International Journal of Material Forming

, Volume 12, Issue 6, pp 1053–1061 | Cite as

On the inverse identification of Lankford coefficients using geometrical changes under quasi-biaxial loading

  • Matthias GraserEmail author
  • Matthias Lenzen
  • Marion Merklein


Finite element simulation has become an important tool of process and production design in various fields, especially in the automotive industry. The calculation of forming processes in the early concept phase of new cars allows virtual adaptions, which can reduce costs of later phases in the product development significantly. Therefore, the precise characterization and modelling of the material behavior is necessary to ensure a robust and reliable numerical process design. The mechanical properties of numerous materials are highly influenced by the rolling or extrusion direction in the production process. This necessitates the characterization of materials in different loading directions. However, depending on the dimensional aspects of the semi-finished product, the manufacturing of specimens can be challenging or even impossible. Thus, in this investigation, an innovative, indirect approach for the identification of the Lankford coefficient in transversal direction is presented. Based on numerical and experimental data of layer compression tests the Lankford coefficient is determined by inverse modelling of the resulting specimen contour. Due to the characteristics of the layer compression test, it can even be used for semi-finished products with small transversal dimensions like extruded profiles. The presented methodology is on the one hand verified by conventional uniaxial tensile tests for aluminum as well as steel blank material. On the other hand it is used to determine Lankford coefficients for an aluminum extrusion hollow profile and the inversely identified material model is validated by comparison of strain distributions of experimental and numerical square tube bending tests.


Layer compression test Inverse parameter identification Lankford coefficient Material modelling 



maximum process Force.


tool velocity.


radius of bending tools.


material thickness.


diameter of layer compression test specimen.


layers of specimen stack.


number of experimental tests.


standard deviation of experimental tests.


width of extrusion profile.


height of extrusion profile.


length of extrusion profile.



The authors would like to thank the German Research Foundation (DFG) for supporting the present investigations which were performed within the scope of the research project “Improvement of formability of extruded aluminium profiles by a local short-term heat treatment (DFG ME2043/45-2)”.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Aegerter J, Keller S, Berk H (2017) Miniaturisierung des Zugversuchs zwecks Ermittlung lokaler Bauteileigenschaften - Versuchstechnik und Vergleich mit Ergebnissen an Standardproben. Tagung Werkstoffprüfung 2017 - Fortschritte in der Werkstoffprüfung für Forschung und Praxis 117–122Google Scholar
  2. 2.
    Konopik P, Farahnak P, Rund M, Dzugan J, Rzepa S (2019) Applicability of miniature tensile test in the automotive sector. IOP Conf. Ser.: mater. Sci Eng 461:1–6Google Scholar
  3. 3.
    Suttner S, Merklein M (2016) Influence of specimen size and sheet thickness on the material behavior of AZ31B under uniaxial tension. IOP Conf. Ser.: mater. Sci Eng 159:1–8Google Scholar
  4. 4.
    Kohyama A, Hamada K, Matsui H (1991) Specimen size effects on tensile properties of neutron-irradiated steels. J Nucl Mater 179-181:417–420CrossRefGoogle Scholar
  5. 5.
    Kanni Raj A (2010) Calculation of Lankford coefficient from orientation distribution function and modelling of forming limit diagram using Marcniak-Kuczynski hypothesis of geometric instability. Indian J Eng Mater Sci:256–264Google Scholar
  6. 6.
    Hammami W, Delannay L, Habraken AM, Duchêne L (2009) Crystal plasticity prediction of Lankford coefficients using the MULTISITE model: influence of the critical resolved shear stresses. Int J Mat For 65-68CrossRefGoogle Scholar
  7. 7.
    Butz A, Pagenkopf J, Baiker M, Helm D (2016) The concept of virtual material testing and its application to sheet metal forming simulations. J Phys Conf Ser 734:1–4CrossRefGoogle Scholar
  8. 8.
    Yoon J, Dick R, Barlat F (2008) Analytical approach to predict anisotropic material properties from cup drawings. Int J Mat Form 301-304CrossRefGoogle Scholar
  9. 9.
    Gösling M (2017) A method to determine lankford coefficients (r-values) for ultra high strength low alloy (UHSLA) steels. J Phys Conf Ser 896:1–6CrossRefGoogle Scholar
  10. 10.
    Chamekh A, Ben Hadj Salah H, Hambli R (2009) Inverse technique identification of material parameters using finite element and neural network computation. Int J Adv Manuf Technol 173-179CrossRefGoogle Scholar
  11. 11.
    Cooreman S, Lecompte D, Sol H, Vantomme J, Debruyne D (2008) Identification of mechanical material behavior through inverse modeling and DIC. Exp Mech 421-433CrossRefGoogle Scholar
  12. 12.
    Güner A, Soyarslan C, Brosius A, Tekkaya AE (2012) Characterization of anisotropy of sheet metals employing inhomogeneous strain fields for Yld2000-2D yield function. Int J Solids Struct 49(25):3517–3527CrossRefGoogle Scholar
  13. 13.
    Merklein M, Kuppert A (2009) A method for the layer compression test considering the anisotropic material behavior. Int J Mater Form 2(S1):483CrossRefGoogle Scholar
  14. 14.
    Tuninetti V, Gilles G, Péron-Lührs V, Habraken A (2012) Compression test for metal characterization using digital image correlation and inverse modeling. Procedia IUTAM 4:206–214CrossRefGoogle Scholar
  15. 15.
    Lankford WT, Snyder SC, Bausher JA (1950) New criteria for predicting the press performance of deep drawing sheets. Trans ASM 42:1197–1205Google Scholar
  16. 16.
    Goedel V, Merklein M (2011) Variation of deep drawing steel grades’ properties in dependency of the stress state and its impact on FEA. Int J Mater Form 4(2):183–192CrossRefGoogle Scholar

Copyright information

© Springer-Verlag France SAS, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Manufacturing TechnologyFriedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany

Personalised recommendations