A Comparative Study on the Formability Prediction of Steel Sheets by Anisotropic Models Based on Associated Flow Rule and Non-Associated Flow Rule

Abstract:

A comparative study on the formability prediction of a ferritic steel sheet by anisotropic models based on associated flow rule and non-associated rule is carried out. The uniaxial tensile tests along seven directions of the sheet from rolling direction to transverse direction with an interval of 15° are performed for the anisotropic yield stress and r-value. For the biaxial stress state, both bulge test and punch test are performed. The BBC2003 based on the associated flow rule is employed and its anisotropic parameters are calibrated to the yield stresses and r-values from the tensile tests along rolling direction, transverse direction and diagonal direction and the biaxial test. The non-associated quadratic Hill48 model is also calibrated to the same set of experimental data. Similar level of the predicative capability on the yield and plastic deformation directionality by the associated and non-associated based models is observed. With the common basis on the anisotropic plasticity characteristics, they are combined with the Marciniak–Kuczynski (MK) model to predict the formability of the steel sheet and distinct difference in the prediction is observed between the two models.

• Periodical: Key Engineering Materials (Volumes 651-653)
• Pages: 150-155
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.651-653.150
• Online since: July 2015
• Authors: Jun He Lian*, Deok Chan Ahn, Dong Chul Chae, Sebastian Münstermann, Wolfgang Bleck
• Keywords: BBC2003 Model, Ferritic Stainless Steels, Hill48 Model, Marciniak–Kuczynski Model

References

[1] J.L. Bassani, Plastic-Flow of Crystals, Adv Appl Mech 30 (1994) 191-258.

[2] V. Racherla and J.L. Bassani, Strain Burst Phenomena in the Necking of a Sheet That Deforms by Non-Associated Plastic Flow, Modell. Simul. Mater. Sci. Eng. 15 (2007) S297-S311.

DOI: 10.1088/0965-0393/15/1/s23

[3] W.A. Spitzig, Effect of Hydrostatic-Pressure on Plastic-Flow Properties of Iron Single-Crystals, Acta Metall. 27 (1979) 523-534.

DOI: 10.1016/0001-6160(79)90004-x

[4] W.A. Spitzig and O. Richmond, The Effect of Pressure on the Flow-Stress of Metals, Acta Metall. 32 (1984) 457-463.

DOI: 10.1016/0001-6160(84)90119-6

[5] O.G. Lademo, O.S. Hopperstad and M. Langseth, An Evaluation of Yield Criteria and Flow Rules for Aluminium Alloys, Int. J. Plast. 15 (1999) 191-208.

DOI: 10.1016/s0749-6419(98)00064-3

[6] T.B. Stoughton, A Non-Associated Flow Rule for Sheet Metal Forming, Int. J. Plast. 18 (2002) 687-714.

DOI: 10.1016/s0749-6419(01)00053-5

[7] T.B. Stoughton and J.W. Yoon, A Pressure-Sensitive Yield Criterion under a Non-Associated Flow Rule for Sheet Metal Forming, Int. J. Plast. 20 (2004) 705-731.

DOI: 10.1016/s0749-6419(03)00079-2

[8] T.B. Stoughton and J.W. Yoon, Anisotropic Hardening and Non-Associated Flow in Proportional Loading of Sheet Metals, Int. J. Plast. 25 (2009) 1777-1817.

DOI: 10.1016/j.ijplas.2009.02.003

[9] R. Hill, A Theory of the Yielding and Plastic Flow of Anisotropic Metals, Proc. R. Soc. London, Ser. A 193 (1948) 281-297.

[10] D. Mohr, M. Dunand and K. -H. Kim, Evaluation of Associated and Non-Associated Quadratic Plasticity Models for Advanced High Strength Steel Sheets under Multi-Axial Loading, Int. J. Plast. 26 (2010) 939-956.

DOI: 10.1016/j.ijplas.2009.11.006

[11] D. Banabic, H. Aretz, D.S. Comsa and L. Paraianu, An Improved Analytical Description of Orthotropy in Metallic Sheets, Int. J. Plast. 21 (2005) 493-512.

DOI: 10.1016/j.ijplas.2004.04.003

[12] J. Lian, P. Liu and S. Münstermann, Modeling of Damage and Failure of Dual Phase Steel in Nakajima Test, Key Eng. Mater. 525-526 (2012) 69-72.

DOI: 10.4028/www.scientific.net/kem.525-526.69

[13] Z. Marciniak and K. Kuczynski, Limit Strains in the Processes of Stretch Forming Sheet Metal, Int. J. Mech. Sci. 9 (1967) 609-612.

[14] H. Aretz, Numerical Analysis of Diffuse and Localized Necking in Orthotropic Sheet Metals, Int. J. Plast. 23 (2007) 798-840.

DOI: 10.1016/j.ijplas.2006.07.005