Comparison of Different Constitutive Models in Sheet Metal Forming

Article Preview

Abstract:

The effects of different constitutive models in sheet metal forming are investigated by considering the cylindrical and square cup drawing and V-bending processes. Numerical analyses are performed by employing eight different constitutive models. These are elastic plastic constitutive model with isotropic hardening, elastic plastic constitutive model with kinematic hardening, elastic plastic constitutive model with combined hardening, power law isotropic plasticity, piecewise linear isotropic plasticity, three-parameter Barlat, anisotropic plasticity and transversely anisotropic elastic plastic models. The simulations are performed for three different materials, St12 steel, Al-5182 aluminum and stainless steel 409 Ni, by using a commercial finite element code. A number of experiments are carried out and the experimental and analytical results are utilized to evaluate the results of simulations.

You might also be interested in these eBooks

Info:

Periodical:

Key Engineering Materials (Volumes 554-557)

Pages:

1203-1216

Citation:

Online since:

June 2013

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2013 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] Z. Marciniak, Mechanics of Sheet Metal Forming, Butterworth-Heinemann, 2002.

Google Scholar

[2] R. Hill, A theory of the yielding and plastic flow of anisotropic metals, Proc. R. Soc. Lond. A, 193 (1948) 281–297.

Google Scholar

[3] P. B. Mellor, Sheet metal forming, Int. Metals. Rev. 26 (1981) 1–20.

Google Scholar

[4] P. B. Mellor, A. Parmer, Plasticity of sheet metal forming, In: D. P. Koistinen, Wang, N. M. (Eds.), Mechanics of Sheet Metal Forming, Plenum Press, New York, p.53–74 1978.

DOI: 10.1007/978-1-4613-2880-3_3

Google Scholar

[5] R. Hill, Theoretical plasticity of textured aggregates, Math. Proc. Camb. Philos. Soc. 85 (1979) 179–191.

DOI: 10.1017/s0305004100055596

Google Scholar

[6] R. Hill, Constitutive modeling of orthotropic plasticity in sheet metals, J. Mech. Phys. Solids 38 (1990) 405–417.

Google Scholar

[7] R. Hill, A user-friendly theory of orthotropic plasticity in sheet metals, Int. J. Mech. Sci. 35 (1993) 19–25.

Google Scholar

[8] F. Barlat, J. Lian, Plastic behavior and stretch ability of sheet metals, Part I: a yield function for orthotropic sheets under plane stress conditions, Int. J. Plast. 5 (1989) 51–56.

DOI: 10.1016/0749-6419(89)90019-3

Google Scholar

[9] F. Barlat, D. J. Lege, J. C. Brem, A six-component yield function for anisotropic materials, Int. J. Plast. 7 (1991) 693–712.

DOI: 10.1016/0749-6419(91)90052-z

Google Scholar

[10] F. Barlat, R. C. Becker, Y. Hayashida, Y.Maeda, M. Yanagawa, K. Chung, J. C. Brem, D. J. Lege, K. Matsui, S. J. Murtha, S. Hattori, Yielding description for solution strengthened aluminum alloys, Int. J. Plast. 13 (1997) 385–401.

DOI: 10.1016/s0749-6419(97)80005-8

Google Scholar

[11] F. Barlat, J. C. Brem, J. W. Yoon, K. Chung, R. E. Dick, S. H. Choi, F. Pourboghrat, E. Chu, D. J. Lege, Plane stress yield function for aluminum alloy sheets, Int. J. Plast. 19 (2003) 1297–1319.

DOI: 10.1016/s0749-6419(02)00019-0

Google Scholar

[12] F. Barlat, H. Aretz, J. W. Yoon, M. E. Karabin, J. C. Brem, R. E. Dick, Linear transformation based anisotropic yield functions, Int. J. Plast. 21 (2005) 1009–1039.

DOI: 10.1016/j.ijplas.2004.06.004

Google Scholar

[13] A. P. Karafillis, M. C. Boyce, A general anisotropic yield criterion using bounds and a transformation weighting tensor, J. Mech. Phys. Solids 41 (1993) 1859–1886.

DOI: 10.1016/0022-5096(93)90073-o

Google Scholar

[14] D. Banabic, H. Aretz, D. S. Comsa, 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

Google Scholar

[15] H. C. Wu, Anisotropic plasticity for sheet metals using the concept of combined isotropic–kinematic hardening, Int. J. Plast. 18 (2002) 1661–1682.

DOI: 10.1016/s0749-6419(01)00060-2

Google Scholar

[16] L. Geng, Y. Shen, R. H. Wagoner, Anisotropic hardening equations derived from reverse-bend testing, Int. J. Plast. 18 (2002) 743–767.

DOI: 10.1016/s0749-6419(01)00048-1

Google Scholar

[17] P. J. Armstrong, C. O. Frederick, A Mathematical representation of the multi-axial Bauschinger effect, Central Electricity Generating Board Report, Berkeley Nuclear Laboratories, RD/B/N731 1966.

Google Scholar

[18] L. Geng, R. H. Wagoner, Role of plastic anisotropy and its evolution on springback, Int. J. Mech. Sci. 44 (2002) 123–148.

DOI: 10.1016/s0020-7403(01)00085-6

Google Scholar

[19] K. Chung, M. G. Lee, D. Kim, C. Kim, M. L. Wenner, F. Barlat, Springback evaluation of automotive sheets based on isotropic–kinematic hardening laws and non-quadratic anisotropic yield functions, Part I: theory and formulation, Int. J. Plast. 21 (2005) 861–882.

DOI: 10.1016/s0749-6419(04)00088-9

Google Scholar

[20] M. G. Lee, D. Kim, C. Kim, M. L. Wenner, R. H. Wagoner, K. Chung, Springback evaluation of automotive sheets based on isotropic–kinematic hardening laws and non-quadratic anisotropic yield functions Part II: characterization of material properties, Int. J. Plast. 21 (2005a) 883–914.

DOI: 10.1016/s0749-6419(04)00089-0

Google Scholar

[21] M. G. Lee, D. Kim, C. Kim, M. L. Wenner, K. Chung, Springback evaluation of automotive sheets based on isotropic–kinematic hardening laws and non-quadratic anisotropic yield functions Part III: applications, Int. J. Plast. 21 (2005b) 915–953.

DOI: 10.1016/j.ijplas.2004.05.014

Google Scholar

[22] R. P. R. Cardoso, J. W. Yoon, Stress integration method for a nonlinear kinematic/isotropic hardening model and its characterization based on polycrystalline plasticity, Int. J. Plast. 25 (2009) 1684–1710.

DOI: 10.1016/j.ijplas.2008.09.007

Google Scholar

[23] Y. F. Dafalias and E. P. Popov, Plastic internal variables formalism of cyclic plasticity, J. Appl. Mech. 98 (1976) 645-651.

DOI: 10.1115/1.3423948

Google Scholar

[24] M. Zampaloni, N. Abedrabbo, F. Pourboghrat, Experimental and numerical study of stamp hydro forming of sheet metals, Int. J. Mech. Sci. 45 (2003) 1815–1848.

DOI: 10.1016/j.ijmecsci.2003.11.006

Google Scholar

[25] J. B. Kim, J. W. Yoon, D. Y. Yang, Investigation into the wrinkling behavior of thin sheets in the cylindrical cup deep drawing process using bifurcation theory, Int. Num. Meth. Eng. 56 (2003)1673–1705.

DOI: 10.1002/nme.629

Google Scholar

[26] J. W. Yoon, F. Barlat, R. E. Dick, M. E. Karabin, Prediction of six or eight ears in a drawn cup based on a new anisotropic yield function, Int. J. Plast. 22 (2006) 174–193.

DOI: 10.1016/j.ijplas.2005.03.013

Google Scholar

[27] M. C. Oliveira, J. L. Alves, B. M. Chaparro, L. F. Menezes, Study on the influence of work-hardening modeling in springback prediction, Int. J. Plast. 23 (2007) 516–543.

DOI: 10.1016/j.ijplas.2006.07.003

Google Scholar

[28] N. Ivaylo Vladimirov, Michael P. Pietryga, Stefanie Reese, Anisotropic finite elastoplasticity with nonlinear kinematic and isotropic hardening and application to sheet metal forming, Int. J. Plast. 26 (2010) 659–687.

DOI: 10.1016/j.ijplas.2009.09.008

Google Scholar

[29] Junehyung Kim, Wonoh Lee, Daeyong Kim, Jinhak Kong, Chongmin Kim, Michael. L. Wenner, and Kwansoo Chung, Effect of hardening laws and yield function types on springback simulations of dual-phase steel automotive sheets, Metals and Materials International 12 (2006) 293–305.

DOI: 10.1007/bf03027546

Google Scholar

[30] P. A. Eggertsen, K. Mattiasson, On the modeling of the bending–unbending behavior for accurate springback predictions, Int. J. Mech. Sci. 51 (2009) 547–563.

DOI: 10.1016/j.ijmecsci.2009.05.007

Google Scholar

[31] Bingtao Tang, Xiaoyang Lu, Zhaoqing Wang, Zhen Zhao, Springback investigation of anisotropic aluminum alloy sheet with a mixed hardening rule and Barlat yield criteria in sheet metal forming, Mater. and Des. 31 (2010) 2043–2050.

DOI: 10.1016/j.matdes.2009.10.017

Google Scholar

[32] Aboozar Taherizadeh, Daniel E. Green, Abbas Ghaei, Jeong-Whan Yoon, A non-associated constitutive model with mixed isotropic-kinematic hardening for finite element simulation of sheet metal forming, Int. J. Plast. 26 (2010) 288–309.

DOI: 10.1016/j.ijplas.2009.07.003

Google Scholar

[33] M. Ucan, Effect of Constitutive Modeling in Sheet Metal Forming, M.Sc. Thesis, Middle East Technical University, Ankara, Turkey 2011.

Google Scholar

[34] William F. Hosford, Mechanical Behavior of Materials, Cambridge, 2005.

Google Scholar

[35] S. Neto, D. Peric, Drj Owen, Computational Methods for Plasticity, Theory and Applications, Willey, 2008.

Google Scholar