RB
(1999
), Damage mechanics: basic variables in continuum theories
, Int. J. Solids Struct.
36
, 747
–761
.82.
Onat
ET
and Leckie
FA
(1988
), Representation of mechanical behavior in the presence of changing internal structure
, ASME J. Appl. Mech.
55
, 1
–10
.83.
Ju
JW
(1990
), Isotropic and anisotropic damage variables in continuum damage mechanics
, J. Eng. Mech. Div.
116
, 2764
–2770
.84.
Pijaudier-Cabot G (1995), Non-local damage, Continuum Models for Materials with Microstructure, H-B Mu¨hlhaus (ed), John Wiley, New York, 105–143.
85.
Aifantis
EC
(1984
), On the micro structural origin of certain inelastic models
, ASME J. Eng. Mater. Technol.
106
, 326
–330
.86.
Mu¨hlhaus
HB
and Aifantis
EC
(1991
), A variational principle for gradient plasticity
, Int. J. Solids Struct.
28
, 845
–857
.87.
Lasry
D
and Belytschko
T
(1988
), Localization limiters in transient problems
, Int. J. Solids Struct.
24
, 581
–597
.88.
de Borst
R
, Benellal
A
, and Heeres
O
(1996
), A gradient enhanced damage approach to fracture
, J. Phys. (France)
6
, 491
–502
.89.
Peerlings
RH
, de Borst
R
, Brekelmans
WA
, and de Vree
JH
(1996
), Gradient enhanced damage for quasi-brittle materials
, Int. J. Numer. Methods Eng.
39
, 3391
–3403
.90.
Kuhl E, Ramm E, and de Borst R (2000), An anisotropic gradient damage model for quasibrittle materials, Comput. Methods Appl. Mech. Eng. (in press).
91.
Valanis
KC
(1996
), Gradient theory of internal variables
, Acta Mech.
116
, 1
–23
.92.
Valanis
KC
(1998
), Gradient thermodynamic theory of self-organization
, Acta Mech.
127
, 1
–23
.93.
Zheng
QS
(1997
), A unified invariant description of micromechanically-based effective elastic properties for two-dimensional damaged solids
, Mech. Mater.
25
, 273
–289
.94.
Hansen
NR
and Schreyer
HL
(1994
), A thermodynamically consistent framework for theories of elastoplasticity coupled with damage
, Int. J. Solids Struct.
31
, 359
–389
.95.
Arnold
SM
and Saleeb
AF
(1994
), On the thermodynamic framework of generalized coupled thermoelastic-viscoplastic-damage modeling
, Int. J. Plast.
10
, 263
–278
.96.
Lubarda
VA
and Krajcinovic
D
(1995
), Some fundamental issues in rate theory of damage-elastoplasticity
, Int. J. Plast.
11
, 763
–797
.97.
Murakami
S
and Kamiya
K
(1997
), Constitutive and damage evolution equations of elastic-brittle materials based on irreversible thermodynamics
, Int. J. Mech. Sci.
39
, 473
–486
.98.
Hayakawa
K
, Murakami
S
, and Liu
Y
(1998
), An irreversible thermodynamics theory for elastic-plastic-damage materials
, Eur. J. Mech. A/Solids
17
, 13
–32
.99.
Kratzig
B
and Polling
R
(1998
), Elasto-plastic damage-theories and elasto-plastic fracturing-theories: A comparison
, Comput. Mater. Sci.
13
, 117
–131
.100.
de Borst
R
, Pamin
J
, and Geers
MGD
(1999
), On coupled gradient-dependent plasticity and damage theories with a view to localization analysis
, Eur. J. Mech. A/Solids
18
, 939
–962
.101.
Gao
XL
and Mall
S
(2000
), A two-dimensional rule-of-mixtures micromechanics model for woven fabric composites
, J. Compos. Technol. Res.
22
, 60
–70
.102.
Gao
XL
and Mall
S
(2001
), Variational solution for a cracked mosaic model of woven fabric composites
, Int. J. Solids Struct.
38
, 855
–874
.103.
Burr
A
, Hild
F
, and Leckie
FA
(1995
), Micro-mechanics and continuum damage mechanics
, Arch. Appl. Mech.
65
, 437
–456
.104.
Perzyna
P
(1986a
), Constitutive modeling for brittle dynamic fracture in dissipative solids
, Arch. Mech.
38
, 725
–738
.105.
Lacy
TE
, McDowell
DL
, and Talreja
R
(1999
), Gradient concepts for evolution of damage
, Mech. Mater.
31
, 831
–860
.106.
Voyiadjis
GZ
and Deliktas
B
(2000
), Multi-scale analysis of multiple damage mechanisms coupled with inelastic behavior of composite materials
, Mech. Res. Commun.
27
, 295
–300
.107.
Steinmann
P
and Carol
I
(1998
), A framework for geometrically nonlinear continuum damage mechanics
, Int. J. Eng. Sci.
36
, 1793
–1814
.108.
Davison
L
and Stevens
AL
(1972
), Continuum measures of spall damage
, J. Appl. Phys.
43
, 988
–994
.109.
Davison
L
and Stevens
AL
(1973
), Thermomechanical constitution of spalling elastic bodies
, J. Appl. Phys.
44
, 668
–674
.110.
Davison
L
, Stevens
AL
, and Kipp
ME
(1977
), Theory of spall damage accumulation in ductile metals
, J. Mech. Phys. Solids
25
, 11
–28
.111.
Cochran
S
and Banner
D
(1977
), Spall studies in uranium
, J. Appl. Phys.
48
, 2729
–2737
.112.
Perzyna
P
(1986b
), Internal state variable description of dynamic fracture of ductile solids
, Int. J. Solids Struct.
22
, 797
–818
.113.
Nemes
JA
, Eftis
J
, and Randles
PW
(1990
), Viscoplastic constitutive modeling of high strain-rate deformation, material damage, and spall fracture
, ASME J. Appl. Mech.
57
, 282
–291
.114.
Nemes JA and Eftis J (1992), Rate-dependent modeling of multidimensional impact and post-spall behavior, Shock-Wave and High-Strain-Rate Phenomena in Materials, MA Meyers et al. (eds), Marcel Dekker, New York, 723–731.
115.
Dornowski
W
and Perzyna
P
(1999
), Constitutive modeling of inelastic solids for plastic flow processes under cyclic dynamic loadings
, ASME J. Eng. Mater. Technol.
121
, 210
–220
.116.
Bruhns OT (1992), A continuum damage theory for high strain rate deformations of metals with application to impact problems, Proc of 6th Int Conf on Mechanical Behavior of Materials, M Jono and T Inoue (eds), Vol. 1, Pergamon, Oxford, 499–506.
117.
Bruhns
OT
and Sluzalec
A
(1989
), Thermal effects in thermoplastic metal with internal variables
, Comput. Struct.
33
, 1459
–1464
.118.
Hong HK and Chyu YA (1988), A continuum damage thermomechanics model for ductile fracture, Impact Loading and Dynamic Behavior of Materials, CY Chiem et al. (eds), Vol 1, Informationsgesellschaft, Verlag, Germany, 499–506.
119.
Kiselev
AB
and Yumashev
MV
(1991
), Deformation and failure under impact loading-model of a thermoelastoplastic medium
, J. Appl. Mech. Tech. Phys.
31
, 775
–782
.120.
Martin
JB
, Kaunda
MAE
, and Isted
RD
(1996
), Internal variable formulations of elastic-plastic dynamic problems
, Int. J. Impact Eng.
18
, 849
–858
.121.
Fahrenthold
EP
and Horban
BA
(1997
), Thermodynamics of continuum damage and fragmentation models for hypervelocity impact
, Int. J. Impact Eng.
20
, 241
–252
.122.
Borvik
T
, Hopperstad
OS
, Berstad
T
, and Langseth
M
(2001
), A computational model of viscoplasticity and ductile damage for impact and penetration
, Eur. J. Mech. A/Solids
20
, 685
–712
.123.
Johnson
G
and Cook
W
(1985
), Fracture characteristics of three metals subjected to various strain, strain rates, temperature and pressures
, Eng. Fract. Mech.
121
, 31
–48
.124.
Subhash
G
(1995
), The constitutive behavior of refractory metals as a function of strain rate
, JOM
5
, 55
–58
.125.
Koeppel
BJ
and Subhash
G
(1999
), Influence of cold rolling and strain rate on plastic response of powder metallurgy and chemical vapor deposition rhenium
, Metall. Mater. Trans. A
30
, 2641
–2648
.126.
Staehler
JM
, Predebon
WW
, Pletka
BJ
, and Subhash
G
(1995
), Strain-rate effects in high-purity alumina
, JOM
5
, 60
–63
.127.
Ravichandran
G
and Subhash
G
(1995
), A micromechanical model for high strain rate behavior of ceramics
, Int. J. Solids Struct.
32
, 2627
–2646
.128.
Naboulsi
SK
and Palazotto
AN
(2001
), Thermodynamic damage model for a composite under severe loading
, J. Eng. Mech.
126
, 1001
–1011
.129.
Olsson
R
(2001
), Analytical prediction of large mass impact damage in composite laminates
, J. Appl. Clin. Med. Phys.
19
, 322
–339
.130.
Hou
JP
, Petrinc
N
, Ruiz
C
, and Hallett
SR
(2000
), Prediction of impact damage in composite plates
, Compos. Sci. Technol.
60
, 273
–281
.131.
Pradhan
B
and Kumar
S
(2000
), Finite element analysis of low-velocity impact damage in composite plates
, Compos. Sci. Technol.
60
, 273
–281
.132.
Yang
X
and Shen
W
(1994
), An advanced dynamic three-dimensional finite element method to simulate deformation damage process of laminates under impact
, Eng. Fract. Mech.
49
, 631
–638
.133.
Luo
RK
, Green
ER
, and Morrison
CJ
(2001
), An approach to evaluate the impact damage initiation and propagation in composite plates
, Composites
B32
, 513
–520
.134.
Christoforou
AP
(2001
), Impact dynamics and damage in composite structures
, Compos. Struct.
52
(2
), 181
–188
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