Skip to main content
SpringerLink
Log in

Effect of Different Yield Criteria and Material Parameter Identification Methods on the Description Accuracy of the Anisotropic Behavior of 5182-O Aluminum Alloy

  • Published:
Journal of Materials Engineering and Performance Aims and scope Submit manuscript

Abstract

Based on the BBC2005 yield criterion, a material model that accounts for the deformation anisotropy of sheet metals is developed, named the BBC2005-different work hardening (BBC05-DWH) yield criterion. In contrast to the standard formulation, in this model the material parameters depend on the equivalent plastic strain. To evaluate the different material models, uniaxial and biaxial tensile tests and hydraulic bulging tests are carried out on a 5182-O aluminum alloy produced by Kobelco. The results show that predictions based on the developed material model are more accurate than predictions based on three other yield criteria that use different material parameter identification methods (Hill48-r, Hill48-σ, Barlat89-r, Barlat89-σ and BBC2005 yield criteria). The developed material model is also used to modify the hardening curve produced by the hydraulic bulging test. In the process of extrapolating the hardening curve in the reference direction, the influences of different yield criteria, material parameter identification methods and different work hardening behavior on the equivalent stress are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Data Availability

All data are presented within the manuscript.

Code Availability

Not applicable.

References

  1. D. Banabic, F. Barlat, O. Cazacu, and T. Kuwabara, Advances in Anisotropy of Plastic Behaviour and Formability of Sheet Metals. Int. J. Mater. Form. 2020, 13, p 749-787

  2. S.H. Zhang, S.F. Chen, Y. Ma, H.W. Song, and M. Chen, Developments of New Sheet Metal Forming Technology and Theory in China. Acta Metall. Sin. Engl. Lett. 2015, 28, p 1452-1470

  3. M. Sigvant, K. Mattiasson, H. Vegter and P. Thilderkvist, A Viscous Pressure Bulge Test for the Determination of a Plastic Hardening Curve and Equibiaxial Material Data, Int. J. Mater. Form., 2009, 2, p 235–242.

    Article  Google Scholar 

  4. F.F. Zhang, J. Chen, J.S. Chen, J. Lu, G. Liu and S.J. Yuan, Overview on Constitutive Modeling for Hydroforming with the Existence of Through-Thickness Normal Stress, J. Mater. Process. Technol., 2012, 212, p 2228–2237.

    Article  Google Scholar 

  5. G. Gutscher, H.C. Wu, G. Ngaile and T. Altan, Determination of Flow Stress for Sheet Metal Forming Using the Viscous Pressure Bulge (VPB) Test, J. Mater. Process. Technol., 2004, 146, p 1–7.

    Article  Google Scholar 

  6. L.M. Smith, C. Wanintrudal, W. Yang and S. Jiang, A New Experimental Approach for Obtaining Diffuse-Strain Flow Stress Curves, J. Mater. Process. Technol., 2009, 209, p 3830–3839.

    Article  CAS  Google Scholar 

  7. R. Hill, A Theory of the Yielding and Plastic Flow of Anisotropic Metals, Proc. R. Soc. London., 1948, 193, p 281–297.

    CAS  Google Scholar 

  8. A. Nasser, A. Yadav, P. Pathak and T. Altan, Determination of the flow stress of five AHSS sheet materials (DP 600, DP 780, DP 780-CR, DP 780-HY and TRIP 780) using the uniaxial tensile and the biaxial Viscous Pressure Bulge (VPB) tests, J. Mater. Process. Technol., 2010, 210, p 429–436.

    Article  CAS  Google Scholar 

  9. R. Hill, Constitutive Modelling of Orthotropic Plasticity in Sheet Metals, J. Mech. Phys. Solids, 1990, 38, p 405–417.

    Article  Google Scholar 

  10. J. Mulder, H. Vegter, H. Aretz, S. Keller and A.H. van den Boogaard, Accurate Determination of Flow Curves Using the Bulge Test with Optical Measuring Systems, J. Mater. Process. Technol., 2015, 226, p 169–187.

    Article  CAS  Google Scholar 

  11. S. Suttner and M. Merklein, Experimental and Numerical Investigation of a Strain Rate Controlled Hydraulic Bulge Test of Sheet Metal, J. Mater. Process. Technol., 2016, 235, p 121–133.

    Article  CAS  Google Scholar 

  12. H. Alharthi, S. Hazra, A. Alghamdi, D. Banabic and R. Dashwood, Determination of the Yield Loci of Four Sheet Materials (AA6111-T4, AC600, DX54D+Z, and H220BD+Z) by Using Uniaxial Tensile and Hydraulic Bulge Tests, Int. J. Adv. Manuf. Technol., 2018, 98, p 1307–1319.

    Article  Google Scholar 

  13. V. Prakash, D.R. Kumar, A. Horn, H. Hagenah and M. Merklein, Modeling Material Behavior of AA5083 Aluminum Alloy Sheet Using Biaxial Tensile Tests and Its Application in Numerical Simulation of Deep Drawing, Int. J. Adv. Manuf. Technol., 2019, 106, p 1133–1148.

    Article  Google Scholar 

  14. R. Hill, S.S. Hecker and M.G. Stout, An Investigation of Plastic Flow and Differential Work Hardening in Orthotropic Brass Tubes Under Fluid Pressure and Axial Load, Int. J. Solids Struct., 1994, 31, p 2999–3021.

    Article  Google Scholar 

  15. M.S. Aydin, J. Gerlach, L. Kessler and A.E. Tekkaya, Yield Locus Evolution and Constitutive Parameter Identification Using Plane Strain Tension and Tensile Tests, J. Mater. Process. Technol., 2011, 211, p 1957–1964.

    Article  CAS  Google Scholar 

  16. M. Ishiki, T. Kuwabara and Y. Hayashida, Measurement and Analysis of Differential Work Hardening Behavior of Pure Titanium Sheet Using Spline Function, Int. J. Mater. Form., 2009, 4, p 193–204.

    Article  Google Scholar 

  17. T. Kuwabara, T. Mori, M. Asano, T. Hakoyama and F. Barlat, Material Modeling of 6016-O and 6016–T4 Aluminum Alloy Sheets and Application to Hole Expansion Forming Simulation, Int. J. Plast., 2017, 93, p 164–186.

    Article  CAS  Google Scholar 

  18. M.O. Andar, T. Kuwabara, and D. Steglich, Material Modeling of AZ31 Mg Sheet Considering Variation of r-Values and Asymmetry of the Yield Locus. Mater. Sci. Eng. 2012, A 549, p 82-92

  19. J.W. Yoon, F. Barlat, R.E. Dick, K. Chung and T.J. Kang, Plane Stress Yield Function for Aluminum Alloy Sheets-Part II: FE Formulation and Its Implementation, Int. J. Plast., 2004, 20, p 495–522.

    Article  CAS  Google Scholar 

  20. H. Aretz, A Simple Isotropic-Distortional Hardening Model and Its Application in Elastic-Plastic Analysis of Localized Necking in Orthotropic Sheet Metals, Int. J. Plast., 2008, 24, p 1457–1480.

    Article  CAS  Google Scholar 

  21. H.B. Wang, M. Wan, X.D. Wu and Y. Yan, The Equivalent Plastic Strain-Dependent Yld 2000–2d Yield Function and the Experimental Verification, Comput. Mater. Sci., 2009, 47, p 12–22.

    Article  CAS  Google Scholar 

  22. P. Peters, N. Manopulo, C. Lange and P. Hora, A Strain Rate Dependent Anisotropic Hardening Model and Its Validation Through Deep Drawing Experiments, Int. J. Mater. Form., 2014, 7, p 447–457.

    Article  Google Scholar 

  23. J.H. Yoon, O. Cazacu, J.W. Yoon and R.E. Dick, Earing Predictions for Strongly Textured Aluminum Sheets, Int. J. Mech. Sci., 2010, 52, p 1563–1578.

    Article  Google Scholar 

  24. T. Kuwabara, Advances in Experiments on Metal Sheets and Tubes in Support of Constitutive Modeling and Forming Simulations, Int. J. Plast., 2007, 23, p 385–419.

    Article  CAS  Google Scholar 

  25. D. Banabic, F. Barlat, O. Cazacu and T. Kuwabara, Advances in Anisotropy and Formability, Int. J. Mater. Form., 2010, 3, p 165–189.

    Article  Google Scholar 

  26. Y. Hou, J.Y. Min, T.B. Stoughton, J.P. Lin, J.E. Carsley, and B.E. Carlson, A Non-quadratic Pressure-Sensitive Constitutive Model Under Non-associated Flow Rule With Anisotropic Hardening: Modeling and Validation. Int. J. Plast., 2020, 135, p 102808

  27. J.Y. Min, J.E. Carsley, J.P. Lin, Y.Y. Wen and B. Kuhlenkotter, A Non-quadratic Constitutive Model Under Nonassociated Flow Rule of Sheet Metals with Anisotropic Hardening: Modeling and Experimental Validation, Int. J. Mech. Sci., 2016, 119, p 343–359.

    Article  Google Scholar 

  28. H.B. Wang, Y. Yan, F. Han and M. Wan, Experimental and Theoretical Investigations of the Forming Limit of 5754O Aluminum Alloy Sheet Under Different Combined Loading Paths, Int. J. Mech. Sci., 2017, 133, p 147–166.

    Article  Google Scholar 

  29. F. Barlat and K. Lian, Plastic Behavior and Stretchability of Sheet Metals. Part I: A Yield Function for Orthotropic Sheets Under Plane Stress Conditions. Int. J. Plast., 1989, 5, p 51-66

  30. J. Pilthammar, D. Banabic, and M. Sigvant, BBC05 with Non-integer Exponent and Ambiguities in Nakajima Yield Surface Calibration. Int. J. Mater. Form., 2020, 3

  31. G.M. Han, C.G. Tian, C.Y. Cui, Z.Q. Hu, and X.F. Sun, Portevin–Le Chatelier Effect in Nimonic 263 Superalloy. Acta Metall. Sin. (Engl. Lett.)., 2015, 28, p 542-549

  32. H. Halim, D.S. Wilkinson and M. Niewczas, The Portevin-Le Chatelier (PLC) Effect and Shear Band Formation in an AA5754 alloy, Acta Mater., 2007, 55, p 4151–4160.

    Article  CAS  Google Scholar 

  33. J.Y. Min, T.B. Stoughton J.E. Carsley, B.E. Carlson J.P. Lin, and X.L. Gao, Accurate Characterization of Biaxial Stress-Strain Response of Sheet Metal from Bulge Testing. Int. J. Plast., 2017, 94, p 192-213

  34. D. Steglich, Y. Jeong, M.O. Andar and T. Kuwabara, Biaxial Deformation Behaviour of AZ31 Magnesium Alloy: Crystal-Plasticity-Based Prediction and Experimental Validation, Int. J. Solids Struct., 2012, 49, p 3551–3561.

    Article  CAS  Google Scholar 

  35. S.B. Lin and J.L. Ding, A Modified form of Hill’s Orientationdashdependent Yield Criterion for Orthotropic Sheet Metals, J. Mech. Phys. Solids, 1996, 44, p 1739–1764.

    Article  CAS  Google Scholar 

  36. J.H. Lian, F.H. Shen, X.X. Jia, D.C. Ahn, D.C. Chae, S. Munstermann and W. Bleck, An Evolving Non-associated Hill48 Plasticity Model Accounting for Anisotropic Hardening and r-Value Evolution and Its Application to Forming Limit Prediction, Int. J. Solids Struct., 2018, 151, p 20–44.

    Article  Google Scholar 

  37. T. Kuwabara and F. Sugawara, Multiaxial Tube Expansion Test Method for Measurement of Sheet Metal Deformation Behavior Under Biaxial Tension for a Large Strain Range, Int. J. Plast., 2013, 45, p 103–118.

    Article  CAS  Google Scholar 

  38. T. Hakoyama and T. Kuwabara, Forming Limit Analyses of Cold Rolled IF Steel Sheet Using Differential Work Hardening Model, Procedia Eng., 2014, 81, p 1246–1251.

    Article  CAS  Google Scholar 

  39. S. Kaya, T. Altan, P. Groche and C. Klopsch, Determination of the Flow Stress of Magnesium AZ31-O Sheet at Elevated Temperatures Using the Hydraulic Bulge Test, Int. J. Mach. Tools Manuf., 2008, 48, p 550–557.

    Article  Google Scholar 

  40. K.M. Zhao, L.M. Wang, Y. Chang and J.W. Yan, Identification of Post-Necking Stress-Strain Curve for Sheet Metals by Inverse Method, Mech. Mater., 2016, 92, p 107–118.

    Article  Google Scholar 

  41. J.H. Kim, A. Serpantié, F. Barlat, F. Pierron and M.G. Lee, Characterization of the Post-Necking Strain Hardening Behavior Using the Virtual Fields Method, Int. J. Solids Struct., 2013, 50, p 3829–3842.

    Article  Google Scholar 

Download references

Acknowledgment

The authors thank the Press Shop and TWA Laboratory of BMW Brilliance Automotive Ltd. for their support and help with the experiments.

Funding

This study was funded by the Promotion China Ph.D. Program of BMW Brilliance Automotive Ltd.

Author information

Authors and Affiliations

  1. School of Materials Science and Engineering, Shenyang University of Technology, Shenyang, 110870, China

    Kai Du, Hongjun Huang, Wentao Zheng & Xiaoguang Yuan

  2. Department of Technical Planning Press Shop and Hang-on Parts, BMW Brilliance Automotive Ltd, Shenyang, 100044, China

    Kai Du, Shaohui Huang, Fanxing Yu & Long Pan

  3. School of Mechanical and Materials Engineering, North China University of Technology, Beijing, 100144, China

    Haibo Wang

Authors
  1. Kai Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shaohui Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haibo Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Fanxing Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Long Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Hongjun Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Wentao Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Xiaoguang Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

KD contributed to conceptualization, formal analysis, validation and writing original draft. SH was involved in supervision and funding acquisition. HW performed review and editing. FY and LP performed project administration. HH contributed to investigation and methodology. WZ was involved in methodology and writing—review and editing. XY performed writing—review and editing, and supervision.

Corresponding authors

Correspondence to Wentao Zheng or Xiaoguang Yuan.

Ethics declarations

Conflict of interest

The authors declare that they have no competing interests.

Ethics Approval

Not applicable.

Consent to Participate

Not applicable.

Consent for Publication

Not applicable.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Du, K., Huang, S., Wang, H. et al. Effect of Different Yield Criteria and Material Parameter Identification Methods on the Description Accuracy of the Anisotropic Behavior of 5182-O Aluminum Alloy. J. of Materi Eng and Perform 31, 1077–1095 (2022). https://doi.org/10.1007/s11665-021-06295-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11665-021-06295-x

Keywords

Search

Navigation