International Journal of Fracture

, Volume 209, Issue 1–2, pp 143–162 | Cite as

Ductile fracture prediction and forming assessment of AA6061-T6 aluminum alloy sheets

Original Paper


In this paper, an extension to a modified Gurson porous ductile material model, namely the Dung’s model, is introduced to investigate ductile fracture processes of AA6061-T6 aluminum alloy sheets. The combined Dung–Hill48 model accounts for anisotropic hardening effects of the matrix material. The constitutive model is implemented as a user-defined material subroutine in ABAQUS/Explicit to predict ductile fracture and formability of the aluminum alloy sheets. Ductile fracture predictability of the model comes from the description of void growth in an anisotropic strain hardening material. After being calibrated the model is applied to establish a fracture plastic strain–triaxiality relation using only tensile test data of smooth and R-notched specimens. Calculations of forming limits from seven deep drawing simulations with Nakajima specimens estimate the formability of the material. Influence of the material anisotropy on the obtained forming limit diagram is discussed.


Ductile fracture Sheet metal Forming limit diagram Anisotropic material Hill 48 criterion 



This research is funded by Vietnam National University Ho Chi Minh City (VNU-HCM) under Grant No. C2017-20-05.


  1. Abbasi M, Shafaat MA, Ketabchi M, Haghshenas DF, Abbasi M (2012) Application of the GTN model to predict the forming limit diagram of IF-Steel. J Mech Sci Technol 26:345–352CrossRefGoogle Scholar
  2. Agarwal H, Gokhale A, Graham S, Horstemeyer M (2003) Void growth in 6061-aluminum alloy under triaxial stress state. Mater Sci Eng A 341:35–42CrossRefGoogle Scholar
  3. Aravas N (1987) On the numerical integration of a class of pressure-dependent plasticity models. Int J Numer Methods Eng 24:1395–1416CrossRefGoogle Scholar
  4. ASTM E (2001) Standard test methods for tension testing of metallic materials annual book of ASTM standards ASTMGoogle Scholar
  5. Bai Y, Wierzbicki T (2008) A new model of metal plasticity and fracture with pressure and Lode dependence. Int J Plast 24:1071–1096CrossRefGoogle Scholar
  6. Benseddiq N, Imad A (2008) A ductile fracture analysis using a local damage model. Int J Press Vessels Pip 85:219–227CrossRefGoogle Scholar
  7. Benzerga AA, Besson J (2001) Plastic potentials for anisotropic porous solids. Eur J Mech A Solids 20:397–434CrossRefGoogle Scholar
  8. Benzerga AA, Leblond J-B (2010) Ductile fracture by void growth to coalescence. Adv Appl Mech 44:169–305CrossRefGoogle Scholar
  9. Chen Z, Dong X (2009) The GTN damage model based on Hill’48 anisotropic yield criterion and its application in sheet metal forming. Comput Mater Sci 44:1013–1021CrossRefGoogle Scholar
  10. Chu CC, Needleman A (1980) Void nucleation effects in biaxially stretched sheets. J Eng Mater Technol 102:249–256CrossRefGoogle Scholar
  11. Corigliano A, Mariani S, Orsatti B (2000) Identification of Gurson–Tvergaard material model parameters via Kalman filtering technique. I. Theory Int J Fract 104:349–373CrossRefGoogle Scholar
  12. Dung NL (1992) Three dimensional void growth in plastic materials. Mech Res Commun 19:227CrossRefGoogle Scholar
  13. Gatea S, Ou H, McCartney G (2015) Numerical simulation and experimental investigation of ductile fracture in SPIF using modified GTN model. In: MATEC Web of conferences, 2015. EDP SciencesGoogle Scholar
  14. Gurson AL (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 99:2–15CrossRefGoogle Scholar
  15. Gurson AL (1978) Porous rigid-plastic materials containing rigid inclusions—yield function, plastic potential, and void nucleation. In: Taplin DMR (ed) The physical metallurgy of fracture. Pergamon, Oxford, pp 357–364CrossRefGoogle Scholar
  16. Haltom SS, Kyriakides S, Ravi-Chandar K (2013) Ductile failure under combined shear and tension. Int J Solids Struct 50:1507–1522CrossRefGoogle Scholar
  17. ISO12004-2:2008 Metallic materials—sheet and strip—determination of forming-limit curves. Part 2: determination of forming-limit curves in the laboratoryGoogle Scholar
  18. Kami A, Mollaei Dariani B, Sadough Vanini A, Comsa D-S, Banabic D (2014) Application of a GTN damage model to predict the fracture of metallic sheets subjected to deep-drawing. Proc Roman Acad Ser A 15:300–309Google Scholar
  19. Kami A, Dariani BM, Vanini AS, Comsa DS, Banabic D (2015) Numerical determination of the forming limit curves of anisotropic sheet metals using GTN damage model. J Mater Process Technol 216:472–483CrossRefGoogle Scholar
  20. Kim J, Gao X, Srivatsan TS (2004) Modeling of void growth in ductile solids: effects of stress triaxiality and initial porosity. Eng Fract Mech 71:379–400CrossRefGoogle Scholar
  21. Koplik J, Needleman A (1988) Void growth and coalescence in porous plastic solids. Int J Solids Struct 24:835–853CrossRefGoogle Scholar
  22. Li Z, Bilby B, Howard I (1994) A study of the internal parameters of ductile damage theory. Fatigue Fract Eng Mater Struct 17:1075–1087CrossRefGoogle Scholar
  23. Liao KC, Pan J, Tang SC (1997) Approximate yield criteria for anisotropic porous ductile sheet metals. Mech Mater 26:213–226CrossRefGoogle Scholar
  24. McClintock FA (1968) A criterion for ductile fracture by the growth of holes. J Appl Mech 35:363–371CrossRefGoogle Scholar
  25. Nahshon K, Hutchinson J (2008) Modification of the Gurson model for shear failure. Eur J Mech A Solids 27:1–17CrossRefGoogle Scholar
  26. Needleman A, Tvergaard V (1984) An analysis of ductile rupture in notched bars. J Mech Phys Solids 32:461–490CrossRefGoogle Scholar
  27. Nguyen HH, Nguyen TN, Vu HC (2016) Implementation and application of Dung’s model to analyze ductile fracture of metallic material. In: AETA 2015: recent advances in electrical engineering and related sciences. Springer, Berlin, pp 903–913Google Scholar
  28. Oh C-K, Kim Y-J, Baek J-H, Kim Y-P, Kim W (2007) A phenomenological model of ductile fracture for API X65 steel. Int J Mech Sci 49:1399–1412CrossRefGoogle Scholar
  29. Rakin M, Cvijovic Z, Grabulov V, Putic S, Sedmak A (2004) Prediction of ductile fracture initiation using micromechanical analysis. Eng Fract Mech 71:813–827CrossRefGoogle Scholar
  30. Rice JR, Tracey DM (1969) On the ductile enlargement of voids in triaxial stress fields. J Mech Phys Solids 17:201–217CrossRefGoogle Scholar
  31. Swift HW (1952) Plastic instability under plane stress. J Mech Phys Solids 1:1–18CrossRefGoogle Scholar
  32. Tvergaard V (1981) Influence of voids on shear band instabilities under plane strain conditions. Int J Fract 17:389–407CrossRefGoogle Scholar
  33. Tvergaard V (1982) On localization in ductile materials containing spherical voids. Int J Fract 18:237–252Google Scholar
  34. Vadillo G, Fernández-Sáez J (2009) An analysis of Gurson model with parameters dependent on triaxiality based on unitary cells. Eur J Mech A Solids 28:417–427CrossRefGoogle Scholar
  35. Weck A, Wilkinson D, Maire E (2008) Observation of void nucleation, growth and coalescence in a model metal matrix composite using X-ray tomography. Mater Sci Eng A 488:435–445CrossRefGoogle Scholar
  36. Xue L (2008) Constitutive modeling of void shearing effect in ductile fracture of porous materials. Eng Fract Mech 75:3343–3366CrossRefGoogle Scholar
  37. Zhang Z (1996) A sensitivity analysis of material parameters for the Gurson constitutive model. Fatigue Fract Eng Mater Struct 19:561–570CrossRefGoogle Scholar
  38. Zhang ZL, Thaulow C, Ødegård J (2000) A complete Gurson model approach for ductile fracture. Eng Fract Mech 67:155–168CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of Engineering MechanicsHo Chi Minh City University of Technology, Vietnam National University - Ho Chi Minh CityHo Chi Minh CityVietnam
  2. 2.School of Mechanical EngineeringPurdue UniversityWest LafayetteUSA

Personalised recommendations