Abstract
A forming limit diagram (FLD) is commonly used as a useful means for characterising the formability of sheet metal forming processes. In this study, the Nakajima test was used to construct the forming limit curve at necking (FLCN) and fracture (FLCF). The results of the FLCF are compared with incremental sheet forming (ISF) to evaluate the ability of the Nakajima test to describe the fracture in ISF. Tests were carried out to construct the forming limit diagram at necking and fracture to cover the strain states from uniaxial tension to equi-biaxial tension with different stress triaxialities—from 0.33 for uniaxial tension to 0.67 for equi-biaxial tension. Due to the fact that the Gurson–Tvergaard-Needleman (GTN) model can be used to capture fracture occurrence at high stress triaxiality, and the shear modified GTN model (Nahshon-Hutchinson’s shear mechanism) was developed to predict the fracture at zero stress or even negative stress triaxiality, the original GTN model and shear modified GTN model may be not suitable to predict the fracture in all samples of the Nakajima test as some samples are deformed under moderate stress triaxiality. In this study, the fractures are compared using the original GTN model, shear modified GTN model and the Nielsen-Tvergaard model with regard to stress triaxiality. To validate the ability of these models, and to assess which model is more accurate in predicting the fracture with different stress triaxialities, finite element (FE) simulations of the Nakajima test were compared with an experimental results to evaluate the applicability of the Nakajima test to characterise the fracture from ISF. The experimental and FE results showed that the shear modified GTN model could predict the fracture accurately with samples under uniaxial tension condition due to low stress triaxiality and that the original GTN model is suitable for an equi-biaxial strain state (high stress triaxiality), whereas the stress triaxiality modified GTN model should be considered for samples which have moderate stress triaxiality (from plain strain to biaxial strain). The numerical and experimental FLCF of pure titanium from the Nakajima test showed a good agreement between the experimental and numerical results of ISF.
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References
Allwood J, Shouler D, Tekkaya AE (2007) The increased forming limits of incremental sheet forming processes. In: Key Engineering Materials. Trans Tech Publ
Jain M, Allin J, Lloyd D (1999) Fracture limit prediction using ductile fracture criteria for forming of an automotive aluminum sheet. Int J Mech Sci 41(10):1273–1288
Vladimirov IN, Pietryga MP, Kiliclar Y, Tini V, Reese S (2014) Failure modelling in metal forming by means of an anisotropic hyperelastic-plasticity model with damage. Int J Damage Mech 23(8):1096–1132
Han HN, Kim K-H (2003) A ductile fracture criterion in sheet metal forming process. J Mater Process Technol 142(1):231–238
Ham M, Jeswiet J (2007) Forming limit curves in single point incremental forming. CIRP Ann Manuf Technol 56(1):277–280
Shim M-S, Park J-J (2001) The formability of aluminum sheet in incremental forming. J Mater Process Technol 113(1):654–658
Jeswiet J, Young D (2005) Forming limit diagrams for single-point incremental forming of aluminium sheet. Proc Inst Mech Eng B J Eng Manuf 219(4):359–364
Isik K, Silva MB, Tekkaya AE, Martins PAF (2014) Formability limits by fracture in sheet metal forming. J Mater Process Technol 214(8):1557–1565
Centeno G, Bagudanch I, Martínez-Donaire AJ, García-Romeu ML, Vallellano C (2014) Critical analysis of necking and fracture limit strains and forming forces in single-point incremental forming. Mater Des 63:20–29
Skjødt M, Silva M, Martins P, Bay N (2010) Strategies and limits in multi-stage single-point incremental forming. J Strain Anal Eng Des 45(1):33–44
Lu B, Fang Y, Xu D, Chen J, Ai S, Long H, Ou H, Cao J (2015) Investigation of material deformation mechanism in double side incremental sheet forming. Int J Mach Tools Manuf 93:37–48
Fang Y, Lu B, Chen J, Xu DK, Ou H (2014) Analytical and experimental investigations on deformation mechanism and fracture behavior in single point incremental forming. J Mater Process Technol 214(8):1503–1515
Haque MZ, Yoon JW (2016) Stress based prediction of formability and failure in incremental sheet forming. Int J Mater Form 9(3):413–421
Mirnia MJ, Shamsari M (2017) Numerical prediction of failure in single point incremental forming using a phenomenological ductile fracture criterion. J Mater Process Technol 244:17–43
Lu B, Fang Y, Xu D, Chen J, Ou H, Moser N, Cao J (2014) Mechanism investigation of friction-related effects in single point incremental forming using a developed oblique roller-ball tool. Int J Mach Tools Manuf 85:14–29
Ai S, Lu B, Chen J, Long H, Ou H (2017) Evaluation of deformation stability and fracture mechanism in incremental sheet forming. Int J Mech Sci 124:174–184
Li Y, Daniel WJ, Meehan PA (2016) Deformation analysis in single-point incremental forming through finite element simulation. Int J Adv Manuf Technol 88(1):1–13
Ozturk F, Lee D (2004) Analysis of forming limits using ductile fracture criteria. J Mater Process Technol 147(3):397–404
Uthaisangsuk V, Prahl U, Münstermann S, Bleck W (2008) Experimental and numerical failure criterion for formability prediction in sheet metal forming. Comput Mater Sci 43(1):43–50
Parsa M, Ettehad M, Matin P (2013) Forming limit diagram determination of Al 3105 sheets and Al 3105/polypropylene/Al 3105 sandwich sheets using numerical calculations and experimental investigations. J Eng Mater Technol 135(3):031003
Min H, Fuguo L, Zhigang W (2011) Forming limit stress diagram prediction of aluminum alloy 5052 based on GTN model parameters determined by in situ tensile test. Chin J Aeronaut 24(3):378–386
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 216:472–483
Gatea S, Lu B, Ou H, McCartney G (2015) Numerical simulation and experimental investigation of ductile fracture in SPIF using modified GTN model. In: MATEC Web of Conferences. EDP Sciences
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(1):2–15
Tvergaard V, Needleman A (1984) Analysis of the cup-cone fracture in a round tensile bar. Acta Metall 32(1):157–169
Tvergaard V (1982) Influence of void nucleation on ductile shear fracture at a free surface. J Mech Phys Solids 30(6):399–425
Nahshon K, Hutchinson J (2008) Modification of the Gurson model for shear failure. Eur J Mech A Solids 27(1):1–17
Nielsen KL, Tvergaard V (2010) Ductile shear failure or plug failure of spot welds modelled by modified Gurson model. Eng Fract Mech 77(7):1031–1047
Silva MB, Nielsen PS, Bay N, Martins PAF (2011) Failure mechanisms in single-point incremental forming of metals. Int J Adv Manuf Technol 56(9–12):893–903
Ortiz M, Simo J (1986) An analysis of a new class of integration algorithms for elastoplastic constitutive relations. Int J Numer Methods Eng 23(3):353–366
Engelmann BE, Whirley RG (1992) Recent developments in NIKE2D for metalforming analysis and low rate impact. Nucl Eng Des 138(1):23–35
Acknowledgements
The first author gratefully acknowledges the scholarship support provided by the Iraqi Ministry of Higher Education and Scientific Research (IMHESR) ref. no. 4720. This work was supported by the Engineering and Physical Sciences Research Council [grant number EP/L02084X/1]; and the International Research Staff Exchange Scheme [IRSES, MatProFuture project, 318,968] within the 7th European Community Framework Programme (FP7).
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Gatea, S., Xu, D., Ou, H. et al. Evaluation of formability and fracture of pure titanium in incremental sheet forming. Int J Adv Manuf Technol 95, 625–641 (2018). https://doi.org/10.1007/s00170-017-1195-z
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DOI: https://doi.org/10.1007/s00170-017-1195-z