Various fracture criteria, based on different assumptions and different mechanical models, have been proposed in the past to predict ductile fracture. The objective of this study is to assess their effectiveness and accuracy in a wide range of process parameters. A series of tests on 2024-T351 aluminum alloy, including upsetting tests and tensile tests is carried out. It is found that none of the existing fracture criteria give consistent results. Two totally different fracture mechanisms are clearly observed from microfractographs of upsetting and tensile specimens. This observation confirms that it is impossible to capture all features of ductile crack formation in different stress states with a single criterion. It is shown that different functions are necessary to predict crack formation for different ranges of stress triaxiality. Weighting functions in a wide range of stress states can be obtained by determining the fracture locus in the space of equivalent strain to fracture and stress triaxiality.

1.
Gurson, A. L., 1975, “
Plastic Flow and Fracture Behavior of Ductile Materials Incorporating Void Nucleation, Growth and Interaction,” Brown University, Ph.D. Thesis.
2.
Gurson
,
A. L.
,
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
, pp.
2
15
.
3.
Tvergaard
,
V.
,
1981
, “
Influence of Voids on Shear Band Instabilities Under Plane Strain Conditions
,”
Int. J. Fract.
,
18
, pp.
237
252
.
4.
Tvergaard
,
V.
,
1982
, “
On Localization in Ductile Materials Containing Spherical Voids
,”
Int. J. Fract.
,
17
, pp.
389
407
.
5.
Tvergaard
,
V.
, and
Needleman
,
A.
,
1984
, “
Analysis of the Cup-Cone Fracture in a Round Tensile Bar
,”
Acta Metall.
,
32
, pp.
157
169
.
6.
Besson
,
J.
,
Steglich
,
D.
, and
Brocks
,
W.
,
2001
, “
Modeling of Crack Growth in Round Bars and Plane Strain Specimens
,”
Int. J. Solids Struct.
,
38
, pp.
8259
8284
.
7.
Faleskog
,
J.
,
Gao
,
X.
, and
Shih
,
C. F.
,
1998
, “
Cell Model for Nonlinear Fracture Analysis—I. Micromechanics calibration
,”
Int. J. Fract.
,
89
, pp.
355
373
.
8.
Gao
,
X.
,
Faleskog
,
J.
, and
Shih
,
C. F.
,
1998
, “
Cell Model for Nonlinear Fracture Analysis—II. Fracture-Process Calibration and Verification
,”
Int. J. Fract.
,
89
, pp.
375
398
.
9.
Kachanov
,
L. M.
,
1958
, “
Time of the Rupture Process Under Creep Conditions
,”
IZV Akad Nauk S.S.R., Otd. Tekhn. Nauk
,
8
, pp.
26
31
.
10.
Lemaitre
,
J.
,
1985
, “
A Continuous Damage Mechanics Model for Ductile Fracture
,”
ASME J. Eng. Mater. Technol.
,
107
, pp.
83
89
.
11.
Wang
,
T. J.
,
1992
, “
Unified CDM Model and Local Criterion for Ductile Fracture-I. Unified CDM Model for Ductile Fracture
,”
Eng. Fract. Mech.
,
42
, pp.
177
183
.
12.
Dhar
,
S.
,
P. M.
D.
, and
Sethuraman
,
R.
,
2000
, “
A Continuum Damage Mechanics Model for Ductile Fracture
,”
Int. J. Pressure Vessels Piping
,
77
, pp.
335
344
.
13.
Barenblatt
,
G. I.
,
1962
, “
The Mathematical Theory of Equilibrium Cracks in Brittle Fracture
,”
Adv. Appl. Mech.
,
7
, pp.
55
129
.
14.
Hillerborg
,
A.
,
Modeer
,
M.
, and
Petersson
,
P. E.
,
1976
, “
Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements
,”
Cem. Concr. Res.
,
6
, pp.
773
782
.
15.
Needleman
,
A.
,
1990
, “
An Analysis of Decohesion Along an Imperfect Interface
,”
Int. J. Fract.
,
42
, pp.
21
40
.
16.
Tvergaard
,
V.
, and
Hutchinson
,
J. W.
,
1996
, “
Effect of Strain-Dependent Cohesive Zone Model on Predictions of Crack Growth Resistance
,”
Int. J. Solids Struct.
,
33
, pp.
3297
3308
.
17.
Que
,
N. S.
, and
Tin-Loi
,
F.
,
2002
, “
Numerical Evaluation of Cohesive Fracture Parameters From a Wedge Splitting Test
,”
Eng. Fract. Mech.
,
69
, pp.
1269
1286
.
18.
Elices
,
M.
,
Guinea
,
G. V.
,
Gomez
,
J.
, and
Planas
,
J.
,
2002
, “
The Cohesive Zone Model: Advantages, Limitations and Challenges
,”
Eng. Fract. Mech.
,
69
, pp.
137
163
.
19.
Tvergaard
,
V.
,
2001
, “
Resistance Curves for Mixed More Interface Crack Growth Between Dissimilar Elastic-Plastic Solids
,”
J. Mech. Phys. Solids
,
49
, pp.
2689
2703
.
20.
Siegmund
,
T.
, and
Brocks
,
W.
,
1999
, “
Prediction of the Work of Separation and Implications to Modeling
,”
Int. J. Fract.
,
99
, pp.
97
116
.
21.
Scheider, I., 2001, “Simulation of Cup-Cone Fracture in Round Bars Using the Cohesive Zone Model,” in First MIT Conference on Computational Fluid and Solid Mechanics, K. J. Bathe, ed. Elsevier, Boston, USA.
22.
McClintock
,
F. A.
,
1968
, “
A Criterion of Ductile Fracture By the Growth of Holes
,”
ASME J. Appl. Mech.
,
35
, pp.
363
371
.
23.
Rice
,
J. R.
, and
Tracey
,
D. M.
,
1969
, “
On the Ductile Enlargement of Voids in Triaxial Stress Fields
,”
J. Mech. Phys. Solids
,
17
, pp.
201
217
.
24.
LeRoy
,
G.
,
Embury
,
J. D.
,
Edward
,
G.
, and
Ashby
,
M. F.
,
1981
, “
A Model of Ductile Fracture Based on the Nucleation and Growth of Voids
,”
Acta Metall.
,
29
, pp.
1509
1522
.
25.
Cockcroft
,
M. G.
, and
Latham
,
D. J.
,
1968
, “
Ductility and the Workability of Metals
,”
J. Inst. Met.
,
96
, pp.
33
39
.
26.
Oh
,
S.
,
Chen
,
C. C.
, and
Kobayashi
,
S.
,
1979
, “
Ductile Failure in Axisymmetric Extrusion and Drawing, Part 2, Workability in Extrusion and Drawing
,”
J. Eng. Ind.
,
101
, pp.
36
44
.
27.
Brozzo, P., Deluca, B., and Rendina, R., 1972, “A New Method for the Prediction of Formability in Metal Sheet, Sheet Metal Forming and Formability,” in Proceedings of the 7th Biennial Conference of the IDDRG.
28.
Clift
,
S. E.
,
Hartley
,
P.
,
Sturgess
,
C. E. N.
, and
Rowe
,
G. W.
,
1990
, “
Fracture Prediction in Plastic Deformation Processes
,”
Int. J. Mech. Sci.
,
32
, pp.
1
17
.
29.
Bao, Y., and Wierzbicki, T., 2001, “Fracture Calibration Procedure From Upsetting Test for Industrial Applications,” Report 57, Impact and Crashworthiness Laboratory, MIT, Cambridge, MA.
30.
Schey
,
J. A.
,
Venner
,
T. R.
, and
Takomana
,
S. L.
,
1982
, “
The Effect of Friction on Pressure in Upsetting at Low Diameter-to-Height Ratios
,”
J. Mech. Work. Technol.
,
6
, pp.
23
33
.
31.
Kudo
,
H.
, and
Aoi
,
K.
,
1967
, “
Effect of Compression Test Conditions Upon Fracturing of Medium Carbon Steel
,”
J. Jpn. Soc. Technol. Plast.
,
18
, pp.
17
27
.
32.
Kuhn, H. A., and Dieter, G. E., 1977, “Workability in Bulk Forming Processes,” in Fracture, ICF4, Waterloo, Canada.
33.
Puttick
,
K. E.
,
1959
, “
Ductile Fracture in Metals
,”
Philos. Mag.
,
4
, pp.
964
969
.
34.
Hancock
,
J. W.
, and
Mackenzie
,
A. C.
,
1976
, “
On the Mechanisms of Ductile Failure in High-Strength Steels Subjected to Multi-Axial Stress-States
,”
J. Mech. Phys. Solids
,
24
, pp.
147
169
.
35.
Johnson
,
G. R.
, and
Cook
,
W. H.
,
1985
, “
Fracture Characteristics of Three Metals Subjected to Various Strains, Strain Rates, Temperatures and Pressures
,”
Eng. Fract. Mech.
,
21
, pp.
31
48
.
36.
Ganser
,
H. P.
,
Atkins
,
A. G.
,
Kolednik
,
O.
,
Fischer
,
F. D.
, and
Richard
,
O.
,
2001
, “
Upsetting of Cylinders: A Comparison of Two Different Damage Indicators
,”
ASME J. Eng. Mater. Technol.
,
123
, pp.
94
99
.
37.
Borvik
,
T.
,
Hopperstad
,
O.
,
Berstad
,
T.
, and
Langseth
,
M.
,
2002
, “
Perforation of 12 mm Thick Steel Plates by 20 mm Diameter Projectiles With Flat, Hemispherical and Conical Noses, Part II: Numerical Simulations
,”
Int. J. Impact Eng.
,
27
, pp.
37
64
.
38.
White
,
C. S.
,
Bronkhorst
,
C. A.
, and
Anand
,
L.
,
1990
, “
An Improved Isotropic-Kinematic Hardening Model for Moderate Deformation Metal Plasticity
,”
Mech. Mater.
,
10
, pp.
127
147
.
39.
Bao, Y., 2003, “Prediction of Ductile Crack Formation in Uncracked Bodies,” in Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA.
40.
Bao
,
Y.
, and
Wierzbicki
,
T.
,
2004
, “
On Fracture Locus in the Equivalent Strain and Stress Triaxiality Space
,”
Int. J. Mech. Sci.
,
46
, pp.
81
98
.
41.
Johnson, G. R., and Cook, W. H., 1983, “A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates and High Temperatures,” in Proceedings of the Seventh International Symposium on Ballistics, Hague, Netherlands.
42.
Borvik
,
T.
,
Langseth
,
M.
,
Hopperstad
,
O.
, and
Kalo
,
K.
,
1999
, “
Ballistic Penetration of Steel Plates
,”
Int. J. Impact Eng.
,
22
, pp.
855
886
.
43.
Alves
,
M.
, and
Jones
,
N.
,
1999
, “
Influence of Hydrostatic Stress on Failure of Axisymmetric Notched Specimens
,”
J. Mech. Phys. Solids
,
47
, pp.
643
667
.
44.
Johnson, G. R., and Holmquist, T. J., 1989, “Test Data and Computational Strength and Fracture Model Contants for 23 Materials Subjected to Large Strain, High Strain Rates, and High Temperature,” Technical Report LA-11463-MS, Los Alamos National Laboratory.
45.
Lesuer, D. R., 2000, “Experimental Investigation of Material Models for Ti-6Al-4V Titanium and 2024-T3 Aluminum,” Lawrence Livermore National Laboratory, Livermore, CA.
46.
Bao
,
Y.
, and
Wierzbicki
,
T.
,
2003
, “
A Cut-Off Value of Stress Triaxiality for Fracture
,” Eng. Fract. Mech., submitted.
47.
McClintock, F. A., 1971, “Plasticity Aspects of Fracture,” In Fracture H. Liebowitz, ed., Academic Press, New York.
48.
French
,
I. E.
, and
Weinrich
,
P. F.
,
1975
, “
The Influence of Hydrostatic Pressure On the Tensile Deformation and Fracture of Copper
,”
Metall. Trans. A
,
6A
, pp.
785
790
.
49.
Kao
,
A. S.
,
Kuhn
,
H. A.
,
Richmond
,
O.
, and
Spitzig
,
W. A.
,
1990
, “
Tensile Fracture and Fractographic Analysis of 1045 Spheroidized Steel Under Hydrostatic Pressure
,”
J. Mater. Res.
,
5
, pp.
83
91
.
50.
Zheng, L., and Wierzbicki, T., 2002, “Numerical Simulation of Crush Behavior of Aluminum Sandwich Panels for Train Collision,” Report 92, Impact and Crashworthiness Laboratory, MIT, Cambridge, MA.
51.
Lee
,
Y. W.
, and
Wierzbicki
,
T.
,
2003
, “
Fracture Prediction of Thin Plates Under Localized Impulsive Loading. Part I: Calibration and Validation
,” Int. J. Impact Eng., submitted.
52.
Teng
,
X.
, and
Wierzbicki
,
T.
,
2004
, “
Effect of Fracture Criteria on High Velocity Perforation of Thin Beams
,” International Journal of Computational Methods, accepted.
53.
Xue, L., Zheng, L., and Wierzbicki, T., 2003, “Interactive Failure in High Velocity Impact of Two Box Beams,” in ASME International Mechanical Engineering Congress and Exposition, Washington D.C., USA.
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