Skip to main content
SpringerLink
Log in

Optimized and validated prediction of plastic yielding supported by cruciform experiments and crystal plasticity

  • Review
  • Published:
International Journal of Material Forming Aims and scope Submit manuscript

Abstract

The predictability of strain distributions and the related prediction of hardening and failure plays a central role in tool and process design for any metal forming process. Studying yielding behaviour, it was discovered that for various well established yield loci no satisfying agreement between DIC (digital image correlation) measurement of strain distribution and simulation result could be obtained, even after optimization of parameters based on associated flow assumption. In parallel, crystal plasticity simulations were investigated with the objective to predict the relation between stress and strain ratios for a large number of load cases based on texture measurement. To include macroscopic data, a secondary strategy uses cruciform tension specimen as defined in ISO16842 to obtain strain and stress ratios. The resulting relations were then applied separately as input parameters for the plastic yield description. Both approaches reach high agreement between forming experiment and simulation. Against the previous assumption, the output can be obtained with either anisotropic or free shape yield loci and associated flow description. The methodology discussed provides an alternative and challenges to rethink the definition of yielding for aluminium alloys on the example of an AA6014-T4 aluminium alloy.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Hirsiger S (2020) A virtual testing method based on crystal plasticity for macroscopic constitutive models. Dissertation, ETH Zurich

  2. Hirsiger S, Berisha B, Hippke H, Hora P (2019) Predicting plastic strain anisotropy of AA6016-t4 and DC05 by mulitobjective parameter calibration of crystal plasticity models and coupling strategies with macroscopic models. In: XV International Conference on Computational Plasticity. COMPLAS2019 Eccomas. https://doi.org/10.3929/ethz-b-000386362

  3. Kuwabara T (2014) Multiaxial stress tests for metal sheets and tubes for accurate material modeling and forming simulations. Acta Metall Slovaca 20(4):428–437. https://doi.org/10.12776/ams.v20i4.423

    Article  Google Scholar 

  4. Barlat F, Brem JC, Yoon JW, Chung K, Dick RE, Lege DJ et al (2003) Plane stress yield function for aluminum alloy sheets - Part 1: Theory. Int J Plasticity. https://doi.org/10.1016/S0749-6419(02)00019-0

  5. Yoon JW, Barlat F, Dick RE, Chung K, Kang TJ (2004) Plane stress yield function for aluminum alloy sheets - Part II: FE formulation and its implementation. Int J Plasticity. https://doi.org/10.1016/S0749-6419(03)00099-8

  6. Stoughton TB (2002) A non-associated flow rule for sheet metal forming. Int J Plasticity. https://doi.org/10.1016/S0749-6419(01)00053-5

  7. Stoughton TB, Yoon JW (2008) On the existence of indeterminate solutions to the equations of motion under non-associated flow. Int J Plasticity 24(4):583–613. https://doi.org/10.1016/j.ijplas.2007.07.002

    Article  MATH  Google Scholar 

  8. Vegter H, Van Den Boogaard AH (2006) A plane stress yield function for anisotropic sheet material by interpolation of biaxial stress states. Int J Plasticity. https://doi.org/10.1016/j.ijplas.2005.04.009

  9. Raemy C, Manopulo N, Hora P (2017) On the modelling of plastic anisotropy, asymmetry and directional hardening of commercially pure titanium: A planar Fourier series based approach. Int J Plasticity. https://doi.org/10.1016/j.ijplas.2017.02.010

  10. Hao S, Xianghuai D (2020) Interpolation-based plane stress anisotropic yield models. Int J Mech Sci 178:105612. https://doi.org/10.1016/j.ijmecsci.2020.105612

    Article  MATH  Google Scholar 

  11. Cazacu O, Plunkett B, Barlat F (2006) Orthotropic yield criterion for hexagonal closed packed metals. Int J Plasticity 22:1171–1194. https://doi.org/10.1016/j.ijplas.2005.06.001

    Article  MATH  Google Scholar 

  12. Verma RK, Kuwabara T, Chung K (2011) Haldar, A Experimental evaluation and constitutive modeling of non-proportional deformation for asymmetric steels. Int J Plasticity. https://doi.org/10.1016/j.ijplas.2010.04.002

  13. Yoshida F, Uemori T (2002) A model of large-strain cyclic plasticity describing the bauschinger effect and workhardening stagnation. Int J Plasticity 18:661–686

    Article  Google Scholar 

  14. Barlat F, Gracio J, Lee M, Rauch E, Vincze G (2011) An alternative to kinematic hardening in classical plasticity. Int J Plasticity 27:1309–1327

    Article  Google Scholar 

  15. Coppieters S, Hakoyama T, Eyckens P, Nakano H, Van Bael A, Debruyne D et al (2018) On the synergy between physical and virtual sheet metal testing: calibration of anisotropic yield functions using a microstructure-based plasticity model. Int J Mater Form. https://doi.org/10.1007/s12289-018-1444-1

  16. Ogasawara Y, Hakoyama T, Takeda H, Kuwabara T, Barlat F (2019) Material modeling and forming limit analysis of 6014-T4 aluminium alloy sheet In: Proceedings of Numiform 2019. pp 135–138

  17. Pilthammer J, Banabic D, Sigvant M (2020) Bbc05 with non-integer exponent and ambiguities in nakajima yield surface calibration. Int J Mater Form. https://doi.org/10.1007/s12289-020-01545-0

  18. Park T, Chung K (2012) Non-associated flow rule with symmetric stiffness modulus for isotropic-kinematic hardening and its application for earing in circular cup drawing. Int J Solids Struct 49(25):3582–3593. https://doi.org/10.1016/j.ijsolstr.2012.02.015

    Article  Google Scholar 

  19. Lou Y, Yoon JW (2017) J2-j3 based anisotropic yield function under spatial loading. Procedia Engineer 207:233–238. https://doi.org/10.1016/j.proeng.2017.10.767

    Article  Google Scholar 

  20. Yoon JW, Barlat F, Dick RE, Karabin ME (2006) Prediction of six or eight ears in a drawn cup based on a new anisotropic yield function. Int J Plasticity. https://doi.org/10.1016/j.ijplas.2005.03.013

  21. Tian H, Brownell B, Baral M, Korkolis YP (2017) Earing in cup-drawing of anisotropic al-6022-t4 sheets. Int J Mater Form 10:329–343. https://doi.org/10.1007/s12289-016-1282-y

    Article  Google Scholar 

  22. Güner A, Yin Q, Soyarslan C, Brosius A, Tekkaya AE (2011) Inverse method for identification of initial yield locus of sheet metals utilizing inhomogeneous deformation fields. Int J Mater Form 4:121–128. https://doi.org/10.1007/s12289-010-1009-4

    Article  Google Scholar 

  23. Vegter H, ten Horn C, Abspoel M (2009) The Corus-Vegter Lite material model: Simplifying advanced material modelling. Int J Mater Form. https://doi.org/10.1007/s12289-009-0640-4

  24. Pijlman HH, Huétink J, Carleer BD, Vegter H (1998) Application of the Vegter yield criterion and a physically based hardening rule on simulation of sheet forming In: Numisheet 98, pp 763–768

  25. Gorji M (2015) Instability and fracture models to optimize the metal forming and bending crack behavior of al-alloy composites, Dissertation, ETH Zurich

  26. Manopulo N, List J, Hippke H, Hora P (2015) A Non-Associated Flow Rule Based Yld2000-2D Model In: IDDRG 2015, pp 1–5

  27. Logan RW, Hosford WF (1980) Upper-bound anisotropic yield locus calculations assuming 〈111〉-pencil glide. Int J Mech Sci. https://doi.org/10.1016/0020-7403(80)90011-9

  28. Stoughton TB, Yoon JW (2011) Paradigm change: Alternate approaches to constitutive and necking models for sheet metal forming. In: AIP Conference Proceedings, ISBN 9780735409491. https://doi.org/10.1063/1.3623589, vol 1383, pp 15–34

  29. Hippke H, Manopulo N, Yoon JW, Hora P (2018) On the efficiency and accuracy of stress integration algorithms for constitutive models based on non-associated flow rule. Int J Mater Form 11(2):239–246. https://doi.org/10.1007/s12289-017-1347-6

    Article  Google Scholar 

  30. ISO 16842 (2014) Metallic materials – Sheet and strip – Biaxial tensile testing method using a cruciform test piece. International Organization for Standardization, pp 16842

  31. Roters F, Diehl M, Shanthraj P, Eisenlohr P, Reuber C, Wong SL, et al. (2019) Damask – the düsseldorf advanced material simulation kit for modelling multi-physics crystal plasticity, damage, and thermal phenomena from the single crystal up to the component scale. Comp Mater Sci 158:420–478. https://doi.org/10.1016/j.commatsci.2018.04.030

    Article  Google Scholar 

  32. Quey R, Dawson P, Barbe F (2011) Large-scale 3d random polycrystals for the finite element method: Generation, meshing and remeshing. Comput Method Appl M 200(17):1729–1745. https://doi.org/10.1016/j.cma.2011.01.002

    Article  MATH  Google Scholar 

  33. Berisha B, Hirsiger S, Hippke H, Hora P, Mariaux A, Leyvraz D, et al. (2019) Modeling of anisotropic hardening and grain size effects based on advanced numerical methods and crystal plasticity. Arch Mech 71(4-5):489–505. https://doi.org/10.24423/aom.3150

    Article  Google Scholar 

  34. Han F, Diehl M, Roters F, Raabe D (2020) Using spectral-based representative volume element crystal plasticity simulations to predict yield surface evolution during large scale forming simulations. J Mater Process Tech 116449:227. https://doi.org/10.1016/j.jmatprotec.2019.116449

    Article  Google Scholar 

  35. Hirsiger S, Berisha B, Raemy C, Hora P (2018) On the prediction of yield loci based on crystal plasticity models and the spectral solver framework. In: Journal of Physics: Conference Series, pp 1–7. https://doi.org/10.1088/1742-6596/1063/1/012056

  36. Hora P, Tong L, Berisha B (2013) Modified maximum force criterion, a model for the theoretical prediction of forming limit curves. Int J Mater Form 6(2):267–279. https://doi.org/10.1007/s12289-011-1084-1

    Article  Google Scholar 

  37. Volk W, Suh J (2013) Prediction of formability for non-linear deformation history using generalized forming limit concept (gflc). In: Numisheet 2014. https://doi.org/10.1063/1.4850035, vol 1567, p 556

Download references

Acknowledgements

This work was conducted within the scope of a Project (No.: 26515.1 PFIW-IW) with Innosuisse - Swiss Innovation Agency. Experimental support was received by E. Polatidis and J. Capek from the Paul-Scherrer-Institute (PSI).

Author information

Authors and Affiliations

  1. ETH Zurich, Institute of Virtual Manufacturing, Tannenstrasse 3, 8092, Zurich, Switzerland

    Holger Hippke, Sebastian Hirsiger & Pavel Hora

  2. inspire AG, Institute of Virtual Manufacturing (inspire-ivp), Tannenstrasse 3, 9092, Zurich, Switzerland

    Bekim Berisha

Authors
  1. Holger Hippke
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sebastian Hirsiger
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bekim Berisha
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Pavel Hora
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Holger Hippke.

Ethics declarations

Conflict of interests

The authors declare that they have no conflict of interest.

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

Hippke, H., Hirsiger, S., Berisha, B. et al. Optimized and validated prediction of plastic yielding supported by cruciform experiments and crystal plasticity. Int J Mater Form 13, 841–852 (2020). https://doi.org/10.1007/s12289-020-01569-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12289-020-01569-6

Keywords

Search

Navigation