Abstract
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.
Copyright © 2004
by ASME
You do not currently have access to this content.
