New Model for Ductile Fracture of Metal Alloys. II: Reverse Loading
This article has been corrected.
VIEW CORRECTIONPublication: Journal of Engineering Mechanics
Volume 142, Issue 2
Abstract
Ductile fracture of metals resulting from large amplitude inelastic reverse straining has been the predominant reason for the failure of structural components under extreme loadings. This kind of fracture, characterized by only a few reverse cycles with large precrack plastic strain, is often termed ultra-low cycle fatigue (ULCF). Ductile failure of metals has recently been recognized to be a function of stress triaxiality and Lode angle parameter. In this paper, a new fracture model with full consideration of stress triaxiality and Lode angle parameter as well as the cutoff regions is proposed from the extension of its equivalence for monotonic loading in the parallel paper. The underlying mechanism and determination of the cutoff region boundary is well-defined and discussed. Additionally, the effect of load excursion on shifting the boundary of the cutoff region and the subsequent damage evolution is assessed. The nonlinearity of damage evolution is also studied and well-characterized. The developed criterion is evaluated against data extracted from a series of multistress states cyclic experimental results, and excellent correlations between the proposed model and experimental results are achieved. Comparison between the proposed model and other existing models is made, and favorable results are shown for the proposed model. The presented model can be used for predicting the potential for ULCF failure in alloys.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors wish to acknowledge the financial support provided by the US Department of Transportation through Mountain Plain Consortium and by the China Scholarship Council, which was used for completing this study.
References
ABAQUS version 6.12 [Computer software]. Simulia, Dassault Systèmes, Providence, RI.
Bai, Y. (2008). “Effect of loading history in necking and fracture.” Ph.D. dissertation, Massachusetts Institute of Technology, Cambridge, MA.
Bai, Y. (2011). “Fracture of 1045 steel under complex loading history.” Proc., Numisheet 2011, Seoul, Korea.
Bai, Y., and Wierzbicki, T. (2008). “A new model of metal plasticity and fracture with pressure and Lode dependence.” Int. J. Plast., 24(6), 1071–1096.
Bai, Y., and Wierzbicki, T. (2010). “Application of extended Mohr-Coulomb criterion to ductile fracture.” Int. J. Fract., 161(1), 1–20.
Bampton, C. C., and Raj, R. (1982). “Influence of hydrostatic pressure and multiaxial straining on cavitation in a superplastic aluminum alloy.” Acta Metall., 30(11), 2043–2053.
Bao, Y. (2003). “Prediction of ductile track formation in uncracked bodies.” Ph.D. dissertation, Massachusetts Institute of Technology, Cambridge, MA.
Bao, Y., and Treitler, R. (2004). “Ductile crack formation on notched Al2024-T351 bars under compression-tension loading.” Mater. Sci. Eng. A, 384(1), 385–394.
Bao, Y., and Wierzbicki, T. (2004). “On fracture locus in the equivalent strain and stress triaxiality space.” Int. J. Mech. Sci., 46(1), 81–98.
Bao, Y., and Wierzbicki, T. (2005). “On the cut-off value of negative triaxiality for fracture.” Eng. Fract. Mech., 72(7), 1049–1069.
Barsoum, I., and Faleskog, J. (2007). “Rupture mechanisms in combined tension and shear—Experiments.” Int. J. Solids Struct., 44(6), 1768–1786.
Benzerga, A., and Leblond, J. B. (2010). “Ductile fracture by void growth to coalescence.” Adv. Appl. Mech., 44, 169–305.
Brozzo, P., Deluca, B., and Rendina, R. (1972). “A new method for the prediction of formability limits in metal sheets, sheet metal forming and formability.” Proc., 7th Biennial Conf. of the Int. Deep Drawing Research Group, International Deep Drawing Research Group, Netherlands.
Chang, W. R., Etsion, I., and Bogy, D. B. (1988). “Static friction coefficient model for metallic rough surfaces.” J. Tribol., 110(1), 57–63.
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(1), 1–17.
Cockcroft, M. G., and Latham, D. J. (1968). “Ductility and the workability of metals.” J. Inst. Metals, 96(1), 33–39.
Gologanu, M., Devaux, J., and Leblond, J. B. (1994). “Approximate models for ductile metals containing nonspherical voids—Case of axisymmetric oblate ellipsoidal cavities.” J. Eng. Mater. Technol., 116(3), 290–297.
Gologanu, M., Leblond, J. B., and Devaux, J. (1993). “Approximate models for ductile metals containing non-spherical voids—Case of axisymmetric prolate ellipsoidal cavities.” J. Mech. Phys. Solids, 41(11), 1723–1754.
Gologanu, M., Leblond, J. B., Perrin, G., and Devaux, J. (1997). Recent extensions of Gurson’s model for porous ductile metals, Springer, Vienna.
Gratts, R. R. (1961). “Cumulative fatigue damage with random loading.” J. Basic Eng., 84(3), 403–409.
Gruben, G., Hopperstad, O. S., and Børvik, T. (2012). “Evaluation of uncoupled ductile fracture criteria for the dual-phase steel Docol 600DL.” Int. J. Mech. Sci., 62(1), 133–146.
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.” J. Eng. Mater. Technol., 99(1), 2–15.
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(1), 31–48.
Kanvinde, A. M., and Deierlein, G. G. (2007). “Cyclic void growth model to assess ductile fracture initiation in structural steels due to ultra low cycle fatigue.” J. Eng. Mech., 701–712.
Khan, A. S., and Liu, H. (2012). “A new approach for ductile fracture prediction on Al 2024-T351 alloy.” Int. J. Plast., 35, 1–12.
Kiran, R., and Khandelwal, K. (2015). “A micromechanical cyclic void growth model for ultra-low cycle fatigue.” Int. J. Fatigue, 70, 24–37.
Ko, Y. K., Lee, J. S., Huh, H., Kim, H. K., and Park, S. H. (2007). “Prediction of fracture in hub-hole expanding process using a new ductile fracture criterion.” J. Mater. Process. Technol., 187, 358–362.
Kuroda, M. (2001). “Extremely low cycle fatigue life prediction based on a new cumulative fatigue damage model.” Int. J. Fatigue, 24(6), 699–703.
Kuwamura, H., and Yamamoto, K. (1997). “Ductile crack as trigger of brittle fracture in steel.” J. Struct. Eng., 729–735.
Li, H., Fu, M. W., Lu, J., and Yang, H. (2011). “Ductile fracture: Experiments and computations.” Int. J. Plast., 27(2), 147–180.
MATLAB version 7.13. 0.564 [Computer software]. MathWorks, Natick, MA.
McClintock, F. A. (1968). “A criterion for ductile fracture by the growth of holes.” J. Appl. Mech., 35(2), 363–371.
Murakami, Y., and Miller, K. J. (2005). What is fatigue damage? A view point from the observation of low cycle fatigue process.” Int. J. Fatigue, 27, 991–1005.
Nahshon, K., and Hutchinson, J. W. (2008). “Modification of the Gurson model for shear failure.” Eur. J. Mech. A. Solids, 27(1), 1–17.
Oh, S. I., Chen, C. C., and Kobayashi, S. (1979). “Ductile fracture in axisymmetric extrusion and drawing—Part 2: Workability in extrusion and drawing.” J. Eng. Ind., 101(1), 36–44.
Oyane, M., Sato, T., Okimoto, K., and Shima, S. (1980). “Criteria for ductile fracture and their applications.” J. Mech. Working Technol., 4(1), 65–81.
Rice, J. R., and Tracey, D. M. (1969). “On the enlargement of voids in triaxial stress fields.” J. Mech. Phys. Solids, 17(3), 201–217.
Tateishi, K., Hanji, T., and Minami, K. (2007). “A prediction model for extremely low cycle fatigue strength of structural steel.” Int. J. Fatigue, 29(5), 887–896.
Teng, X. (2005). “High velocity impact fracture.” Ph.D. dissertation, Massachusetts Institute of Technology, Cambridge, MA.
Tvergaard, V. (1982). “On localization in ductile materials containing spherical voids.” Int. J. Fract., 18(4), 237–252.
Tvergaard, V., and Needleman, A. (1984). “Analysis of the cup-cone fracture in a round tensile bar.” Acta Metall., 32(1), 157–169.
Voyiadjis, G. Z., Hoseini, S. H., and Farrahi, G. H. (2012). “Effects of stress invariants and reverse loading on ductile fracture initiation.” Int. J. Solids Struct., 49(13), 1541–1556.
Wierzbicki, T., Bao, Y., Lee, Y. W., and Bai, Y. (2005). “Calibration and evaluation of seven fracture models.” Int. J. Mech. Sci., 47(4), 719–743.
Wilkins, M. L., Streit, R. D., and Reaugh, J. E. (1980). “Cumulative-strain-damage model of ductile fracture: Simulation and prediction of engineering fracture tests.”, Science Applications, San Leandro, CA.
Xue, L. (2008). “Constitutive modeling of void shear effect in ductile fracture of porous materials.” Eng. Fract. Mech., 75(11), 3343–3366.
Xue, L., and Wierzbicki, T. (2009). “Ductile fracture characterization of aluminum alloy 2024-T351 using damage plasticity theory.” Int. J. Appl. Mech., 1(2), 267–304.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 142 • Issue 2 • February 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: May 8, 2015
Accepted: Aug 4, 2015
Published online: Sep 23, 2015
Published in print: Feb 1, 2016
Discussion open until: Feb 23, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.