A Comparative Study on Various Ductile Crack Formation Criteria

[+] Author and Article Information
Yingbin Bao, Tomasz Wierzbicki

Impact and Crashworthiness Laboratory, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139

J. Eng. Mater. Technol 126(3), 314-324 (Jun 29, 2004) (11 pages) doi:10.1115/1.1755244 History: Received September 15, 2003; Revised January 16, 2004; Online June 29, 2004
Copyright © 2004 by ASME
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Gurson, A. L., 1975, “Plastic Flow and Fracture Behavior of Ductile Materials Incorporating Void Nucleation, Growth and Interaction,” Brown University, Ph.D. Thesis.
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.
Tvergaard,  V., 1981, “Influence of Voids on Shear Band Instabilities Under Plane Strain Conditions,” Int. J. Fract., 18, pp. 237–252.
Tvergaard,  V., 1982, “On Localization in Ductile Materials Containing Spherical Voids,” Int. J. Fract., 17, pp. 389–407.
Tvergaard,  V., and Needleman,  A., 1984, “Analysis of the Cup-Cone Fracture in a Round Tensile Bar,” Acta Metall., 32, pp. 157–169.
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.
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.
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.
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.
Lemaitre,  J., 1985, “A Continuous Damage Mechanics Model for Ductile Fracture,” ASME J. Eng. Mater. Technol., 107, pp. 83–89.
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.
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.
Barenblatt,  G. I., 1962, “The Mathematical Theory of Equilibrium Cracks in Brittle Fracture,” Adv. Appl. Mech., 7, pp. 55–129.
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.
Needleman,  A., 1990, “An Analysis of Decohesion Along an Imperfect Interface,” Int. J. Fract., 42, pp. 21–40.
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.
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.
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.
Tvergaard,  V., 2001, “Resistance Curves for Mixed More Interface Crack Growth Between Dissimilar Elastic-Plastic Solids,” J. Mech. Phys. Solids, 49, pp. 2689–2703.
Siegmund,  T., and Brocks,  W., 1999, “Prediction of the Work of Separation and Implications to Modeling,” Int. J. Fract., 99, pp. 97–116.
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.
McClintock,  F. A., 1968, “A Criterion of Ductile Fracture By the Growth of Holes,” ASME J. Appl. Mech., 35, pp. 363–371.
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.
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.
Cockcroft,  M. G., and Latham,  D. J., 1968, “Ductility and the Workability of Metals,” J. Inst. Met., 96, pp. 33–39.
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.
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.
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.
Bao, Y., and Wierzbicki, T., 2001, “Fracture Calibration Procedure From Upsetting Test for Industrial Applications,” Report 57, Impact and Crashworthiness Laboratory, MIT, Cambridge, MA.
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.
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.
Kuhn, H. A., and Dieter, G. E., 1977, “Workability in Bulk Forming Processes,” in Fracture, ICF4, Waterloo, Canada.
Puttick,  K. E., 1959, “Ductile Fracture in Metals,” Philos. Mag., 4, pp. 964–969.
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.
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.
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.
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.
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.
Bao, Y., 2003, “Prediction of Ductile Crack Formation in Uncracked Bodies,” in Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA.
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.
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.
Borvik,  T., Langseth,  M., Hopperstad,  O., and Kalo,  K., 1999, “Ballistic Penetration of Steel Plates,” Int. J. Impact Eng., 22, pp. 855–886.
Alves,  M., and Jones,  N., 1999, “Influence of Hydrostatic Stress on Failure of Axisymmetric Notched Specimens,” J. Mech. Phys. Solids, 47, pp. 643–667.
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.
Lesuer, D. R., 2000, “Experimental Investigation of Material Models for Ti-6Al-4V Titanium and 2024-T3 Aluminum,” Lawrence Livermore National Laboratory, Livermore, CA.
Bao,  Y., and Wierzbicki,  T., 2003, “A Cut-Off Value of Stress Triaxiality for Fracture,” Eng. Fract. Mech., submitted.
McClintock, F. A., 1971, “Plasticity Aspects of Fracture,” In Fracture H. Liebowitz, ed., Academic Press, New York.
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.
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.
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.
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.
Teng,  X., and Wierzbicki,  T., 2004, “Effect of Fracture Criteria on High Velocity Perforation of Thin Beams,” International Journal of Computational Methods, accepted.
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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Undeformed specimens: (a) upsetting specimens; and (b) tensile specimens
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Specimens at different stages of compression
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Deformed specimens with different aspect ratios
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Stress-strain curve from upsetting and tensile tests
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Deformed tensile specimens (a) smooth; (b) r=12 mm; and (c) r=4 mm, where r is the radius of the notch
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Evolution of the equivalent plastic strain (upsetting)
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Comparison of force-displacement response (upsetting)
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Evolution of equivalent plastic strain (smooth)
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Comparison of force-displacement response of experiment and numerical simulations for the smooth round bar. Relative elongation is the read of the extensometer divided by the initial gauge length of the extensometer
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Comparison of force-displacement response of experiment and numerical simulations for the notched bar with 12 mm radius of notch
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Comparison of force-displacement response of experiment and numerical simulations for the notched bar with 4 mm radius of notch
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Deformed shapes of tensile test specimens: (a) smooth; (b) R=12 mm; and (c) R=4 mm
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Material constants of fracture criteria for A12024T351, A: upsetting (d=12.5 mm,h=25 mm), B: upsetting (d=12.5 mm,h=12.5 mm), C: standard round, D: notched round (r=12 mm), E: notched round (r=4 mm)
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Fractograph showing dimples in the tensile specimen (r=4 mm)
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Fractograph showing flat fracture surface in the upsetting specimen
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Void nucleation, growth and linkage in the tensile specimen (r=4 mm)
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“Shear fracture” through the matrix in the upsetting specimen
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A fracture curve in the equivalent strain and stress triaxiality space
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A photograph of specimens used to calibrate A12024-T351 for failure locus
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Comparison of the present and Johnson-Cook fracture locus
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A possible mode transition between the void growth dominated mode and “shear fracture” dominated mode




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