Skip to main content
SpringerLink
Log in

Potential of the Cross Biaxial Test for Anisotropy Characterization Based on Heterogeneous Strain Field

  • Published:
Experimental Mechanics Aims and scope Submit manuscript

Abstract

The mechanical behavior in cross biaxial tension was investigated for two metallic sheets, an aluminium alloy and a dual phase steel. The heterogeneous strain field in the central gauge area of a cruciform specimen was analyzed by digital image correlation. Minor and major strains were output along several paths, for a given load level just before necking, showing a wide range of strain states, from uniaxial tension to biaxial state. The applied loads along the two loading directions were also recorded, the gap between the two signals being all the most important that the material anisotropy was significant. Moreover, the strain path ratio, defined as the ratio of the minor strain over the major strain, exhibited a sensible non-monotonic evolution along the transverse direction, compared to the rolling direction. Finally, a material parameter identification process with only biaxial tensile test for Bron and Besson anisotropic yield model was proposed, based on the minimization of experimental and numerical principal strains along a specified path in the gauge area of the cruciform specimen.

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
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

  1. Hill R (1948) A theory of the yielding and plastic flow of anisotropic metals. Proc R Soc Lond Ser Math Phys Sci 193:281–297

    Article  MATH  Google Scholar 

  2. Barlat F, Lege DJ, Brem JC (1991) A six-component yield function for anisotropic materials. Int J Plast 7:693–712

    Article  Google Scholar 

  3. Barlat F, Brem JC, Yoon JW, Chung K, Dick RE, Lege DJ, Pourboghrat F, Choi SH, Chu E (2003) Plane stress yield function for aluminum alloy sheets—part 1: theory. Int J Plast 19:1297–1319

    Article  MATH  Google Scholar 

  4. Barlat F, Aretz H, Yoon JW, Karabin ME, Brem JC, Dick RE (2005) Linear transfomation-based anisotropic yield functions. Int J Plast 21:1009–1039

    Article  MATH  Google Scholar 

  5. Bron F, Besson J (2004) A yield function for anisotropic materials application to aluminum alloys. Int J Plast 20:937–963

    Article  MATH  Google Scholar 

  6. Banabic D (2010) Sheet metal forming processes: Constitutive modeling and numerical simulation. Springer.

  7. Aretz H (2005) A non-quadratic plane stress yield function for orthotropic sheet metals. J Mater Process Technol 168:1–9

    Article  Google Scholar 

  8. Aretz H, Hopperstad O, Lademo O (2007) Yield function calibration for orthotropic sheet metals based on uniaxial and plane strain tensile tests. J Mater Process Technol 186:221–235

    Article  Google Scholar 

  9. Aretz H (2004) Applications of a new plane stress yield function to orthotropic steel and aluminium sheet metals. Model Simul Mater Sci Eng 12:491–509

    Article  Google Scholar 

  10. Banabic D, Kuwabara T, Balan T, Comsa DS (2004) An anisotropic yield criterion for sheet metals. J Mater Process Technol 157–158:462–465

    Article  Google Scholar 

  11. Comsa DS, Banabic D (2008) Plane-stress yield criterion for highly-anisotropic sheet metals. NUMISHEET 2008, Interlaken, Switzerland, pp 43–48.

  12. Hu W (2007) Constitutive modeling of orthotropic sheet metals by presenting hardening-induced anisotropy. Int J Plast 23:620–639

    Article  MATH  Google Scholar 

  13. Zang SL, Thuillier S, Le Port A, Manach PY (2011) Prediction of anisotropy and hardening for metallic sheets in tension, simple shear and biaxial tension. Int J Mech Sci 53:338–347

    Article  Google Scholar 

  14. Wang H, Wan M, Wu X, Yan Y (2009) The equivalent plastic strain-dependent Yld 2000–2d yield function and the experimental verification. Comput Mater Sci 47:12–22

    Article  Google Scholar 

  15. Zang S, Lee M (2011) A general yield function within the framework of linear transformations of stress tensors for the description of plastic-strain-induced anisotropy. AIP Conf Proc 1383:63–70

    Article  Google Scholar 

  16. Grédiac M (2004) The use of full-field measurement methods in composite material characterization: interest and limitations. Compos Part A 35:751–761

    Article  Google Scholar 

  17. Avril S, Bonnet M, Bretelle A, Grediac M, Hild F, Ienny P, Latourte F, Lemosse D, Pagano S, Pagnacco E, Pierron F (2008) Overview of identification methods of mechanical parameters based on full-field measurements. Exp Mech 48:38–402

    Google Scholar 

  18. Güner A, Soyarslan C, Brosius A, Tekkaya AE (2012) Characterization of anisotropy of sheet metals employing inhomogeneous strain fields for Yld 2000–2D yield function. Int J Solids Struct 49–25:3517–3527

    Article  Google Scholar 

  19. Latourte F (2007) Identification des paramètres d’une loi elastoplastic de prager et calcul de champs de contrainte dans des matériaux heterogènes. PhD thesis at Université Montpellier II - Sciences et Techniques du Languedoc.

  20. Pottier T, Vacher P, Toussaint F, Louche H, Coudert T (2012) Out-of-plane testing procedure for inverse identification purpose: application in sheet metal plasticity. Exp Mech 52:951–963

    Article  Google Scholar 

  21. Lubineau G (2009) A goal-oriented field measurement filtering technique for the identification of material model parameters. Comput Mech 44:591–603

    Article  MATH  Google Scholar 

  22. Blaysat B, Florentin E, Lubineau G, Moussawi A (2012) A dissipation gap method for full-field measurement-based identification of elasto-plastic material parameters. Int J Num Method Eng 91:685–704

    Article  MATH  MathSciNet  Google Scholar 

  23. Kulawinski D, Nagel K, Henkel S, Hübner P, Fischer H, Kuna M, Biermann H (2011) Characterization of stress–strain behavior of a cast TRIP steel under different biaxial planar load ratios. Eng Fract Mech 78:1684–1695

    Article  Google Scholar 

  24. Prates PA, Fernandes JV, Oliveira MC, Sakharova NA, Menezes LF (2010) On the characterization of the plastic anisotropy in orthotropic sheet metals with a cruciform biaxial test. IOP Conf Ser: Mater Sci Eng 10:1–10

    Article  Google Scholar 

  25. Teaca M, Charpentier I, Martiny M, Ferron G (2010) Identification of sheet metal plastic anisotropy using heterogeneous biaxial tensile tests. Int J Mech Sci 52:572–580

    Article  Google Scholar 

  26. Ferron G, Makkouk R, Morreale J (1994) A parametric description of orthotropic plasticity in metal sheets. Int J Plast 10:431–449

    Article  MATH  Google Scholar 

  27. Hayhurst DR (1973) A biaxial-tension creep-rupture testing machine. J Strain Anal Eng Des 8:119–123

    Article  Google Scholar 

  28. Ferron G, Makinde A (1988) Design and development of a biaxial strength testing device. J Test Eval 16:253–256

    Article  Google Scholar 

  29. Fraunhofer (2005) Dynamic material testing.

  30. Makinde A, Thibodeau L, Neale KW (1992) Development of an apparatus for biaxial testing using cruciform specimens. Exp Mech 32:138–144

    Article  Google Scholar 

  31. Leotoing L, Guines D, Zhang S, Ragneau E (2013) A cruciform shape to study the influence of strain paths on forming limit curves. Key Eng Mater 554–557:41–46

    Article  Google Scholar 

  32. Makinde A, Thibodeau L, Neale KW, Lefebvre D (1992) Design of a biaxial extensometer for measuring strains in cruciform specimens. Exp Mech 32:132–137

    Article  Google Scholar 

  33. Zhang S, Léotoing L, Guines D, Thuillier S, Zang S (2014) Calibration of anisotropic yield criterion with conventional tests or biaxial test. Int J Mech Sci 85:142–151

    Article  Google Scholar 

  34. Ohtake Y, Rokugawa S, Masumoto H (1999) Geometry determination of cruciform- type specimen and biaxial tensile test of C/C composites. Key Eng Mater 164–165:151–154

    Article  Google Scholar 

  35. Zhang S (2014) Characterization of anisotropic yield criterion with biaxial tensile test. PhD thesis at INSA de Rennes.

  36. Müller W, Pöhlandt K (1996) New experiments for determining yield loci of sheet metal. J Mater Process Technol 60:643–648

    Article  Google Scholar 

  37. Banabic D, Siegert K (2004) Anisotropy and formability of AA5182-0 aluminium alloy sheets. CIRP Ann - Manuf Technol 53:219–222

    Article  Google Scholar 

  38. Kuwabara T, Ikeda S, Kuroda K (1998) Measurement and analysis of differential work hardening in cold-rolled steel sheet under biaxial tension. J Mater Process Technol 80–81:517–523

    Article  Google Scholar 

  39. Hill R, Hutchinson JW (1992) Differential hardening in sheet metal under biaxial loading: a theoretical framework. J Appl Mech 59:S1–S9

    Article  MATH  Google Scholar 

  40. Zidane I, Guines D, Leotoing L, Ragneau E (2010) Development of an in-plane biaxial test for forming limit curve (FLC) characterization of metallic sheets. Meas Sci Technol 21:055701

    Article  Google Scholar 

  41. Lecompte D, Smits A, Sol H, Vantomme J, Van Hemelrijck D (2007) Mixed numerical-experimental technique for orthotropic parameter identification using biaxial tensile test on cruciform specimens. Int J Solids Struct 44:1643–1656

    Article  Google Scholar 

  42. Périé JN, Leclerc H, Roux S, Hild F (2009) Digital image correlation and biaxial test on composite material for anisotropic damage law identification. Int J Solids Struct 46:2388–2396

    Article  MATH  Google Scholar 

  43. Promma N, Raka B, Grédiac M, Toussaint E, LeCam JB, Balandraud X, Hild F (2009) Application of the virtual fields method to mechanical characteriza-tion of elastomeric materials. Int J Solids Struct 46:698–715

    Article  MATH  Google Scholar 

  44. Mishra A, Thuillier S (2014) Investigation of the rupture in tension and bending of DP980 steel sheet. Int J Mech Sci 84C:171–181

    Article  Google Scholar 

  45. Meuwissen MHH, Oomens CWJ, Baaijens FPT, Petterson R, Janssen JD (1998) Determination of the elasto-plastic properties of aluminium using a mixed numerical-experimental method. J Mater Process Technol 75:204–211

    Article  Google Scholar 

  46. Cooreman S, Lecompte D, Sol H, Vantonne J, Debruyne D (2007) Elasto-plastic material parameter identification by inverse methods: Calculation of the sensitivity matrix. Int J Solids Struct 44:4329–4341

    Article  MATH  Google Scholar 

  47. Pottier T, Toussaint F, Vacher P (2011) Contribution of heterogeneous strainfield measurements and boundary conditions modelling in inverse identification of material parameters. Eur J Mech A/Solids 30:373–382

    Article  MATH  Google Scholar 

  48. Piecewise cubic hermite interpolating polynomial (PCHIP) for given data in MATLAB and then finding area. http://stackoverflow.com/questions/17140658/piecewise-cubic-hermite- interpolating-polynomial-pchip-for-given-data-in-matla. Accessed: 17 April 2014.

  49. ModeFrontier | ESTECO. http://www.esteco.com/modefrontier. Accessed: 03 November 2013.

  50. Simplex Optimization. http://www.chem.uoa.gr/applets/AppletSimplex/Appl_Simplex2. html. Accessed: 10 April 2014.

Download references

Author information

Authors and Affiliations

  1. EA 3913, LGCGM, INSA of Rennes, 35708, Rennes, France

    S. Zhang, L. Léotoing & D. Guines

  2. EA 4250, LIMATB, University of Bretagne-Sud, 56100, Lorient, France

    S. Thuillier

Authors
  1. S. Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Léotoing
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. Guines
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. Thuillier
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Guines.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, S., Léotoing, L., Guines, D. et al. Potential of the Cross Biaxial Test for Anisotropy Characterization Based on Heterogeneous Strain Field. Exp Mech 55, 817–835 (2015). https://doi.org/10.1007/s11340-014-9983-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11340-014-9983-y

Keywords

Search

Navigation