Forming limit prediction of AA7075-T6 sheet based on ductile fracture criterion and the error analysis of parameters calibration


It is worthy to investigate how it will affect the parameters calibration using an average stress state variable before the practical application of a ductile fracture criterion. In order to study this problem, ten notch specimens of AA7075-T6 sheet were designed to implement the tension tests and a parallel simulation of each test was run to obtain the variation of related variables such as stress triaxiality, Lode parameter and fracture strain. The Lou-Huh criterion was selected to research the prediction error through the difference between the damage value calculated by integral expression and that calculated by analytical expression. Based on the error analysis method, a clear answer was given on how to choose the tension tests of notch specimens in the calibrating process of fracture parameters. The studying results show that the stress state variation of notch specimens has a significant influence on the calibration result. It turns out that how to choose specimens from the ten notch specimens to calibrate the fracture parameters also has big influence on the result. Therefore, it is necessary to conduct an error analysis after the calibration of fracture parameters. Based on the error analysis results, the fracture parameters of AA7075-T6 sheet were optimized and its forming limit diagram (FLD) was deduced based on the optimized parameters. The predictive result of FLD is safe compared with the experimental forming limit results.

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  1. 1.

    Hill R (1952) On discontinuous plastic states, with special reference to localized necking in thin sheets. J Mech Phys Solids 1:19–30

  2. 2.

    Swift HW (1952) Plastic instability under plane stress. J Mech Phys Solids 1:1–18

  3. 3.

    Marciniak Z, Kuczynski K (1967) Limit strains in the processes of stretch-forming sheet metal. Int J Mech Sci 9:609–620

  4. 4.

    Lou Y, Huh H (2013) Prediction of ductile fracture for advanced high strength steel with a new criterion: experiments and simulation. J Mater Process Technol 213:1284–1302

  5. 5.

    Zhuang X, Meng Y, Zhao Z (2017) Evaluation of prediction error resulting from using average state variables in the calibration of ductile fracture criterion. Int J Damage Mech 27:1231–1251

  6. 6.

    McClintock FA (1968) A criterion for ductile fracture by the growth of holes. J Appl Mech-T ASME 35:363–371

  7. 7.

    Rice JR, Tracey DM (1969) On the ductile enlargement of voids in triaxial stress fields. J Mech Phys Solids 17:201–217

  8. 8.

    Cockcroft MG, Latham DJ (1968) Ductility and the workability of metals. J Inst Met 96:33–39

  9. 9.

    Brozzo P, Deluca B, Rendina R. A new method for the prediction of formability in metal sheets 1972. in: Proceedings of the 7th Biennial Conference of IDDRG on Sheet Metal Forming and Formability

  10. 10.

    Oh SI, Chen CC, Kobayashi S (1979) Ductile fracture in axisymmetric extrusion and drawing—part 2: workability in extrusion and drawing. J Eng Indust 101:36–44

  11. 11.

    Oyane M, Sato T, Okimoto K, Shima S (1980) Criteria for ductile fracture and their applications. J Mech Work Technol 4:65–81

  12. 12.

    Clift SE, Hartley P, Sturgess CEN, Rowe GW (1990) Fracture prediction in plastic deformation processes. Int J Mech Sci 32:1–17

  13. 13.

    Han HN, Kim KA (2003) A ductile fracture criterion in sheet metal forming process. J Mater Process Technol 142:231–238

  14. 14.

    Ozturk F, Lee D (2004) Analysis of forming limits using ductile fracture criteria. J Mater Process Technol 147:397–404

  15. 15.

    Ko YK, Lee JS, Huh H, Kimet HK, Park SH (2007) Prediction of fracture in hub-hole expanding process using a new ductile fracture criterion. J Mater Process Technol 187:358–362

  16. 16.

    Bao Y, Wierzbicki T (2004) On fracture locus in the equivalent strain and stress triaxiality space. Int J Mech Sci 46:81–98

  17. 17.

    Lou Y, Huh H (2013) Extension of a shear-controlled ductile fracture model considering the stress triaxiality and the lode parameter. Int J Solids Struct 50:447–455

  18. 18.

    Wierzbicki T, Bao Y, Lee Y, Bai Y (2005) Calibration and evaluation of seven fracture models. Int J Mech Sci 47:719–743

  19. 19.

    Lou Y, Huh H, Lim SJ, Pack K (2012) New ductile fracture criterion for prediction of fracture forming limit diagrams of sheet metals. Int J Solids Struct 49:3605–3615

  20. 20.

    Lou Y, Chen L, Clausmeyer T, Tekkayaet AE, Yoon JW (2017) Modeling of ductile fracture from shear to balanced biaxial tension for sheet metals. Int J Solids Struct 112:169–184

  21. 21.

    Li H, Fu MW, Lu J, Yang H (2011) Ductile fracture: experiments and computations. Int J Plast 27(2):147–180

  22. 22.

    Qian LY, Fang G, Zeng P, Wang Q (2015) Experimental and numerical investigations into the ductile fracture during the forming of flat-rolled 5083-O aluminum alloy sheet. J Mater Process Technol 220:264–275

  23. 23.

    Gross AJ, Ravi-Chandar K (2016) On the deformation and failure of Al 6061-T6 at low triaxiality evaluated through in situ microscopy. Int J Fract 200(1–2):185–208

  24. 24.

    Lou Y, Yoon JW, Huh H, Chao Q, Song J (2018) Correlation of the maximum shear stress with micro-mechanisms of ductile fracture for metals with high strength-to-weight ratio. Int J Mech Sci 146:583–601 

  25. 25.

    Bai Y, Wierzbicki T (2008) A new model of metal plasticity and fracture with pressure and lode dependence. Int J Plast 24(6):1071–1096

  26. 26.

    Cao J, Li F, Ma X, Sun Z (2018) A modified elliptical fracture criterion to predict fracture forming limit diagrams for sheet metals. J Mater Process Technol 252:116–127

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The present work is financed by the National Natural Science Foundation of China (contract no. 51775481), the Key Project of Science and Technology Plan of Hebei Higher School of Education Department (grant number ZD2017078) and the Natural Science Foundation of Hebei Province (project number E2019203418). The authors would like express their sincere appreciation to the funds.

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Correspondence to Guojiang Dong.

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Table 10 The solving results of fracture parameters and the statistics of assessment error

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Yang, Z., Zhao, C., Dong, G. et al. Forming limit prediction of AA7075-T6 sheet based on ductile fracture criterion and the error analysis of parameters calibration. Int J Mater Form (2020).

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  • Ductile fracture criterion
  • Error analysis
  • Forming limit diagram
  • AA7075-T6 sheet